Static and vibrational shape and topology optimization using homogenization and mathematical programming (Q1912209)

The homogenization method together with mathematical optimization concepts are combined to perform two-dimensional shape and topology optimization of structures under volume constraint. Static, as well as single or multi-eigenvalue vibrational optimization of structures is considered. The basic assumption is that the structure under consideration is formed by the spatial repetition of a non-homogeneous microstructure, composed of solid material and void regions. The method, upon convergence, allocates material or voids at different parts of the structure, and thus an optimum shape is achieved. A detailed study is made to assess the effect of various microstructural models on the final optimum shape.