利用变厚度单元进行平面连续体的拓扑优化

Topology optimization of plane continuum using non-uniform thickness finite element

提出了用变厚度矩形有限单元求解变厚度平面连续体拓扑优化问题的方法 .根据计算出的每一节点处的应力 ,利用满应力设计方法的应力比公式 ,改变板在节点处的厚度 ,删除厚度过小处的单元 ,重新形成结构拓扑和刚度矩阵 .按以上过程反复迭代 ,实现拓扑优化 .这种方法使得各单元间的厚度连续变化 ,在未增加单元及节点数量的情况下 ,提高了计算精度 ,减少了迭代次数 .迭代过程中 ,矩形单元可退化为常应变三角元 ,使结果的边界过渡更为光顺 .文中推导了变厚度矩形有限单元的单元刚度矩阵 .

To get the topology optimization of plane non-uniform continuum,the non-uniform thickness rectangular finite element was presented.The plate thickness at nodes are changed according to the stresses calculated and the stress ratio equation suggested by full stress design methods.The elements,which thickness are less than a threshold,are deleted.The structure topology and stiff matrix are reformed.Topology optimization was achieved by the iteration procedure mentioned above.For the plate thickness being continuous between elements,the calculating accuracy is increased and the iteration times is decreased.These works do not increase the numbers of elements and nodes.During iteration process,rectangular elements may degenerate to triangular element,which makes boundary of plate more smooth.In this paper,non-uniform thickness rectangular finite element stiffness matrix was derived.