Analysis of inhomogeneous structures in small and large deformations using the finite element-meshless coupling method - El Kadmiri, Redouane; Belaasilia, Youssef; Timesli, Abdelaziz (Computers & mathematics with applications (1987), 2024)
In this work, a finite element-meshless coupling method for modeling the inhomogeneous structures composed of functionally graded materials is presented. Coupling the two methods is usually based on the continuity and equilibrium conditions at the finite element-meshless interface. In the proposed hybrid method, the equilibrium condition is satisfied by the action-reaction principle to ensure the coupling between the finite element method and the strong-form meshless method. The idea is to satisfy the equilibrium condition by calculating the interface force vector in the finite element formulation using a strong-form meshless technique. In the weak formulation the forces are modeled by the interface force functional. This hybrid method has been used to study the behavior of functionally graded materials in small deformations, with a comparison between the results of other numerical methods and those of analytical solutions. Following this validation, the hybrid numerical approach is adapted to the simulation of static computational problems for inhomogeneous functionally graded materials with geometric nonlinearity. In this context, a high-order algorithm has been developed by associating a high-order development, continuation procedure and hybrid method. Numerical analysis is performed to prove the accuracy and efficiency of the present approach, through a comparative study with solutions provided by high-order algorithms derived from the finite element method and strong-form meshless methods. In addition, the good qualities of the solution are controlled by the residues, which do not exceed 10−6.