Bézier extraction based isogeometric approach to multi‐objective topology optimization of periodic microstructures

Abstract

This article presents the Bézier extraction based isogeometric approach to multi‐objective topology optimization of periodic microstructures. The approach utilizes the B‐splines based Bézier elements as the finite element representation at both macro and micro levels. The equivalent elastic properties of the representative volume element (RVE) are computed by the numerical homogenization method with the periodic boundary conditions on the control points (CPs) of the B‐spline mesh. The multi‐objective optimization problems including the material bulk modulus maximization, negative Poisson's ratio, and concurrent topology optimization of the composite structures are formulated by using the Bézier elements based isogeometric analysis. The distance‐based density distribution on the CPs of the B‐spline mesh is proposed as the initialization for designing the RVE, which is more robust than the uniform density distribution towards the optimal results. Several numerical examples are presented to illustrate the effectiveness of the proposed approach, and a variety of isotropic and anisotropic RVEs and composite structures are obtained. Meanwhile, various influences on the optimal design of the RVE and macrostructure are also discussed.

Proportional Topology Optimization algorithm for two-scale concurrent design of lattice structures

“…Not only the shape of the structure, but also the shape of the unit cell(s) (and their arrangement as well) have influence on the overall performance. Recently, many authors have explored the employment of two-scale topology optimization in design of lattice structures, such that both the topology of the macro-scale structure and the micro-scale structure (the unit cell) are simultaneously optimized [14][15][16][17][18]. Two finite element models are established, one for each structure.…”