Bending analysis of functionally graded rectangular plates using the dual mesh control domain method

Abstract

The dual mesh control domain method (DMCDM) introduced by Reddy employs one mesh for the approximation of the primary variables (primal mesh) and another mesh for the satisfaction of the governing equations (dual mesh). The present study deals with the extension and application of the DMCDM to functionally graded rectangular plates. The formulation makes use of the traditional finite element interpolation of the primary variables with a primal mesh and a dual mesh to satisfy the integral form of the governing differential equations, the basic premise of the finite volume method. The method is used to analyze bending of through-thickness functionally graded rectangular plates using the first-order shear deformation plate theory. Numerical results are presented to illustrate the methodology, and a comparison of the displacements and stresses computed using the DMCDM with those of the finite element model shows excellent agreement while requiring less formulative (and possibly computational) effort. The influence of the extensional-bending coupling stiffness (due to the through-thickness grading of the material) on the deflections is also brought out.

Keywords:

• Dual mesh control domain method
• first-order shear deformation theory
• functionally graded materials
• numerical results

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research reported herein was supported, in parts, by O’Donnell Foundation Chair IV, Technical Data Analysis (TDA), and the NSF Grant (FAIN) 1952873.