Concurrent hierarchical optimization for structures composed of modules considering size effects

The concurrent optimization model and algorithm formodular structures are developed in this paper. The effects of actual sizeof the basic design module on optimization results are investigated for structures composed of periodic modules. The size of modules can greatlyaffect the optimization results of configuration and distribution of basicdesign modules. The concurrent optimizations of macro structures and designmodules are implemented by introducing independent densities inmacro-structure and micro-module hierarchies as design variables. Theoptimal designs of configurations of macro structure and modules in twohierarchies are obtained via topology optimization and penalty technique.The interactions of structures and modules can be considered automaticallyby the optimization model. Two numerical examples with single load and multiloads are presented to validate the proposed optimization model andalgorithm.