Static Analysis of Composite Plates with Periodic Curvatures in Material Using Navier Method

Abstract

Fiber-reinforced and laminated composite materials, widely used in engineering applications, may develop periodic curvature during manufacturing due to technological requirements. Given such curvatures in widely used composites, static and dynamic analyses of plates and shells under loads, along with related stability issues, have been extensively investigated. However, studies focusing specifically on the static analysis of such materials remain limited. Composite materials with structural curvature exhibit complex mechanical behavior, making their analysis particularly challenging. Predicting their mechanical response is crucial in engineering. In response to this need, the present study conducts a static analysis of plates made of periodically curved composite materials using the Navier method. The plate equations were derived based on the Kirchhoff-Love plate theory within the framework of the Continuum Theory proposed by Akbarov and Guz'. Using the Navier method, deflection, stress, and moment distributions were obtained at every point of the plate. Numerical results were computed using MATLAB. After verifying the convergence and accuracy of the developed MATLAB code by comparing it with existing solutions for rectangular homogeneous isotropic and laminated composite plates, results were obtained for periodically curved plates. This study offers valuable insights that may guide future research, as it employs the Navier method to provide an analytical solution framework. This study contributes to the limited literature with a novel evaluation of the static analysis of composite plates with periodic curvature.