A topology, material and beam section optimization method for complex structures

This article presents an engineering method for optimizing the topology, materials and beam cross-sectional types of complex structures comprising bars, beams or shells, or their combinations. The optimization problem is established based on an extended ground structure where each location contains multiple components or cross-sectional beams with different materials. This problem is solved through explicit sequence approximate problems involving discrete 0/1 variables to determine the optimal topology, materials and beam section types of components, and continuous size variables. The 0/1 variables are determined with a genetic algorithm, in which size variables are optimized with a dual method after determining 0/1 variables in each generation. The final design is restricted to a condition where at most one component can exist per location, realized through modified operators in the genetic algorithm. Structural analyses are conducted before establishing approximate problems in iteration cycles. Numerical examples, including an engineering application, demonstrate the efficiency of this method.