TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES USING INCOMPATIBLE FINITE ELEMENTS
采用非协调元的连续体拓扑优化设计

Topology design has been one of the main research topics in the structural optimization area since Bendsoe and Kikuchi revived its interest using homogenization method and material distribution technique in their landmark paper in 1988. Till now, there are still some numerical difficulties in solving a topology optimization problem. A well-known error is the checkerboard pattern that occurs because of the artificial high stiffness and certain elements in the optimal process whose stability are not guaranteed. In recent years, different ways are presented to prevent the checkerboard pattern. One is using the higher-order elements, but this increases the cpu time in the iteration process due to the large freedoms; the others are using the filtering techniques or density redistribution algorithm based on the low-order isoparametric compatible elements, however there are still some gray area in the final layout structure which makes the engineering applications very difficult. To overcome the numerical problems, the topology design using incompatible finite elements generated according to PTC is carried out. And expressions have been derived for analytical response sensitivity computation and numerical computation in topology optimization process. The final optimal results indicate that the solutions for the layout structure in the domain using 4-node incompatible elements can be used directly in engineering fields. Further, the optimal layout structure using the filtering technique and incompatibles elements shows less intermediate density or gray area compared with that using 4-node isoparametric compatible elements. Moreover, the iteration times and cpu time for topology optimization using the two kinds of elements are close to each other. Thus the improvement in the accuracy of the final optimal results using incompatible elements is validated and the checkerboard pattern problem is also overcome completely.