Topology Optimization of Continuum Structure by Using Two-Level Multipoint Approximation

Considering the characteristics of continuum structure in SIMP concept based topology optimization design, a topology optimization model was established. The objective function of this model is minimum structural mass, which is subject to displacement constraints and frequency constraints. With respect to continuum topological design variables, the original topology optimization problem was transformed to a sequence of the first-level explicitly approximate problems, which were constructed based upon the values and the first-order derivatives of the critical constraint functions at the points obtained in the procedure of optimization; each of them was approached again by the second-level approximate problems, which was developed by using linear Taylor series expansion and then solved efficiently with dual method. Filtering was used on the sensitivities of the optimization to prevent checkerboard patterns in the design. The stiffness of low density elements was penalized to avoid localized mode in optimization problem with frequency constraints. The general finite element program NASTRAN was adopted in structural analysis and sensitivity calculation within the optimization procedure. Numerical examples show that this method can be applied to solving topology optimization problem with displacement and frequency constraints efficiently.