ICM应力全局化方法克服连续体拓扑优化的载荷病态

LOAD SICKNESS TREATMENT IN TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURE BY ICM METHOD WITH STRESS GLOBALIZATION

在连续体结构拓扑优化中,由于载荷通常非常复杂,存在一种类似于结构分析中"总刚病态"的"载荷病态"现象。引起载荷病态的原因是由于大多数拓扑优化算法没有考虑大载荷、小载荷间的不同影响,使得小载荷的传力路径在优化过程中消失。该文对载荷病态问题进行了剖析,并将其分为三种情况:1)多工况间有载荷病态,但工况内无载荷病态;2)仅在工况内有载荷病态;3)多工况间有载荷病态,同时某工况内也有载荷病态。为解决载荷病态问题,该文提出了应变能策略,利用应力全局化的ICM方法,逐一采用不同的补充方法解决了上述三种载荷病态问题。对多工况下应力约束的连续体结构拓扑优化问题,应力全局化意指基于第四强度理论将局部性应力约束转化为全局性的应变能约束。数值算例表明:全局性的应变能约束代替局部性应力约束可以更好地得到传力路径,并能更方便地处理各种复杂载荷病态问题。

Because the load case is often very complicated in the topology optimization of continuum structures, there is a phenomenon of the load sickness that likes stiffness sickness in the structural analysis. The reason caused the load sickness is that most algorithms of the topology optimization have not considered different influences between the loads with small forces and the loads with big forces. Therefore, some of topology paths of transferring small forces may disappear during iterative process. This paper dissects the phenomenon of the load sickness and classifies the phenomenon into three cases： 1） load sickness exists between load cases, but not within each load case; 2） load sickness exists within some load cases; 3） load sickness exists not only between load cases, but also within some load cases. To deal with problem of load sickness, a strategy based on strain energy is put forward, using ICM method with stress globalization, the problems of above three cases of load sickness are solved by adopting different complementary approaches one by one. For topology optimization with stress constraints under multiple load cases, the stress globalization means that local stress constraints are transformed into global energy constraints based on the fourth strength criterion. Several numerical examples reveal that the topology paths of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of load sickness can be dealt with more conveniently.