Static Analysis of Laminated Composite Plates with Periodic Curvature Using Reissner–Mindlin Plate Theory

Fiber-reinforced laminated composite materials are widely used in engineering applications and may exhibit periodic curvatures due to technological requirements arising during manufacturing processes. Such geometric features directly influence the mechanical behavior of structural elements. Although the dynamic and stability behaviors of curved plates have been extensively investigated in the literature, studies addressing the static analysis of composite plates with periodic curvature, particularly those incorporating transverse shear deformations, remain limited. In this study, the static behavior of laminated composite plates with periodic curvature is investigated using the Navier solution method within the framework of Reissner–Mindlin plate theory. The governing equations are derived from the Continuum Theory developed by Akbarov and Guz’, and the effects of transverse shear deformations on displacements and internal forces are examined within the Reissner–Mindlin formulation. Numerical computations are carried out using MATLAB. The accuracy and convergence of the proposed approach are verified by comparing them with existing analytical solutions in the literature for rectangular homogeneous isotropic and laminated composite plates. Considering the limited number of analytical studies on the static analysis of composite plates with periodic curvature that account for shear deformations, the present study contributes to the literature by providing benchmark results for future research.