Application of approximate concept and graph theory to beam and plate topology optimization

Approximate concept and graph theory are developed and applied to solve the integrated optimization problem of engineering structure containing both beam and plate discrete variables. Firstly, both structural responses and explicit requirements for process manufacturing are considered as constraints, which makes an optimization system based on the two-level multi-point approximation method more engineering oriented. Secondly, a practical evaluation method of topology rationality is proposed based on graph theory in order to avoid invalid structural analysis and improve optimization efficiency. The finite element model corresponding to the binary point-line relation in graph theory and judgements of force nodes, lump masses, structural integrity, etc. are unified. An engineering example shows that the two-level multi-point approximation method is still efficient in solving topology optimization problems with participating plates and beams, and the proposed topological rationality evaluation method can effectively eliminate about 15% of unreasonable configurations.