تحليل خمش ورق هاي مركب لايه اي و مدرج تابعي با استفاده از روش بدون شبكه محلي توابع پايه متعادل شده بر مبناي تئوري تغييرشكل برشي مرتبه سوم

This thesis investigates the bending analysis of laminated an‎d functionally graded composite plates using a meshless method based on equilibrated basis functions. The third-order shear deformation theory is employed to derive the governing equilibrium equations for the plate. The proposed approach falls within the category of Trefftz methods, utilizing basis functions capable of satisfying the equilibrium equation independently of the boundary conditions. Consequently, the satisfaction of the governing equation an‎d the boundary conditions is achieved in two separate stages, thereby enhancing solution speed while improving the accuracy an‎d convergence of the resulting solution. Another key feature of the proposed method is the use of a weighted residual weak form of the governing equation to satisfy its homogeneous form; notably, Trefftz methods primarily rely on satisfying the strong form of the equation, which limits their scope of application. In contrast, the proposed method—akin to energy-based approaches—satisfies the weak form of the equation (in a Petrov-Galerkin formulation), thereby reducing the order of differentiation in the final formulation. Consequently, a simple meshless method is developed wherein independent sets of points are employed to enforce the governing equation an‎d solution continuity across the domain, as well as to impose boundary conditions. This feature simplifies the discretization of the solution domain using a regular grid of points, offering an advantage over the meshing required in the finite element method. The numerical examples clearly demonstrate the success of the proposed method in achieving the thesis objectives.

نيما نورمحمدي

رضا عبدالهي , حسين عموشاهي