Multi-objective optimization of controllable configurations for bistable laminates using NSGA-Ⅱ

Abstract

A multi-objective optimization technique for bistable laminates is proposed in the present study. Bistable laminates have wide application prospects as deployable structures of aerospace structures and wind turbines, but the design of their mechanical characteristics and configurations might be a hard job considering the conflicting requirements. Surrogate models of the bistable laminates are created by response surface method. The non-dominated sorting genetic algorithm-II (NSGA-Ⅱ) is used to obtain Pareto-optimal solution where the presence of a trade-off relation between the mechanical performances and configurations of bistable laminates has been established. The trigger forces of bistable laminates during snapping to another stable configuration are the mechanical objective functions, while the curvatures of their different stable configurations are used as the conflicting objective functions. And the relationship between different stable configurations is considered as the constraints which is a basis to judge the existence of bistable characteristics. The maximum relative error between finite element analysis results and optimal designs of surrogate models is 2.29%, which also reflects the accuracy of surrogate models. Two optimal designs of bistable laminates that verifies by the experimental investigations have been obtained. The maximum relative error of trigger force between the experimental and finite element analysis results is 14.28%, and the maximum relative error of the sum curvature of different stable states between the experimental and finite element analysis results is 9.22%. The proposed optimization technique can be applied to optimize composite structures in consideration of multi-objective.