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1999 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 72, no 4, p. 579-593Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

1999. Vol. 72, no 4, p. 579-593
##### Keywords [en]

Computational methods, Finite element method, Stiffness, Strain, Nonlinear mechanics, Symbolic software, Computer aided software engineering
##### National Category

Applied Mechanics
##### Identifiers

URN: urn:nbn:se:kth:diva-117941DOI: 10.1016/S0045-7949(98)00333-2OAI: oai:DiVA.org:kth-117941DiVA, id: diva2:603978
#####

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##### Note

Symbolic software has been used in a number of projects concerned with the development of finite element procedures, primarily aiming at complex, i.e. interacting and higher order instabilities, where high accuracy in formulations is required. The symbolic tools improve the efficiency and documentation of the developed procedures, in order to facilitate comparisons between different element assumptions. Beam formulations for plane and space models were developed, in total displacement and co-rotational contexts, respectively. Symbolic derivation allowed analytical verification of equivalence between certain formulations within these two contexts. Treatment of finite space rotations, based on the rotational vector makes the history-less treatment of rotations easier, which is needed in the evaluation of critical equilibrium subsets in higher-dimensional parameter space. A co-rotational viewpoint, where local element displacements can be obtained from global variables in a systematic manner, allowed different element expressions in a common framework. Different simple, linear elements have been tested with respect to computational efficiency. A field consistence approach was used to develop highly accurate beam and plane stress elements. The common element formulations, based on the matrix multiplications BTDB, is often inefficient, due to the large number of operations needed in the matrix product. Other formulations, based on an analytical integration and differentiation of the strain energy, producing explicit expressions for the stiffness terms, were considerably more efficient for certain elements.

References: Pacoste, C., Eriksson, A., Element behaviour in post-critical plane frame analysis (1995) Comput Meth Appl Mech Engng, 125, pp. 319-343; Pacoste, C., Eriksson, A., Beam elements in instability problems (1997) Comput Meth Appl Mech Engng, 144, pp. 163-197; Eriksson, A., Pacoste, C., Zdunek, A., Numerical analysis of complex post-buckling behaviour using incremental-iterative strategies Comput Meth Appl Mech Engng, , (in press); Eriksson, A., Structural instability analyses based on generalised path-following (1998) Comput Meth Appl Mech Engng, 156, pp. 45-74; Rheinboldt, W.C., On the computation of multi-dimensional solution manifolds of parameterized equations (1988) Numer Math, 53, pp. 165-181; Lanzo, A.D., Garcea, G., Koiter's analysis of thin-walled structures by a finite element approach (1996) Int J Numer Meth Engng, 39, pp. 3007-3031; Pacoste, C., Co-rotational flat facet triangular elements for shell instability analyses (1998) Comput Meth Appl Mech Engng, 156, pp. 75-110; Korelc, J., (1996) Symbolic Approach in Computational Mechanics and Its Application to the Enhanced Strain Method, , Dr.-Ing. thesis, Department of Mechanics, TH Darmstadt; Reissner, E., On one-dimensional, large displacement, finite-strain beam theory (1973) Stud Appl Math, 52, pp. 87-95; Char, C.W., Geddes, K.O., Gonnet, G.H., Leong, B.L., Monagan, M.B., Watt, S.M., (1991) Maple V Language Reference Manual, , Berlin: Springer; Crisfield, M.A., A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements (1990) Comput Meth Appl Mech Engng, 81, pp. 131-150; Crisfield, M.A., (1991) Non-linear Finite Element Analysis of Solids and Structures, , Chichester: Wiley; Luo, Y.H., Explanation and elimination of shear locking and membrane locking with field consistence approach (1999) Comput Meth Appl Mech Engng, 162, pp. 249-269; Luo, Y.H., (1997) On Shear Locking in Finite Elements, , Lic. thesis, Department of Structural Engineering, Royal Institute of Technology, Stockholm; Simo, J.C., A finite strain beam formulation. The three-dimensional dynamic problem. Part I (1985) Comput Meth Appl Mech Engng, 49, pp. 55-70; Nour-Omid, B., Rankin, C.C., Finite rotation analysis and consistent linearization using projectors (1991) Comput Meth Appl Mech Engng, 93, pp. 353-384; LidstrÃ¶m, T., (1995) Computational Methods for Finite Element Instability Analyses, , Dr. thesis, Department of Structural Engineering, Royal Institute of Technology, Stockholm; Argyris, J., Tenek, L., A natural triangular layered element for bending analysis of isotropic, sandwich, laminated composite and hybrid plates (1993) Comput Meth Appl Mech Engng, 109, pp. 197-218; (1992) Matlab Reference Guide, , Natick, MA: The Math Works Inc. version 4.0; Luo, Y.H., Eriksson, A., Extension of field consistence approach into developing plane stress elements Comput Meth Appl Mech Engng, , (in press); Eriksson, A., Pacoste, C., Element formulations from symbolic manipulation (1998) Advances in Finite Element Procedures and Techniques, , B.H.V. Topping. Edinburgh: Civil-Comp; Wolfram, S., (1996) The Mathematica Book 3rd, , Wolfram Media Inc; Yagawa, G., Ye, G.-W., Yoshimura, S., A numerical integration scheme for finite element method based on symbolic manipulation (1990) Int J Numer Meth Engng, 29, pp. 1539-1549; Mizukami, A., Some integration formulas for a four-node isoparametric element (1986) Comput Meth Appl Mech Engng, 59, pp. 111-121; Zienkiewicz, O.C., (1977) The Finite Element Method 3rd, , London: Mcgraw-Hill; Cook, R.D., Malkus, D.S., Plesha, M.E., (1989) Concepts and Applications of Finite Element Analysis 3rd, , Chichester: Wiley

NR 20140805Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2017-12-06Bibliographically approved
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