中文摘要：

针对基于变密度法的连续体拓扑优化中设计变量连续性的特点，建立了以结构重量最小为目标，考虑位移和频率约束的连续体结构拓扑优化模型；原拓扑优化问题先转化为具有较高精度的第一级多点近似序列问题，该问题的约束函数由优化过程中历史设计点的临界约束函数值及其一阶导数构造；再通过线性泰勒展开建立可由对偶法快速求解的第二级近似序列问题，以逼近各第一级近似问题的解．采用敏度过滤技术，避免棋盘格引起的数值缺陷问题，并对低密度区域的单元刚度进行惩罚，以消除频率约束问题的局部模态现象．优化过程中采用通用有限元程序Nastran进行结构分析和敏度分析．数值算例结果表明：应用该方法可以有效地解决具有位移和频率约束的连续体拓扑优化问题．

英文摘要：

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.