An accurate model for a composite smart beam, which has embedded or surface-bonded piezoelectric layers as actuators or sensors, is presented, based on two-way piezoelectric–mechanical coupled theory. The third-order displacement theory is employed to account for shearing deformation, and a new set of cubic functions is proposed to accurately describe the distribution of the electric potential field through the thickness of the piezoelectric layers. The beam is discretized with a two-node flexural–extensional element, and the formulation is deduced using the variational principle. The beam model is applied to solve several problems, and its performance is verified by comparing with the analytical solutions and the results of ANSYS software using a solid element.

The tensile strength and compressive strength are indispensable indexes during the design process of composite laminates. For hygro-thermally curvature-stable extension-twist coupled laminates, the improved Differential Evolution Algorithm combined with penalty function is adopted to solve the nonlinear strong constraint of free-layer laminates. The synchronous optimization of multiple targets is achieved, which includes extension-twist coupled effect, tensile strength, compressive strength and buckling strength. Results are presented for free-layer graphite/epoxy composites laminates that consist of 1–18 plies. Finally the hygro-thermal effect, extension-twist coupled effect and buckling strength are simulated and verified.