zbMATH — the first resource for mathematics

Topology optimization using nonlinear finite elements and control-point-based parametrization. (English) Zbl 1401.74274
Summary: This paper presents an approach to shape/topology optimization of continuous structures. The proposed approach combines the design element technique and the level set function in order to obtain an efficient topology parameterization of the domain under consideration. The shape and the level set function are both parameterized by the control points and corresponding blending functions of the design elements. For the sake of generality, nonlinear finite elements are employed, which have to be adapted adequately in order to be able to describe full material, void, and any intermediate state. In this way the design element technique has not yet been used for topology optimization, partially because it requires that the domain geometry and finite element mesh have to be defined by utilizing control-point-based design elements. In spite of this drawback, the proposed approach offers several attractive benefits. Namely, in contrast to other level set methods, the proposed approach does not make any use of the Hamilton-Jacobi differential equation. Consequently, the boundary evolution stage of the process need not to be treated separately, but is integrated with the strain/stress analysis stage into a rather conventional optimization scheme. Furthermore, the proposed approach allows for any type of finite elements (linear/nonlinear) to be implemented into the procedure if adjusted adequately. The formulation of the optimization problem is also completely arbitrary. The properties of the proposed approach are illustrated by several numerical examples.

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74P15 Topological methods for optimization problems in solid mechanics
Full Text: DOI