Design of compliant mechanisms using meshless level set methods

This paper presents a meshless Galerkin level-set method (MGLSM) for shape and topology optimization of compliant mechanisms of geometrically nonlinear structures. The design boundary of the mechanism is implicitly described as the zero level set of a Lipschitz continuous level set function of higher dimension. The moving least square (MLS) approximation is used to construct the meshless shape functions with the global Galerkin weak-form in terms of a set of arbitrarily distributed nodes. The MLS shape function is first employed to parameterize the level set function via the surface fitting rather than interpolation, and then used to implement the meshless approximations of the discrete state equations. Since the MLS shape function lacks of Kronecker delta function property, a constrained Galerkin global weak-form using the penalty method is applied to enforce the essential boundary conditions. In this way, the shape and topology optimization of the design boundary is just a question of advancing the discrete level set function in time by updating the unknown parameters for the parameterized size optimization. Compared to most conventional level set methods, the proposed MGLSM is able to (1) propagate the discrete level set function and solve the state equations at the same time with one unified set of meshes, (2) avoid numerical difficulties in solving the complicate Hamilton-Jacobi partial differential equations (PDEs), and (3) describe the implicit moving boundaries without remeshing for discontinuities. A benchmark numerical example is used to demonstrate the effectiveness of the proposed method. Copyright © 2012 Tech Science Press