Simultaneous sizing and topology optimization of extruded elastic thin-walled beams

Abstract

This paper presents a novel approach for optimizing extruded thin-walled beams. The main idea of the proposed approach is to formulate the problem’s design variables as line segments with unknown thicknesses. This is attained by viewing the beam’s cross-section as a set of connected line segments, representing the flat folded plates that form its geometry. The design space is defined based on the ground structure approach, enabling layout optimization and the design of general cross-sections. This special parameterization enables leveraging algorithms developed for truss layout optimization.

Under the assumption of extruded beams, the finite strip method is employed for efficient linear elastic structural analysis, resulting in a significant reduction in computational burden compared with other methods, such as shell elements. Since the proposed parameterization is general, regardless of the structural analysis method, it can also be used with more general finite element formulations of flat-shell structures.

The numerical studies show that the method enables designs equivalent to full 3D optimization with a significant reduction in computational burden. Additionally, it is shown that the method converges to intuitive solutions for simple cases and more sophisticated solutions in complex cases, especially when traditional beam theory is not applicable.