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Topology Optimization for Large-displacement Compliant Mechanisms Using Element Free Galerkin Method  

Du, Yixian (College of Mechanical & Material Engineering, China Three Gorges University)
Chen, Liping (CAD Center, School of Mechanical Science & Engineering, HuaZhong University of Science and Technology)
Publication Information
International Journal of CAD/CAM / v.8, no.1, 2009 , pp. 1-10 More about this Journal
Abstract
This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.
Keywords
Compliant mechanisms; Topology optimization; Element-free Galerkin methods; Method of moving asymptotes; Geometrical nonlinearity;
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