The decarbonization of the aviation industry is a critical challenge in the mitigation of climate change, with hydrogen proposed as a viable alternative fuel. However, integrating liquid hydrogen storage into aircraft structures presents technical hurdles. Traditional cylindrical pressure vessels, while structurally efficient, lead to poor volume utilization within the non-cylindrical spaces of an airframe. Given that liquid hydrogen requires approximately four times the storage volume of conventional jet fuel, maximizing volumetric efficiency is vital. 

This study develops a preliminary design optimization framework for non-cylindrical, conformable liquid hydrogen tanks. The model utilizes 316L stainless steel and polyurethane foam insulation, integrating quasi-static thermodynamic dormancy requirements with structural mechanics based on analytical plate theory and internal stiffeners. While neglecting localized thermal and stress concentrations, the resulting nonlinear programming problem is solved using the Interior Point Optimizer algorithm.

The results demonstrate that while a rectangular 316L tank structure is approximately ten times heavier than a cylindrical aluminum baseline, it enables a 20\% increase in fuel capacity within a fixed airframe section. This energy surplus results in a 24.6\% (115.8 km) increase in mission range, while aircraft fuel consumption increases by only 2.16\%. These findings suggest that hydrogen-powered aircraft are primarily volume-limited rather than weight-limited. Consequently, conformable tank geometries offer a feasible design alternative for regional hydrogen aviation, where the benefits of increased fuel volume outweigh the structural mass penalties.