Element stacking method for topology optimization with material-dependent boundary and loading conditions

Abstract

A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have independent degrees of freedom. Some test problems are considered to check the effectiveness of the proposed stacking method

Topology optimization for nonlinear dynamic problem with multiple materials and material-dependent boundary condition

“…To rigorously approach topology optimization considering the challenging conditions above, we expand the concept of the element connectivity parameterization (ECP) method combined with the element stacking method [9,12,13]. The advantage of the ECP method lies in the fact that its treatment of the unstable elements (flipped elements) is very straightforward.…”

“…A drawback, however, is that the ECP method uses more degrees of freedom than conventional FE-based optimization methods. Recently, this ECP method was applied to the nonlinear dynamic problem by developing a patch mass method that defines mass matrix interpolation for the ECP method [13]. However, it is still challenging and imprecise to apply the ECP method to systems with multiple materials that have different material properties, in spite of some research into the application of existing densitybased topology optimization methods to systems with multiple materials.…”

“…To effectively cope with multiple materials and material-dependent boundary conditions in a dynamic problem, the element stacking method, which was researched in Ref. [13] in the framework of the standard element density method, is expanded to the present patch stacking method in the framework of the ECP method.…”

Magnetic circuit design by topology optimization for Lorentz force maximization in a microspeaker

“…Therefore, design variables assigned to discretizing finite elements should be able to pick up one of three material states, i.e., a magnet, a yoke and air. To deal with multiple material states, the formulations developed earlier for structural [14,15] will be modified for the present magnetic circuit design problems. Wang et al [16] formulated a multi-material for magnetic problems, but the technique used in [15] will be employed here.…”

“…To deal with multiple material states, the formulations developed earlier for structural [14,15] will be modified for the present magnetic circuit design problems. Wang et al [16] formulated a multi-material for magnetic problems, but the technique used in [15] will be employed here. The analysis of a magnetic circuit needed for topology optimization is carried out by a finite element method (see, e.g., [17,18]).…”