Optimization of laminated composite plates for maximizing buckling load using improved differential evolution and smoothed finite element method

This paper proposes a novel numerical optimization procedure with mixed integer and continuous design variables for optimal design of laminated composite plates subjected to buckling loads. In the present optimization problem, the objective function is to maximize the buckling load factor. The design variables are fibre orientation angles and thickness of layers, in which the fibre orientation angles are integer variables and thickness are continuous variables. The constraints include the limitation of variables and the total thickness of the plate. For analyzing the buckling behavior of laminated composite plates, a recently proposed smoothed finite element method named the cell-based smoothed discrete shear gap method (CS-DSG3) is employed. For solving the current optimization problems which contain both integer and continuous variables, an improved different evolution algorithm, named mixed-variable different evolution (mDE) is proposed. In the mDE, the mutation and selection phases of the original DE are replaced by an adaptive mutation mechanism and an elitist selection technique, respectively. These improvements not only help balance effectively the global and local search abilities of the DE, but also help deal with integer and continuous design variables. The reliability and effectiveness of the proposed optimization procedure are investigated through some numerical examples for optimal design of laminated composite plates with 2, 3, 4 and 10 layers subjected to buckling loads. Additionally, the influence of different loading and boundary conditions on the optimal solution is also investigated.