Shape optimization by the level-set method applied to architectured flexural panels

Architectured materials (such as foams, corrugated structures, trusses, hollow spheres) are used, alone or as core material in a sandwich structure, for flexural panels. The idea is to take advantage of the architecture to combine multiple functionalities (e.g. lightweight, stiffness, thermal insulation). Therefore it seems relevant to design the distribution of matter in order to obtain the desired performances. Multi-functional and conflicting specifications lead to non-trivial selection and/or optimization problems. It is hence proposed to use numerical shape optimization procedures into a "material by design" approach applied to periodically architectured flexural panels. A finite element analysis on the unit cell is presented to compute the effective stiffness of each panel depending on its architecture. Then, shape optimization by the level-set method is made on the unit cell with regard to the effective stiffness and a volume constraint. Multiple start geometries and objective functions are tested. The four-point bending test, which usually characterizes flexural panels performance, is used as a reference for both homogenization and optimization.