A general framework for constructing the feasibility-constraint function of lamination parameters in optimization

Lamination parameters are extensively employed as design variables in the optimization design of composite laminates. The feasibility-constraint function of the lamination parameters in optimization is essential since it is related to the accuracy of the optimal results. In the existing literature, the feasible region for lamination parameters is expressed by multiple inequalities, which is inaccurate and unsmooth at some corners and tedious in the cases of high dimensions. This paper aims at proposing a general framework for constructing the feasibilityconstraint functions in optimization for any given set of lamination parameters with higher precision compared to the functions given by the inequalities. The feasibility-constraint function is generated by training an artificial neural network with the backpropagation algorithm based on the idea of the level set method. The training data mainly comes from the boundary points shaped by the hyperplanes calculated by a variational method. The proposed framework consists of four parts: obtaining the hyperplanes, generating the boundary points of the feasible region, constructing the feasibility-constraint function, and evaluating the accuracy of the generated function. Several experiments are implemented to validate the proposed method in the cases of four-, six-, and eight-dimensional lamination parameters. The 4D results show that the generated feasibility-constraint functions have the advantage in precision compared to the existing constraint functions in literature in the real application of structural optimization. Besides, in the 6D and 8D cases, the smoothness and accuracy of the generated feasible boundaries are also shown. The performance of enforcing the generated constraint in optimization is also studied in all three cases, which indicates that the generated constraint functions are applicable in the optimization design of composite laminates.