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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.
Aiming to the continuity of design variables in continuum topology optimization based on variable density method, a topology optimization model of continuum structure with minimum structural weight and displacement and frequency constraints is established. The original topology optimization problem is transformed into a topology with higher Accuracy of the first order multi-point approximation sequence problem, the constraint function of the problem by the history of the design process of the critical constraint function values and the first derivative of the structure constructed; and then through the linear Taylor expansion established by the dual method fast solution to the second stage Approximation of the sequence to approximate the solution of the first order approximation problem.Using the sensitivity filtering technique to avoid the numerical defect caused by the checkerboard and to punish the element stiffness in the low density region to eliminate the local modal of the frequency constraint problem Phenomenon.The Nastran finite element program Nastran was used in the optimization process to perform structural analysis and sensitivity analysis.The numerical results show that this method can effectively solve the continuum topology optimization problem with displacement and frequency constraints.