# Static Analysis of Composite Plates with Periodic Curvatures in Material Using Navier Method
## 1 Introduction
The effectiveness of the approach was validated through convergence studies conducted on plates with various arbitrary geometries. [PERSON] [23] proposed a higher-order shear deformation theory derived from 3D elasticity solutions using an inverse method. The theory satisfies the stress boundary conditions exactly and provides highly accurate results for bending and stress analysis compared to classical five-degree-of-freedom models, offering improvements, particularly for laminated composite plates. [PERSON] and [PERSON] [24] introduced a region-by-region modeling strategy for laminated composite plates, which enables the combination of equivalent, intermediate, and layerwise models within different zones of the plate domain. Instead of applying a single model throughout the structure, their approach allows the assignment of different models with varying orders in the thickness direction to specific areas of interest. This strategy offers a balance between computational efficiency and local accuracy, especially in complex regions with unsymmetric laminae, cut-outs, local damage, or material transitions. Their numerical results demonstrated that the method accurately captures local stresses and displacements while maintaining a low computational cost. [PERSON], [PERSON], [PERSON] and [PERSON] [25] proposed a mixed finite element model based on the least-squares variational principle for the static analysis of laminated composite plates. The formulation adopts the first-order shear deformation theory, considering generalized displacements and stress resultants as independent variables. High-order C\({}^{0}\) Lagrange interpolation functions are employed to enhance accuracy while maintaining computational efficiency. The numerical results, obtained for various boundary conditions and side-to-thickness ratios, demonstrate the effectiveness of the proposed method and its insensitivity to shear-locking when using high-order interpolation functions. Predicting the mechanical behavior of composite plates with periodic curvature in structural analyses is of great significance, especially for advanced engineering applications, due to their geometric complexity. In response to this need, the present study investigates the static behavior of rectangular plates with periodic curvature, using the Navier method within the framework of the Continuum Theory of Akbarov and Guz', based on the Kirchhoff-Love plate theory. While the literature offers numerous studies on the mechanical behavior of homogeneous isotropic or classically laminated composite materials [12; 13; 14], systematic static analyses focusing on deflection, bending moments, and stress distribution in periodically curved composite plates remain limited. Although both the Navier method and Kirchhoff-Love plate theory are well-established analytical tools, their integration with periodically curved geometries in laminated composite plates remains unexplored. While the Kirchhoff-Love plate theory remains a reliable analytical tool for thin plate behavior, its neglect for transverse shear deformation can limit its accuracy in the analysis of moderately thick and thick plates. Recent studies have addressed these limitations by proposing refined theoretical models and advanced numerical methods that incorporate shear deformation and thermomechanical coupling in layered or functionally graded structures, as seen in [26; 27]. This study thoroughly examines the influence of material curvature on deflection, bending moments, and stress distribution. It also aims to address the research gap proposed by [PERSON] and [PERSON]' [1] by numerically evaluating the effects of periodic curvature on the static response. Plates made of homogeneous isotropic, laminated composite, and periodically curved laminated materials were analyzed through coding carried out in the MATLAB 2024a environment.