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  • 1.
    Alaniz, Monica
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Belyayev, Serhiy
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Bergman, David
    Casselbrant, Gustav
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Honeth, Mark
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Huang, Jiangwei
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Ivchenko, Nickolay
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Laukkanen, Mikko
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Michelsen, Jacob
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Pronenko, Vira
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Paulson, Malin
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Schlick, Georg
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Valle, Mario
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    The SQUID sounding rocket experiment2011In: Proceedings of the 20th ESA Symposium on European Rocket and Balloon Programmes and Related Research, European Space Agency, 2011, 159-166 p.Conference paper (Refereed)
    Abstract [en]

    The objective of the SQUID project is to develop and in flight verify a miniature version of a wire boom deployment mechanism to be used for electric field measurements in the ionosphere. In February 2011 a small ejectable payload, built by a team of students from The Royal Institute of Technology (KTH), was launched from Esrange on-board the REXUS-10 sounding rocket. The payload separated from the rocket, deployed and retracted the wire booms, landed with a parachute and was subsequently recovered. Here the design of the experiment and post fight analysis are presented.

  • 2.
    Ashwear, Nasseradeen
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Vibration Frequencies as Status Indicators for Tensegrity Structures2014Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

     Applications of vibration structural health monitoring (VHM) techniques are increasing rapidly. This is because of the advances in sensors and instrumentation during the last decades. VHM uses the vibration properties to evaluate many civil structures during the design steps, building steps and service life.

    The stiffness and frequencies of tensegrity structures are primarily related to the level of pre-stress. The present work investigates the possibilities to use this relation in designing, constructing and evaluating the tensegrity structures.

    The first part of the  present work studies the improvement of current models for resonance frequency simulation of tensegrities by introducing the bending behaviour of all components, and by a one-way coupling between the axial force and the stiffness. From this, both local and global vibration modes are obtained. The resonance frequencies are seen as non-linearly dependent on the pre-stress level in the structure, thereby giving a basis for diagnosis of structural conditions from measured frequencies. The new aspects of tensegrity simulations are shown for simple, plane structures but the basic methods are easily used also for more complex structures.

    In the second part, the environmental temperature effects on vibration properties of tensegrity structures have been investigated, considering primarily seasonal temperature differences (uniform temperature differences). Changes in dynamic characteristics due to temperature variations were compared with the changes due to decreasing pre-tension in one of the cables. In general, it is shown that the change in structural frequencies made by temperature changes could be equivalent to the change made by damage (slacking). Different combinations of materials used and boundary conditions are also investigated. These are shown to have a significant impact on the pre-stress level and the natural frequencies of the tensegrity structures when the environment temperature is changed.

  • 3.
    Ashwear, Nasseradeen
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Vibration-based Assessment of Tensegrity Structures2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Vibration structural health monitoring (VHM) uses the vibration properties to evaluate many civil structures during the design steps, building steps and service life.The whole function, expressed by stiffness and frequencies of tensegrity structures are primarily related to the level of pre-stress. The present work investigates the possibilities to use this relation in designing, constructing and evaluating the tensegrity structures.One of the aims of the thesis was to improve the current models for resonance frequency simulation of tensegrities. This has been achieved by introducing the bending behaviour of all components, and by a one-way coupling between the axial force and the stiffness.The environmental temperature effects on vibration properties of tensegrity structures have been also  investigated. Changes in dynamic characteristics due to temperature variations were compared with the changes due to decreasing pre-tension in one of the cables. In general, it is shown that the change in structural frequencies coming from temperature changes could of several magnitude as those from damage.Coinciding natural frequencies and low stiffness are known issues of tensegrity structures. The former can be an obstacle in VHM, while the later normally limits their uses in real engineering applications. It has been shown that the optimum self-stress vector of tensegrity structures can be chosen such that their lowest natural frequency is high, and separated from others.The environmental temperature effects on vibration properties of tensegrity structures were revisited to find a solution such that the natural frequencies of the tensegrity structures are not strongly affected by the changes in the environmental temperature. An asymmetric self-stress vector can be chosen so that the criterion is fulfilled as well as possible. The level of pre-stress can also be regulated to achieve the solution. The last part of this thesis, services as a summary of the work.

  • 4.
    Ashwear, Nasseradeen
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Influence of Temperature on the Vibration Properties of Tensegrity Structures2015In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 99, 237-250 p.Article in journal (Refereed)
    Abstract [en]

    Vibration health monitoring methods use the sensitivity of the natural frequencies to structural damage. Natural frequencies are sensitive to damage, but are also affected by environmental conditions like temperature changes. It is important to be able to distinguish between the effects of these different factors when using the vibration properties as a monitoring tool. This paper discusses the impact of damage and environment temperature changes on the natural frequencies of tensegrity ("tensile-integrity") structures, in particular noting that component bending is a prominent vibration mode, which motivates a use of non-linear beam elements with axial-bending coupling. The model considers not only thermal expansion effects, but also the change of the elastic modulus with temperature. Changes in natural frequencies produced by environment temperature changes are shown to be similar to the ones produced by damage. The geometry of tensegrity structures, the support conditions and the materials are found to be important factors. The sensitivity of the natural frequency to temperature changes is found to be dependent on pre-stress level.

  • 5.
    Ashwear, Nasseradeen
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Natural frequencies describe the pre-stress in tensegrity structures2014In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 136, 162-171 p.Article in journal (Refereed)
    Abstract [en]

    This paper investigates the effect of pre-stress level on the natural frequencies of tensegrity structures. This has been established by using Euler–Bernoulli beam elements which include the effect of the axial force on the transversal stiffness. The axial-bending coupling emphasizes the non-linear dependence of the natural frequencies on the pre-stress state. Pre-stress is seen as either synchronous, considering a variable final pre-stress design or as tuning, when increasing pre-stress is followed in a planned construction sequence. It is shown that for a certain tensegrity structure, increasing the level of pre-stress may cause the natural frequencies to rise or fall. This effect is related to whether the structural behavior can be seen as compression or tension dominant. Vanishing of the lowest natural frequency of the system is shown to be related to the critical buckling load of one or several compressed components. Modes of vibration show that when the force in the compressed components approaches any type of critical buckling load, this results in lower vibration frequencies. The methods in this study can be used to plan the tuning of the considered tensegrity structure towards the design level of pre-stress, and as health monitoring tools.

  • 6.
    Ashwear, Nasseradeen
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Reducing effects from environmental temperature on the natural frequencies of tensegrity structuresIn: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568Article in journal (Other (popular science, discussion, etc.))
    Abstract [en]

    n vibration health monitoring, dynamic properties such as natural frequencies and mode shapes are used as tools for assessing the structures health condition.~They are, however, also affected by environmental conditions like wind, humidity and temperature changes. Of particular importance is the change of the environmental temperature, and it is the most commonly considered environmental variable that influences the vibration health monitoring algorithms.~This paper discusses how the tensegrity structures can be designed such that some of their lowest natural frequencies are less sensitive to the temperature changes. A genetic algorithm is used to solve the optimization problem. In the form-finding stage, an asymmetric self-stress vector can be chosen so that the criterion is fulfilled as well as possible. The level of pre-stress can also be regulated to achieve the solution, particularly when a symmetric self-stress vector is chosen.

  • 7.
    Ashwear, Nasseradeen
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Vibration health monitoring for tensegrity structures2017In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 85, 625-637 p.Article in journal (Refereed)
    Abstract [en]

    Tensegrities are assembly structures, getting their equilibrium from the interaction between tension in cables and compression in bars. During their service life, slacking'in their cables and nearness to buckling in their bars need to be monitored to avoid a sudden collapse. This paper discusses how to design the tensegrities to make them feasible for vibrational health monitoring methods. Four topics are discussed; suitable finite elements formulation, pre-measurements analysis to find the locations of excitation and sensors for the interesting modes, the effects from some environmental conditions, and the pre-understanding of the effects from different slacking scenarios.

  • 8. Bartonek, Asa
    et al.
    Lidbeck, Cecilia M.
    Pettersson, Robert
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Weidenhielm, Eva Brostrom
    Eriksson, Marie
    Gutierrez-Farewik, Elena
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Influence of heel lifts during standing in children with motor disorders2011In: Gait & Posture, ISSN 0966-6362, E-ISSN 1879-2219, Vol. 34, no 3, 426-431 p.Article in journal (Refereed)
    Abstract [en]

    Heel wedges may influence standing posture but how and to what extent are unknown. Thirty-two children with motor disorders - 16 with arthrogryposis multiplex congenita (AMC) and 16 with cerebral palsy (CP) - and 19 control children underwent a three-dimensional motion analysis. Unassisted standing during 20s with shoes only and with heel lifts of 10,20 and 30 mm heights was recorded in a randomized order. The more weight-bearing limb or the right limb was chosen for analysis. In both the AMC and CP groups, significant changes were seen between various heel lifts in ankle, knee and pelvis, and in the control group in the ankle only. Between orthosis and non-orthosis users significant differences were seen between different heel lift conditions in ankle, knee and trunk in the AMC group and in the ankle in the CP group. Pelvis position changed toward less anterior tilt with increasing heel height, but led to increasing knee flexion in most of the children, except for the AMC Non-Ort group. Children with AMC and CP represent different motor disorders, but the heel wedges had a similar influence on pelvis, hip and knee positions in all children with CP and in the AMC orthosis users. A challenge is to apply heel heights adequate to each individual's orthopaedic and neurologic conditions to improve biomechanical alignment with respect to all body segments.

  • 9.
    Bartonek, Åsa
    et al.
    Karolinska Institutet, Dept. of Women's and Child's Health.
    Wang, Ruoli
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Eriksson, Marie
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Gutierrez-Farewik, Elena
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics. KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Comparison of two carbon fibre spring orthoses' effect on gait in children with myelomeningocele2012In: Gait & Posture, ISSN 0966-6362, E-ISSN 1879-2219Article in journal (Refereed)
  • 10.
    Belyayev, S. M.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Dudkin, F. L.
    Minimization of nanosatellite low frequency magnetic fields2016In: Review of Scientific Instruments, ISSN 0034-6748, E-ISSN 1089-7623, Vol. 87, no 3, 034705Article in journal (Refereed)
    Abstract [en]

    Small weight and dimensions of the micro- and nanosatellites constrain researchers to place electromagnetic sensors on short booms or on the satellite body. Therefore the electromagnetic cleanliness of such satellites becomes a central question. This paper describes the theoretical base and practical techniques for determining the parameters of DC and very low frequency magnetic interference sources. One of such sources is satellite magnetization, the reduction of which improves the accuracy and stability of the attitude control system. We present design solutions for magnetically clean spacecraft, testing equipment, and technology for magnetic moment measurements, which are more convenient, efficient, and accurate than the conventional ones. (C) 2016 AIP Publishing LLC.

  • 11.
    Bissal, Ara
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Magnusson, Jesper
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Salinas, Ener
    ABB AB Corporate Research, Sweden.
    Engdahl, Göran
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On the Design of Ultra-Fast Electromechanical Actuators: A Comprehensive Multi-Physical Simulation Model2012In: Sixth International Conference on Electromagnetic Field Problems and Applications (ICEF), 2012, IEEE conference proceedings, 2012, 1-4 p.Conference paper (Refereed)
    Abstract [en]

    In this paper, a simulation of an ultra-fast electromechanical drive was performed by using a two-dimensional axi-symmetric multi-physical finite element model. The aim of this paper is to primarily show that the following model can be used to simulate and design those actuators with good accuracy, secondly, to study the behavior and sensitivity of the system and thirdly, to demonstrate the potential of the model for industrial applications. The simulation model is coupled to a circuit and solves for the electro-magnetic, thermal, and mechanical dynamics utilizing a moving mesh. The actuator under study is composed of a spiral-shaped coil and a disk-shaped 3mm thick copper armature on top. Two numerical studies of such an actuator powered by 2640 J capacitor banks were performed. It is shown that forces up to 38 kN can be achieved in the range of 200 μs. To add credibility, a benchmark prototype was built to validate this experimentally with the use of a high speed camera and image motion analysis.

  • 12.
    Bordogna, Marco Tito
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Fidjeland, Leo
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Fjällid, Markus
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Galrinho, Miguel
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Haponen, Anders
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Hou, Anton
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Ivchenko, Nickolay
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Kristmundsson, Darri
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Lárusdóttir, Ólafía
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lejon, Marcus
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Lindh, Marcus
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Lozano, Emilio
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Magnusson, Patrick
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Myleus, Andreas
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Oakes, Ben D.
    KTH, School of Electrical Engineering (EES), Space and Plasma Physics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    MUSCAT experiment: active free falling units for in situ measurements of temperature and density in the middle atmosphere2013In: European Space Agency: (Special Publication) ESA SP / [ed] L. Ouwehand, ESTEC, Noordwijk, The Netherlands: ESA Communications , 2013, 575-582 p.Conference paper (Other academic)
    Abstract [en]

    The main scientific objective of the MUSCAT Experimentis to develop a technique to reconstruct temperatures and density profiles in the middle atmosphere using active spherical probes. The MUSCAT experiment was launched on May 9, 2013 on the REXUS-13 sounding rocket from Esrange, in northern Sweden. The experiment ejected four probes that collected raw GPS signal. The experiment design and preliminary results are presented here.

  • 13.
    Bröchner, Jan
    et al.
    KTH.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Lundequist, Jerker
    Byggprjktet som dataförädling: Processaspekter på informationsstrukturer1990Book (Other academic)
  • 14.
    Dalil Safaei, Seif
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Stiffness and vibration properties of slender tensegrity structures2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The stiffness and frequency properties of tensegrity structures are functions of the pre-stress, topology, configuration, and axial stiffness of the elements. The tensegrity structures considered are tensegrity booms, tensegrity grids, and tensegrity power lines.

    A study has been carried out on the pre-stress design. It includes (i) finding the most flexible directions for different pre-stress levels, (ii) finding the pre-stress pattern which maximizes the first natural frequency.

    To find the optimum cross-section areas of the elements for triangular prism and Snelson tensegrity booms, an optimization approach is utilized. A constant mass criterion is considered and the genetic algorithm (GA) is used as the optimization method.

    The stiffness of the triangular prism and Snelson tensegrity booms are modified by introducing actuators. An optimization approach by means of a GA is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness improves significantly, but still an active tensegrity boom is less stiff than a passive truss boom. The GA shows high accuracy in searching the non-structural space.

    The tensegrity concept is employed to design a novel transmission power line .A tensegrity prism module is selected as the building block. A complete parametric study is performed to investigate the influence of several parameters such as number of modules and their dimensions on the stiffness and frequency of the structure. A general approach is suggested to design the structure considering wind and ice loads. The designed structure has more than 50 times reduction of the electromagnetic field and acceptable deflections under several loading combinations.

    A study on the first natural frequencies of Snelson, prisms, Micheletti, Marcus and X-frame based tensegrity booms has been carried out. The result shows that the differences in the first natural frequencies of the truss and tensegrity booms are significant and not due to the number of mechanisms or pre-stress levels. The tensegritybooms of the type Snelson with 2 bars and prism with 3 bars have higher frequencies among tensegrity booms.

  • 15.
    Dalil Safaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimum pre-stress design for frequency requirement of tensegrity structures2011In: Proceeding of 10th World Congress on Computational Mechanics, 2011Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Structures composed of tension and compression elements in equilibrium are denoted tensegrity structures. Stability of tensegrity structures is achieved through introducing initial member forces (pre-stress). The pre-stress design can be seen consisting of three different stages: (i) finding the bases of possible pre-stress states, (ii) finding admissible distributions considering unilateral properties of the elements and stability of the structure, (iii) finding the optimum pre-stress pattern for certain magnitude from compatible pre-stress states. So far, no research has been carried out to connect the three steps, i.e. finding a suitable pre-stress pattern which also considers mechanical properties of the highly pre-stressed structure e.g. its natural frequencies. This paper aims at finding an optimum pre-stress pattern and level of pre-stress for the maximum frequency. The pre-stress problem is on a linear static level where no slackening is allowed. An optimization is performed to find the optimum pre-stress pattern fromthe self-stress modes obtained by a singular value decomposition (SVD) of the equilibrium matrix. The objective function is the first natural frequency of the structure. Finite element analysis is employed for the linear analysis of the structure and a genetic algorithm for optimization i.e., a non-gradient method. The example considered is a double layer tensegrity grid consisting of 29 independent self-stress states. The method is applicable to complex asymmetric three-dimensional structures. The new aspect of this work is a link between the SVD analysis, finite element analysis and genetic algorithm.

  • 16.
    Dalil Safaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Stiffness visualization for tensegrity structures2010In: Proc. NSCM-23, 2010Conference paper (Refereed)
  • 17.
    Dalilsafaei, Seif
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Stiffness modification of tensegrity structures2011Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Although the concept of tensegrity structures was invented in the beginning of the twentieth century, the applications of these structures are limited, partially due to their low stiffness. The stiffness of tensegrities comes from topology, configuration, pre-stress and initial axial element stiffnesses.

     The first part of the present work is concerned with finding the magnitude of pre-stress. Its role in stiffness of tensegrity structures is to postpone the slackening of cables. A high pre-stress could result in instability of the structure due to buckling and yielding of compressive and tension elements, respectively. Tensegrity structures are subjected to various external loads such as self-weight, wind or snow loads which in turn could act in different directions and be of different magnitudes. Flexibility analysis is used to find the critical load combinations. The magnitude of pre-stress, in order to sustain large external loads, is obtained through flexibility figures, and flexibility ellipsoids are employed to ensure enough stiffness of the structure when disturbances are applied to a loaded structure.

     It has been seen that the most flexible direction is very much sensitive to the pre-stress magnitude and neither analytical methods nor flexibility ellipsoids are able to find the most flexible directions. The flexibility figures from a non-linear analysis are here utilized to find the weak directions.

     In the second part of the present work, a strategy is developed to compare tensegrity booms of triangular prism and Snelson types with a truss boom. It is found that tensegrity structures are less stiff than a truss boom when a transversal load is applied. An optimization approach is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness can be significantly improved, but still an active tensegrity boom is less stiff than a truss boom. Genetic algorithm shows high accuracy of searching non-structural space.

  • 18.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Micheletti, A.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Parametric study of various tensegrity modules asbuilding blocks for slender boomsArticle in journal (Other academic)
  • 19.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Application of flexibility analysis for design of tensegrity structures2011In: Proceeding of the 4th Structural Engineering World Congress, 2011Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    Tensegrity structures have been the subject of research for many years, but very few of them have been built. One major disadvantage of tensegrities compared to typical trusses is their stiffness, which can be significantly reduced when a cable goes slack. This paper aims to introduce a method for stiffness characterization of tensegrity structures for the following purposes: (i) comparison of the stiffness of tensegrity structures with other truss structures, (ii) comparison of the stiffness of different form-found geometries, (iii) finding the most flexible nodes and the principal flexibility directions and (iv) finding stiffness effects of different pre-stress levels and patterns. The method is based on the flexibility analysis of tensegrity structures and the finite element method is used for the non-linear static analysis of the structure to obtain the flexibility figures which visualize the flexibility for different plane and spatial truss and slender boom tensegrity structures.

     

  • 20.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Flexibility-based pre-stress design of tensegrity structuresManuscript (preprint) (Other academic)
    Abstract [en]

    Tensegritiy structures have been subjects of research for many years, but very few of them have been built. One major disadvantage of tensegrities compare to regular truss structures is their low stiffness. This papers aims to have a new look at the stiffness problem of tensegrity structures. Here, it is assumed that the form-finding step has been completed and the axial stiffness of the elements is known. We introduce a tool for stiffness characterization of a given tensegrity structure for different pre-stress magnitudes. Since the pre-stress has a critical influence on the stability of the structure with a role to prevent or postpone slackening, the magnitude of pre-stress of the structure exposed to large external loads and disturbances are found. Finite elements are utilized in the solution for the non-linear static analysis. The method is based on geometrical interpretation of flexibility of unconstrained nodes. Suggested concept, flexibility analysis, shows promising properties in finding flexible nodes, weak directions of structure, detection of cable elements with higher risk of going slack and better knowledge of influence of various external loads. The authors believe results of this research could help the researchers and designer of better understanding the behavior of tensegrity structures.

     

  • 21.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Improving bending stiffness of tensegrity booms2012In: International Journal of Space Structures, ISSN 0956-0599, Vol. 27, no 2-3, 117-129 p.Article in journal (Refereed)
    Abstract [en]

    There is a high interest in employing lightweight, low-cost, deployable structures for space missions. Utilization of tensegrity structures in space application is limited, due to their low stiffness, while a number of high stiffness-to-mass truss booms have been launched. This paper aims to describe and improve the bending stiffness of tensegrity booms. Tensegrity booms of Snelson and triangular prism type are selected for the study. These structures are excellent samples of class 1 tensegrities, with a single state of self-stress and one mechanism, and class 2 tensegrities, with multiple states of self-stress and mechanisms. The stiffness modification procedure includes three steps: (Step 1) developing a strategy for a fair comparison of tensegrity booms with a high performance truss boom. A genetic algorithm is employed to find the optimum cross-section areas of the boom elements. Sources of low stiffness of tensegrities are discussed. (Step 2) an effort is made to find the optimum placement of actuators for improving the stiffness of the tensegrity booms. (Step 3) a genetic algorithm is utilized to calculate their optimum actuation. All three stages have been performed based on a link between non-linear finite element analysis and a genetic algorithm. The genetic algorithm shows high accuracy of searching non-structural space, and also dealing with above steps. Results indicate that the stiffness of tensegrity booms is highly improved by activating the structures.

  • 22.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Sensitivity analysis of tensegrity booms due to member loss2011In: Proceedings NSCM-24, 2011Conference paper (Other academic)
  • 23.
    Dalilsafaei, Seif
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Tibert, Gunnar
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Design and analysis of tensegrity power lines2012In: International Journal of Space Structures, ISSN 0956-0599, Vol. 27, no 2-3, 139-154 p.Article in journal (Refereed)
    Abstract [en]

    Overhead transmission power lines have undergone very small aesthetic and technical changes over time. Studies on mitigation of the electromagnetic field shows that utilizing a helix configuration is an effective way to reduce the electromagnetic field. This study proposes to use tensegrity structures as power lines. Tensegrity structures are composed of tension and compression elements in equilibrium. Modules, simple units with a certain rotation, are connected together to design of overhead power lines with considerable electromagnetic field reduction. A form-finding method enables the design of various free-form configurations. A parametric study is performed to investigate the influence of the module dimensions on the stiffness of the power line. A design algorithm was used for determining the optimum size of elements and the pre-stress level. The selected baseline structure was able to tolerate the wind and ice loads in severe conditions with a 50 times reduction in electromagnetic field. Finally a sensitivity analysis is performed to show the effects of element loss or damage.

  • 24. Dhavale, Nikhil N.
    et al.
    Tamadapu, Ganesh
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    DasGupta, Anirvan
    Finite Inflation Analysis of Two Circumferentially Bonded Hyperelastic Circular Flat Membranes2014In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 81, no 9, 091012Article in journal (Refereed)
    Abstract [en]

    A finite inflation analysis of two circumferentially bonded hyperelastic circular flat membranes with uniform internal pressure is presented. The governing equations of equilibrium are obtained using the variational formulation. By making a suitable change in the field variables, the problem is formulated as a set of two coupled nonlinear two point boundary value problem (TPBVP) and is solved using the shooting method. Membranes of identical and dissimilar material properties are considered in the analysis. For dissimilar membranes, asymmetric inflation, and remarkably, deflation (after an initial phase of inflation) in one of the membranes in certain cases, has been observed. The effect of inflation pressure and material properties on the geometry of inflated configuration, state of stress, and the impending wrinkling condition of the membranes are also studied. This work has relevance to tunable inflated reflectors and lenses among other applications.

  • 25. Ekstrand, Vilhelm
    et al.
    Wiksell, Hans
    Schulz, I
    Sandstedt, B.
    Rotstein, S
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Influence of electrical and thermal properties on RF ablation of breast cancer: is the tumour preferentially heated?2005In: Biomedical engineering online, ISSN 1475-925X, Vol. 4, 41-41 p.Article in journal (Refereed)
    Abstract [en]

    Background: Techniques based on radio frequency (RF) energy have many applications in medicine, in particular tumour ablation. Today, mammography screening detects many breast cancers at an early stage, facilitating treatment by minimally invasive techniques such as radio frequency ablation (RFA). The breast cancer is mostly surrounded by fat, which during RFA-treatment could result in preferential heating of the tumour due to the substantial differences in electrical parameters. The object of this study was to investigate if this preferential heating existed during experimental in vitro protocols and during computer simulations. Methods: Excised breast material from four patients with morphologically diagnosed breast cancers were treated with our newly developed RFA equipment. Subsequently, two finite element method (FEM) models were developed; one with only fat and one with fat and an incorporated breast cancer of varying size. The FEM models were solved using temperature dependent electrical conductivity versus constant conductivity, and transient versus steady-state analyses. Results: Our experimental study performed on excised breast tissue showed a preferential heating of the tumour, even if associated with long tumour strands. The fat between these tumour strands was surprisingly unaffected. Furthermore, the computer simulations demonstrated that the difference in electrical and thermal parameters between fat and tumour tissue can cause preferential heating of the tumour. The specific absorption rate (SAR) distribution changed significantly when a tumour was present in fatty tissue. The degree of preferential heating depended on tissue properties, tumour shape, and placement relative to the electrode. Temperature dependent electrical conductivity increased the thermal lesion volume, but did not change the preferential heating. Transient solutions decreased the thermal lesion volume but increased the preferential heating of the tumour. Conclusions: Both the computer model and the in vitro study confirmed that preferential heating of the tumour during RFA exists in breast tissue. However, the observed preferential heating in the in vitro studies were more pronounced, indicating that additional effects other than the difference in tissue parameters might be involved. The existing septa layers between the cancer tissue and the fatty tissue could have an additional electrical or thermal insulating effect, explaining the discrepancy between the in vitro study and the computer model.

  • 26.
    Engström, Pähr
    et al.
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Bartonek, Åsa
    Karolinska Institutet, Dept. of Women's and Child's Health.
    Tedroff, Kristina
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Orefelt, Christina
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Haglund-Åkerlind, Yvonne
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Gutierrez-Farewik, Elena
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics. KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Botulinum toxin A does not improve cast treatment for idiopathic toe-walking - a randomized controlled trial2013In: Journal of Bone and Joint Surgery. American volume, ISSN 0021-9355, E-ISSN 1535-1386, Vol. 95, no 5, 400-407 p.Article in journal (Refereed)
    Abstract [en]

    Background: There are many treatments for idiopathic toe-walking, including casts with or without injection of botulinum toxin A. Combined treatment with casts and botulinum toxin A has become more common even though there have been few studies of its efficacy and safety problems. Our aims were to conduct a randomized controlled trial to test the hypotheses that combined treatment with casts and botulinum toxin A is more effective than casts alone in reducing toewalking by patients five to fifteen years of age, and that the treatment effect correlates with the extent of coexisting neuropsychiatric problems. Methods: All patients who had been consecutively admitted to the pediatric orthopaedics department of our institution because of idiopathic toe-walking between November 2005 and April 2010 were considered for inclusion in the study. Forty-seven children constituted the study population. The children were randomized to undergo four weeks of treatment with below-the-knee casts either as the sole intervention or to undergo the cast treatment one to two weeks after receiving injections of botulinum toxin A into the calves. Before treatment and three and twelve months after cast removal, all children underwent three-dimensional (3-D) gait analysis. The severity of the idiopathic toe-walking was classified on the basis of the gait analysis, and the parents rated the time that their child spent on his/her toes during barefoot walking. Passive hip, knee, and ankle motion as well as ankle dorsiflexor strength were measured. Before treatment, all children were evaluated with a screening questionnaire for neuropsychiatric problems. Results: No differences were found in any outcome parameter between the groups before treatment or at three or twelve months after cast removal. Several gait-analysis parameters, passive ankle motion, and ankle dorsiflexor strength were improved at both three and twelve months in both groups, even though many children still demonstrated some degree of toe-walking. The treatment outcomes were not correlated with coexisting neuropsychiatric problems. Conclusion: Adding botulinum toxin-A injections prior to cast treatment for idiopathic toe-walking does not improve the outcome of cast-only treatment. Level of Evidence: Therapeutic Level I. See Instructions for Authors for a complete description of levels of evidence.

  • 27.
    Engström, Pähr
    et al.
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Gutierrez-Farewik, Elena
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics. KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Bartonek, Åsa
    Karolinska Institutet, Dept. of Women's and Child's Health.
    Tedroff, Kristina
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Orefelt, Christina
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Haglund-Åkerlind, Yvonne
    Karolinska Institutet, Dept. of Women's and Children's Health.
    Does Botulinum toxin A improve the walking pattern in children with idiopathic toe-walking?2010In: Journal of Children's Orthopaedics, ISSN 1863-2521, Vol. 4, no 4, 301-308 p.Article in journal (Refereed)
    Abstract [en]

    Background: Numerous recommendations have been made for treating idiopathic toe-walking (ITW), but the treatment results have been questioned. The purpose of this study was to investigate whether botulinum toxin A (BTX) improves the walking pattern in ITW as examined with 3-D gait analysis. Participants and methods: A consecutive series of 15 children (aged 5-13 years) were enrolled in the study. The children underwent a 3-D gait analysis prior to treatment with a total of 6 units/kg bodyweight Botox® in the calf muscles and an exercise program. The gait analysis was repeated 3 weeks and 3, 6, and 12 months after treatment. A classification of toe-walking severity was made before treatment and after 12 months. The parents rated the perceived amount of toe-walking prior to treatment and 6 and 12 months after treatment. Results: Eleven children completed the 12-month follow-up. The gait analysis results displayed a significant improvement, indicating decreased plantarflexion angle at initial contact and during swing phase and increased dorsiflexion angle during midstance at all post-treatment testing instances. According to the parents' perception of toe-walking, 3/11 children followed for 12 months had ceased toe-walking completely, 4/11 decreased toe-walking, and 4/11 continued toe-walking. After 6-12 months, the toe-walking severity classification improved in 9 of the 14 children for whom data could be assessed. Conclusions: A single injection of BTX in combination with an exercise program can improve the walking pattern in children with ITW seen at gait analysis, but the obvious goal of ceasing toe-walking is only occasionally reached.

  • 28.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Constraint paths in non-linear structural optimization2014In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 140, 39-47 p.Article in journal (Refereed)
    Abstract [en]

    Optimization of significantly non-linear structures is a demanding task. The paper discusses how boundaries of the feasible region can be followed as generalized equilibrium paths in parametric space, reflecting engineering demands on stiffness, strains and stability. Solutions on the constraint paths are then evaluated with respect to any chosen objective function. For few design parameters, this approach is efficient and robust. This is demonstrated for a pre-stressed pressurized membrane of three parameters, showing several constraint paths for the problem, and indicating how these are used in optimization. The view is often closer to engineering design analyses than the mathematical optimization settings, which often has problems in handling stability constraints.

  • 29.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Criteria for optimality in movements2006In: Journal of Biomechanics, ISSN 0021-9290, E-ISSN 1873-2380, Vol. 39, no s1, S54-S54 p.Article in journal (Refereed)
  • 30.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Derivatives of tangential stiffness matrices for equilibrium path descriptions1991In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 32, no 5, 1093-1113 p.Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures, based on expressions from analytical elastic stability theory, are introduced as numerical tools in a general Finite Element program for geometrically non-linear structural analysis. Especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm. These include improved predictions for the step-wise solution of equilibrium states, identification of critical points and accurate descriptions of initial post-bifurcation behaviour. For two plane beam and bar elements, formulations have been developed giving analytical expressions for these derivatives. The corresponding numerical approximations, needed in other element types, are also discussed. The paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies. Some numerical examples, showing different types of behaviour, are analysed and discussed.

  • 31.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Fold lines for sensitivity analyses in structural instability1994In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 114, no 1-2, 77-101 p.Article in journal (Refereed)
    Abstract [en]

    The paper describes how a two-parameter formulation of a structural equilibrium problem can be used for a more accurate description of the occurring critical states. A fold line concept is used to evaluate the dependence of these states on an added variable, describing a disturbing load case or a disturbed geometry. The concept describes the local behaviour for small disturbances, but can also be used for parameter dependence analyses, e.g. in connection with optimization algorithms. Two different augmentations of the equilibrium relations are discussed; they describe the criticality of a solution state in different ways. Numerical adoption for a general equilibrium path following algorithm is discussed. A postponed factorization method for solution of the augmented sets of equations is proposed. Two simple examples are used to show the properties and the possibilities of the fold line concept. It is concluded that the suggested numerical procedure can give a better description of critical structural behaviour, especially with respect to imperfections in the structure and idealizations in the model. © 1994.

  • 32.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Multi-parametric constraint paths in optimization of pre-stressed membraneArticle in journal (Refereed)
    Abstract [en]

    Optimization of significantly non-linear structures is a demanding task. The paper discusses how boundaries of the feasible region are followed as generalized equilibrium paths in parametric space. As the optimum normally activates one or more inequalities, solutions on the constraint paths are evaluated with respect to the cost function. For few design parameters, this method is efficient and robust. The method is demonstrated for a pre-stressed pressurized membrane of three parameters, with displacement and instability constraints, and with strain limits. Numerical examples show several constraint paths for theproblem, and indicate how these are used in optimization.

  • 33.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Multi-parametric stability investigations for pressurized thin membranes2012In: ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers / [ed] J. Eberhardsteiner et al., ECCOMAS , 2012, 7357-7371 p.Conference paper (Refereed)
    Abstract [en]

    The contribution describes how the quasi-static, conservative problem of pressurized space membranes, i.e., balloons, can be seen in a multi-dimensional context, and how one- and two-dimensional solution manifolds can reveal further information on the structural response. The discussed viewpoint can be seen as the natural extension of the common one-dimensional path-following methods for load-displacement traces, when additional variables are introduced to describe the parameter dependence in structural response, and in instability analyses. The paper describes the general setting of the balloon problem, and the generalized equilibrium form, with some aspects of its treatment. Numerical examples show applications of these models.

  • 34.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Multi-parametric stability investigations for pressurized thin membranes2012In: Proceedings NSCM-25 / [ed] K. Persson, J. Revstedt, G. Sandberg & M. Wallin, Lund: Lund University , 2012Conference paper (Refereed)
    Abstract [en]

    Pressurized thin membranes are frequently encountered in engineering and medical con-texts. Membranes subjected to pneumatic pressurization respond by changing volume and internal over-pressure, and can exhibit different instability conditions.  The response is significantly dependent onparameters for the loading, geometry and material. We used generalized equilibrium path and surfaceevaluation algorithms to describe and investigate the parameter dependence in different response aspects.We describe the algorithmic setting, but also give some aspects of quasi-static instability for pneumaticallypressurized thin membranes. Two examples are used to illustrate the methodology and the obtainableresults

  • 35.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Numerical modeling of thin pressurized membranes2012In: Proc CST-2012 / [ed] BHV Topping, Stirling, U.K.: Civil-Comp , 2012Chapter in book (Refereed)
    Abstract [en]

    The contribution describes how thequasi-static, conservative  problem of pressurized space membranes, i.e., balloons, can be seen in amulti-dimensional context, and how one- and two-dimensionalsolution manifolds can reveal further information on thestructural response. The discussed viewpoint can be seen as thenatural extension of the common one-dimensional path-followingmethods  for load-displacement traces, when additional variables are introduced to describe theparameter dependence in structural response, and in instabilityanalyses. The paper describes the generalsetting of the balloon problem, and the generalized equilibrium form, with some aspects of itstreatment.  Numerical examples showapplications of these models.

  • 36.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On a thin shell element for non-linear analysis, based on the isoparametric concept1992In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 42, no 6, 927-939 p.Article in journal (Refereed)
    Abstract [en]

    This paper discusses a finite element method model for the large displacement, moderate strain analysis of thin shells. The model is based on an 'adapted' reference configuration for a displaced element, separating the displacements into rigid body displacements and strain-producing deformations. A strategy is developed, making use of the isoparametric concept for both the choice of reference configuration and in the element formulation. This makes the use of arbitrarily shaped elements possible. The model is shown to give accurate results for a range of relevant problems. Some problems in the general application of this type of model are discussed. © 1992.

  • 37.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On accurate descriptions for primary and secondary paths in equilibrium problems1992In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 44, no 1-2, 229-242 p.Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures, based on ideas and expressions from the analytical elastic stability theory, have been introduced as numerical tools in a general finite element program for geometrically non-linear structural analysis. Derivatives of the tangential stiffness matrix are utilized for improved predictions in the step-wise solution of equilibrium states, for identification of critical points and for accurate descriptions of initial post-bifurcation behaviour. The methods are used in a general solution algorithm, based on a parameterizing component formulation. For some element types, analytical expressions for these derivatives can be developed. The corresponding numerical approximations, needed in other element types, are also discussed. Other practical details in the numerical implementation are given. Two numerical frame examples, showing different types of limit and bifurcation behaviours, are used to discuss the numerical properties of the methods. © 1992.

  • 38.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On improved predictions for structural equilibrium path evaluations1993In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 36, no 2, 201-220 p.Article in journal (Refereed)
    Abstract [en]

    The paper describes how several procedures for higher-order predictions have been introduced in order to improve the convergence speed in a general finite element program for non-linear structural analysis. In addition to higher-order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post-bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re-creation of the tangential stiffness matrix, used for equilibrium iterations. Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods. The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.

  • 39.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems1989In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 28, no 6, 1317-1334 p.Article in journal (Refereed)
    Abstract [en]

    The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.

  • 40.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    ON SOME PATH-RELATED MEASURES FOR NON-LINEAR STRUCTURAL F. E. PROBLEMS.1988In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 26, no 8, 1791-1803 p.Article in journal (Refereed)
    Abstract [en]

    In the paper, the solution of a non-linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behavior, guiding the iteration strategy in coming steps. Two path-related stiffness measures are derived, giving information concerning the behavior of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.

  • 41.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimal simulations in musculoskeletal posture and movement2008In: Computer and experimental simulations in engineering and science, Vol. 1, 39-56 p.Article in journal (Refereed)
  • 42.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimization for targeted movements2006In: Proc. III Eur. Conf. Comp. Mech.: Solids, structures and coupled problems in engineering / [ed] CA Mota-Soares, 2006Conference paper (Refereed)
  • 43.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimization in target movement simulations2008In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 197, no 49-50, 4207-4215 p.Article in journal (Refereed)
    Abstract [en]

    This paper discusses a methodology for fixed-time simulations of optimal movements of a mechanical system, between specified initial and target configurations, without any a priori knowledge on the trajectory between those. It is primarily aimed at human movement simulations with muscular controls. The basic formulation considers both displacements and forces as unknowns during the movement, connects them, and utilizes a finite element time discretization for solving the whole fixed-time interval simultaneously. Through a consistent interpolation of all kinetic and kinematic variables, the formulation becomes general, needing only minimal input for description of a particular problem, but also eliminating errors inherent in many forms of time-integration. The same consistency allows systematic formulations of a large class of optimization cost functions, primarily focussing on the mechanical behavior of the system rather than on the matching of previously measured movements. It thereby allows the use of robust and efficient general optimization algorithms. Kinetic and kinematic constraints can restrict the movement. As an example of the general setting, a simplified human movement is studied, with different choices of controls (joint moments or muscular tensions), and with different optimization criteria. The example shows that the simulation results are strongly dependent on these choices, in particular that smoothness of movement demands forces considerably higher than the strictly minimum ones. A larger example shows that more complex constraints can be handled within the setting proposed, but also the effects from the fixed-time assumption.

  • 44.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Optimization of power input in simulated cross-country skiingManuscript (preprint) (Other academic)
    Abstract [en]

    Optimal simulations for a simplified skier in a cross-country track are considered.  The skier is modeled considering air resistance drag, friction and normal forces when following a track of cubic splines in a vertical plane. The race is modeled as a time-evolution problem, where the acting forces give the movement. Based on an assumption on how the driving  power variation along the track is limited by capacity measures, a mathematical optimization problem is formulated. This  minimizes the race time under a constraint of maximum integrated cost of the mechanical work rate. The paper discusses the mathematical and numerical formulations of the problem, and shows some aspects of discretization and accuracy. It is obvious from the simulations, that significant reductions in race time can be reached by strategically using the available power resources, rather than using a uniform work rate. With the fatigue criterion used, the conclusion from simulations is that it is advantageous  for the skier to input extra power in parts of the track where resistance is high, i.e., in up-slopes, in parts where friction is locally higher, and in parts where a head-wind is affecting the performance. Although the criterion used catches some aspects of how power production causes fatigue, it is concluded that better descriptions are needed for fatigue accumulation and reduction during a regime with different work rates.

  • 45.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Quasi-static simulations of thin membranes, aiming at stability analyses of balloon-like structures.2011In: Proc. Compdyn 2011 ECCOMAS Thematic Conference, 2011Conference paper (Refereed)
  • 46.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Quasi-static simulations of thin space membranes, aiming at stability analyses of balloon-like structures2011In: ECCOMAS Thematic Conference - COMPDYN 2011, 2011Conference paper (Refereed)
    Abstract [en]

    This paper discusses the evaluation of quasi-static equilibrium solutions for inflatable space membrane structures, such as balloons. A flat linearly interpolated triangular element is used for simulations, with a Mooney-Rivlin hyper-elastic material model, with variable constitutive constants. A compressible medium is used to introduce a one-parametric over-pressure loading within the membrane. Complex path-following procedures are used to find generalized equilibrium paths, with different parameterizations. Numerical examples show that the methods developed can give information on the stability of the structures, but that the medium and means for introducing the internal pressure is of importance for the interpretation of stability.

  • 47.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Structural instability analyses based on generalised path-following1998In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 156, no 1-4, 45-74 p.Article in journal (Refereed)
    Abstract [en]

    This paper describes how quasi-static, conservative instability problems can be completely described, using generalised path-following procedures for augmented equilibrium formulations. In particular, methods for treatment of compound critical states are discussed. The numerical methods are seen as extensions to common equilibrium path methods, allowing the solution of subsets of equilibrium states, also fulfilling auxiliary relations, e.g. criticality. These formulations are in general used to describe the parameter dependence in structural response, in instability analyses and in optimisation. The paper describes the general setting of these generalised equilibrium problems, and discusses some details in their numerical treatment. Emphasis is given to the evaluation of path tangent vectors, in the presence of critical eigenvectors for the structural tangential stiffness matrix. Also, the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, is discussed. Numerical examples are used to show the possibilities and properties of the obtained solution paths, together with some aspects of the numerical procedures.

  • 48.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Temporal finite element descriptions in structural dynamics2004In: Proceedings of the Seventh International Conference on Computational Structures Technology / [ed] B.H.V. Topping, C.A. Mota Soares, Civil-Comp , 2004Conference paper (Refereed)
    Abstract [en]

    This paper discusses a temporal finite element approximation in the analysis of dynamics of mechanical systems, with a special emphasis on problems where a targeted control is desired. This is defined as a situation where forces are to be introduced for the movement of a structure from an initial to one or more target states, but where the behavior between these states is arbitrary. The primary applications are related to bio-mechanical simulations of skeleto-muscular systems, or to robotic analyses. By interpolating simultaneously displacements and velocities in the discrete degrees of freedom, a collocation over the time interval can be used to decide the necessary control variations. As a second step, the control can be optimized for chosen criteria on the integrated force components. By the introduced interpolation of control forces and discrete displacements, a degree of continuity is introduced in the obtained results.

    The presentation focusses on the similarity in computational formulations between several types of dynamic simulations, and sets them in a common algorithmic context. The temporal descriptions of all discrete displacement components are thereby based on a Hermitian finite element form, where each variable is represented by its value and its time differential at a set of discrete time stations. All displacement variables are thereby represented as piecewise cubic polynomials.

    Using the basic equilibrium for the stated problem, and introducing the temporal interpolation of the variables, a finite element form of the problem can be established, with elements in the time dimension, supplementing the discrete or discretized description at each time instance. A set of equations is then established by using a two-point collocation within each time element. This view allows equilibrium equations of any complexity, but is primarily suited for problems of low to moderate numbers of degrees of freedom. The acting forces consist of prescribed external forces and a priori unknown control forces. Prescribed boundary conditions add equations to the system to be solved.

    Dependent on the formulation of the problem, the solution method handles three basic classes of problems. These are distinguished by the number of boundary conditions on the displacements and velocities, and the number of free control force values. For the evolution problem, without control forces, the problem formulation must specify two values for each displacement component. For the fixed control problem, where a target state is desired, the number of free control force values is equal to the number of excessive boundary conditions, and their values can be determined. For an optimal control problem, the number of free control force values is higher than the number of excessive displacement conditions, allowing the optimization of their values.

    For all the three classes of problems, a set of equation is established. In the optimal control problem, the set will add equations of optimality, increasing the size of the problem; a general algorithm can, however, be easily established, where only the number of prescribed displacement values and the number of free control force components decide the used method.

    Performed tests indicate that the developed viewpoint and algorithm can be efficient in the study of complex, but primarily small to moderate size problems, with an improved continuity in the description of motion, and a good stability in dynamic solution. Comparing accuracy and computational effort, the method is efficient for a small problem, compared to Euler and Newmark methods, [1], and comparable to a Runge-Kutta 4th order method.

    The method avoids the common shooting procedure to find a target displacement state, by solving for all discrete time stations at once. For a target controlled non-linear mechanism problem, the convergence with discretization is studied, and shown to be quick, given that a reasonably good initial approximation can be introduced. The method also allows full Newton iterations, leading to high accuracy in results. Alternative local optima in control force cost are discussed, starting from a well-known problem, [2].

    With a sparse matrix for the established system, the efficiency of the method can in many cases be improved. Ongoing work expands the method to allow redundant force systems, limits in control force values, and interpolation of activation measures in the muscular system, rather than in forces themselves.

  • 49.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Temporal finite elements for target control dynamics of mechanisms2007In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 85, no 17-18, 1399-1408 p.Article in journal (Refereed)
    Abstract [en]

    This paper discusses a temporal finite element description in the analysis of dynamics of mechanical systems, with a special emphasis on problems where target control is desired. This is defined as a situation where forces are sought for the movement of a structure from an initial to one or more specified target states. The primary applications lie in robotics and in bio-mechanical forward simulations of musculoskeletal systems. A temporal discretization of the movement and forces is introduced. By interpolating simultaneously displacements and velocities in the spatial discrete degrees of freedom, a collocation over the time interval can be used to decide the necessary system. The needed control can be optimized for chosen criteria on the integrated force components. The temporal interpolation of control forces and discrete displacements introduces a degree of continuity in the obtained results. The viewpoint allows variation of many aspects of problem formulation, and leads to efficient solutions for systems of high complexity but moderate size.

  • 50.
    Eriksson, Anders
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    USING EIGENVECTOR PROJECTIONS TO IMPROVE CONVERGENCE IN NON-LINEAR FINITE ELEMENT EQUILIBRIUM ITERATIONS.1987In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 24, no 3, 497-512 p.Article in journal (Refereed)
    Abstract [en]

    In an earlier paper a method for calculation of non-linear structural response was described. A method for selective damping of solution components parallel to critical eigenvectors was proposed, reducing the risk for diverging equilibrium iterations. This method is, in the present paper, shown to be related to the 'dynamic relaxation' approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N-R schemes. In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.

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