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以节点相对密度为设计变量,以固有频率最大为目标函数,通过修正低密度区质量矩阵建立了基于重构核粒子法(RKPM)的结构动力拓扑优化数学模型.采用罚函数法施加本质边界条件,利用直接微分法推导了结构固有频率灵敏度方程,同时研究了受横向载荷弯曲的基尔霍夫薄板柔度最小的拓扑优化问题.最后对比分析了节点依赖性以及设计变量对最优拓扑结构的影响,并结合以上算法和优化准则法编写程序完成了2个拓扑优化算例.优化结果表明:所建立的模型不仅能有效抑制局部模态和重特征频率的出现,而且因通过重构核近似提高了计算点密度场的连续性,棋盘格现象得以消除,可以得到清晰光滑的拓扑边界.
Taking node’s relative density as design variable and maximum natural frequency as objective function, a structural dynamic topology optimization mathematical model based on reconstructed kernel particle method (RKPM) was established by modifying the low density region mass matrix. The penalty function method was used to impose the essential boundary conditions , The direct-difference method is used to derive the natural frequency sensitivity equation of the structure, and at the same time the topological optimization problem of Kirchhoff plate subjected to transverse load bending is studied.Finally, the node dependence and the influence of design variables on the optimal topological structure Two topological optimization examples are completed based on the above algorithm and optimization criterion method.The optimization results show that the proposed model can not only effectively suppress the occurrence of local modalities and heavy eigenfrequencies, Improve the continuity of the calculated point density field, eliminate the checkerboard phenomenon, and obtain a clear and smooth topological boundary.