Strategies for computational efficiency in continuum structural topology optimization

A methodology of enhanced computational efficiency is presented for continuum topology optimization of sparse structural systems. Such systems are characterized by the structural material occupying only a small fraction of the structure's envelope volume. When modeled within a continuum mechanics and topology optimization framework such structures require models of very high refinement which is computationally very expensive. The methodology presented herein to deal with this issue is based on the idea of starting with a relatively coarse mesh of low refinement and employing a sequence of meshes featuring progressively greater degrees of uniform refinement. One starts by solving for an initial approximation to the final material layout on the coarse mesh. This design is then projected onto the next finer mesh in the sequence, and the material layout optimization process is continued. The material layout design from the second mesh can then be projected onto the third mesh for additional refinement, and so forth. The process terminates when an optimal design of sufficient sparsity, and sufficient mesh resolution is achieved. Within the proposed methodology, additional computational efficiency is realized by using a design-dependent analysis problem reduction technique. As one proceeds toward sparse optimal designs, very large regions of the structural model will be devoid of any structural material and hence can be excluded from the structural analysis problem resulting in great computational efficiency. The validity and performance characteristics of the proposed methodology are demonstrated on three different problems, two involving design of sparse structures for buckling stability, and the third involving design of a hinge-free gripper compliant mechanism.