Solution to Bending Problem of Trapezoid Composite Laminates

The optimized design of composite adaptive structures puts forward higher requirements and challenges to the actual configuration of the structural section. In this paper, a trapezoidal laminate model of composite materials is established. Based on the classical laminates theory, the bending problem of trapezoidal laminates is solved by using the Kantorovich method and the principle of minimum potential energy. The analytic form of the solution is found to satisfy the Euler equation and displacement boundary conditions. Taking the wing of a jet transport aircraft as an example, the accuracy of the analytical solution is verified by the finite element method. The Differential Evolution algorithm is used to realize the multi-objective optimal design of the bending–twisting coupled trapezoidal laminates, and the hygrothermal stability of laminates is verified by the finite element method. Finally, based on the Monte Carlo method, the robustness analysis of the bending–twisting coupling effect of laminate is realized; meanwhile the feasibility and reliability of the design scheme are verified. The stress and strain functions at each point of the trapezoidal laminate can be further obtained by the analytical solution, making it more convenient to analyze the stresses and calculate the static forces of the trapezoidal laminate and its composite structures, which is of great significance to effectively improve the comprehensive mechanical properties of the cross-section structure of composite materials.