Design optimization of multi-coupled trapezoid laminates

•The introduction of multi-coupling can greatly improve stiffness performance.•Universal analytical conditions of hygro-thermal stability have been deduced.•The shape of laminate is expanded from rectangle to trapezoid.•Research method is also applicable to multi-coupled laminate with other coupling.•Method of combining theoretical calculation and numerical simulation is adopted.•Research objective can be extended to more complex structure with variable size. Novel pavement design and size design are important factors to improve the mechanical properties and applicability of composite structures. Based on the multi-coupling of laminates, the universal analytical conditions for multi-coupled laminates are derived. Then four types of laminates with extension-shear coupling capable of forming bending-twisting coupled structure are designed, including three types of multi-coupled laminates. The shape of laminate is no longer limited to rectangular laminate, which is considered as a variable in the design process. Through the combination of theoretical calculation and numerical simulation, the optimal design of trapezoidal laminates with multiple coupling is achieved. The effect of the multi-coupling effect on the stiffness performance has been explored for free-layer laminates, and it has been found that the introduction of the multi-coupling can greatly improve the stiffness performance of laminates. Finally, the hygro-thermal stability performance is verified by numerical simulation and the robust analysis is obtained for stiffness performance.