Search

In conventional level set methods for topology optimization, the evolution of level set function is solved by upwind scheme and needs to be reinitialized frequently throughout the optimization. The upwind scheme is complicated in numerical implementation and the reinitialization is time-consuming and slows down the optimization efficiency. This paper presents a level set method updated with finite difference scheme for structural topology optimization. The velocity field used to update the level set function is interpolated by piecewise basis function in order to incorporate the universal mathematical programming algorithm into the optimization. The diffusion is introduced into the Hamilton-Jacobi equation and the three-step splitting method is adopted to solve the equation. By applying the proposed method, the evolution of the level set can be updated by simple central difference scheme and the procedure of reinitialization is avoided without sacrificing the numerical stability. The classical mean compliance minimization problem with several numerical examples is used to test the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper develops an extended bi-directional evolutionary structural optimization (BESO) method for topology optimization of continuum structures with smoothed boundary representation. In contrast to conventional zigzag BESO designs and removal/addition of elements, the newly proposed evolutionary topology optimization (ETO) method, determines implicitly the smooth structural topology by a level-set function (LSF) constructed by nodal sensitivity numbers. The projection relationship between the design model and the finite element analysis (FEA) model is established. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. The introduction of sensitivity LSF results in intermediate volume elements along the solid-void interface of the FEA model, thus contributing to the better convergence of the optimized topology for the design model. The effectiveness and robustness of the proposed method are verified by a series of 2D and 3D topology optimization design problems including compliance minimization and natural frequency maximization. It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation; meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution. [ABSTRACT FROM AUTHOR]