Generalization of two- and three-dimensional structural topology optimization

This paper explores fundamental issues on the quality of structural topology optimization results and presents a generalized topology optimization process. In the generalized process, non-rectangular design domains with geometrical constraints can be accepted, and the use of an automatic mesh generator to mesh the design domain is allowed. The proper number of elements in the design domains to avoid the mesh-dependence problem is also suggested. Higher order elements are used to deal with the checkerboard problem, and a two-stage penalty function method is proposed for the topology optimization. Finally a continuity analysis is used to deal with the porous topology, and two filters are implemented to filter out the trivial solids and voids. The whole process is generalized to two- and three-dimensional structures and can be fully automated. Fourteen two-dimensional and six three-dimensional examples are used to demonstrate the effectiveness of this process.