Domain Decomposition in Displacement Based Multi-Level Structural Optimization

*† ‡ This paper presents the latest efforts to increase the capabilities of the Displacement based Multilevel Structural Optimization (DMSO) methodology and to improve the efficiency of DMSO in the treatment of large models. The DMSO approach optimizes structures for minimum weight by utilizing a single system level and multiple subsystems level optimizations. In the system level optimization, the load unbalance resulting from the use of approximate nodal displacements in the stiffness equations is minimized to ensure that the calculated loads match the actual applied loads. The system level optimization can be replaced with a system level FEM analysis to reduce execution time, but then the system level design can no longer be constrained. In the subsystems level optimizations, the weight of each element is minimized. Since the subsystems level optimizations are independent of each other, they can be performed in parallel. This has been done previously using the Message Passing Interface (MPI) on PCs, a network of SUN workstations, and on a Linux cluster. Now, the system level FE analysis and optimization are parallelized as well by using domain decomposition and a superelement formulation. Results are presented for a 30element truss, a 240-element truss, and a 2514-element truss for evaluation purposes. These demonstrate that runtime decreases due to the parallelization of the system level and/or the subsystems level.