Topology optimization with simultaneous analysis and design

Abstract

Strategies for topology optimization of trusses and plane stress domains for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. For the truss topology optimization, a penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints for truss topology optimization is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. One case where the SAND approach could not predict a singular topology obtained by compliance minimization is discussed in detail. A member elimination strategy to save CPU time is developed.

For the plane stress topology optimization problem, the ground structure is obtained by using 3 noded constant stress triangular elements. A chess board pattern is observed in the optimal topologies which may be attributed to the triangular elements. Some suggestions for future research are made.