Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Modeling of Functionally Graded Material (FGM) plates bending via GFEM
Submission Author:
Bruno Pereira Santos , SC , Brazil
Co-Authors:
Bruno Pereira Santos, Paulo de Tarso Mendonça
Presenter: Paulo de Tarso Mendonça
doi://10.26678/ABCM.COBEM2023.COB2023-2128
Abstract
This paper presents a formulation of Generalized Finite Element Method (GFEM) capable of analyzing Functionally Graded Material (FGM) plates acting under both mechanical loadings and high gradient thermal fields. Due to the increasing usage of FGM in the construction of space shuttles and other structures designed to operate in environments with harsh thermal conditions, it is important to further develop analysis models capable of representing the coupling of mechanical and thermal effects in this kind of composite. Parallel to this, in recent years, GFEM has risen as a valuable alternative to conventional FEM and meshless methods in the solution of boundary value problems, having less dependency on mesh geometry than conventional FEM and lower computational cost than the main meshless methods as well as easier implementation of Dirichlet boundary conditions. In this context, this work aims to develop and apply a GFEM formulation for FGM plates, based on a Reissner-Mindlin’s first-order shear theory model for composite materials. Given the boundary conditions and base materials’ thermomechanical properties, this formulation uses Finite Difference Method to solve the stead-state heat conduction problem along the structure’s thickness and obtain the temperature field of the plate. Temperature dependence of thermal conductivities, elasticity moduli and thermal expansion coefficients is considered, and stiffness matrices and force vectors are computed via numerical integration along the plate’s thickness. The GFEM model considers a linear stress-strain relationship, using three-noded triangular elements and Shephard’s Partitions of Unit with smooth approximation functions enriched by linearly independent polynomials. Weak thermomechanical coupling is considered and the elastic problem’s solution is found applying Newton-Raphson’s method. As well as the formulation developed, this report shows its application in the solution of a plate-bending problem under thermal gradient and mechanical loading effects. A comparison between the numerical solution and an analytical first-order counterpart validates the method’s implementation, obtaining distributed relative errors based on a L_2-norm with order under 10^(-4)% for Mindlin's displacements.
Keywords
Functionally Graded Material, Composite Materials, Generalized Finite Element Method, Reissner-Mindlin’s model
