Guide-Weight method for topology optimization of continuum structures including body forces

摘要

This paper introduces the Guide-Weight method (GW) into the topology optimization of continuum structures subjected to body force loads. Given the design-dependent characteristic of body-forces, three main difficulties are encountered when dealing with topology optimization problems under this load condition, namely, the non-monotonous behavior of the compliance, inactive volume constraint of the optimum, and parasitic effect in low-density regions. Numerous researchers have attempted to solve this problem with mathematical programming or heuristic methods, but all these methods share the significant weakness of low computational efficiency. Accordingly, we propose to solve this problem with an Optimality Criteria method, i.e. the GW method. First, all theoretical derivations of topology optimization with the GW method are carried out, and the iteration procedure with GW is presented. Then, some typical examples of withstanding body forces are tested, and the topologies got in this paper are compared with corresponding results obtained by former researchers. The iteration speed is found to improve significantly when utilizing the GW method to deal with this kind of problems. Finally, considering all the above examples are optimized with SIMP model, we try to combine RAMP model with the GW method. The distinction between the models of SIMP and RAMP when using GW to solve topology optimization problems under body forces are investigated, which indicates that although both these two interpolation models are able to yield very similar optimal results if suitable parameters are chosen, there is more superiority for RAMP model to get clearer topologies.