Stress-based topology optimization approach using binary variables and geometry trimming

In this paper a new approach to handle stress-based topology optimization problems by using the Topology Optimization of Binary Structures method is presented. The design update is carried out with binary values (0 or 1) and a boundary identification scheme is employed to smooth the structural contours to avoid artificial stress concentrations that can occur because of the jagged nature of the topology optimization process. Because of the boundary identification, re-meshing is necessary at each iteration. To minimize the discontinuity of the moving domain through the iterations, we define two domains. The first one is the extended domain (called topology domain) which is fixed, meshed only in the beginning of the optimization process. It is where the design variables are defined, and the mass constraint and its sensitivity are calculated. The second one (called analysis domain) is the structure with the boundary already identified, where the finite element analysis is carried out and the objective function and its sensitivity are calculated. The objective function sensitivity must be interpolated to the optimization domain only where the design variables indicate solid regions. A spatial filtering technique is applied to avoid numerical instabilities and to extrapolate to void regions. Numerical examples are presented to demonstrate the methodology efficiency.