Abstract
The dual mesh finite domain method (DMFDM) 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 DMFDM to functionally graded circular plates under axisymmetric conditions. 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 axisymmetric bending of through-thickness functionally graded circular plates using the classical plate theory (CPT) and first-order shear deformation plate theory (FST). The displacement model of the FST and the mixed model of the CPT using the DMFDM are developed along with the displacement and mixed finite element models. Numerical results are presented to illustrate the methodology and a comparison of the generalized displacements and bending moments computed with those of the corresponding finite element models. The influence of the extensional-bending coupling stiffness (due to the through-thickness grading of the material) on the deflections is also brought out.
Highlights
1.1 Functionally graded structuresStructures whose material properties are continuously varied in one or more coordinate directions are abundant in nature
The governing equations of functionally graded (FG) axisymmetric circular plate based on classical plate theory in terms of {uu, ww, MMrrrr} would be given by Eq (2.9), Eq (2.17) and Eq (3.5); wherein the expressions for NNrrrr, NNθθθθ and MMθθθθ are obtained from Eqs. (3.1), (3.4) and (3.3) respectively
To illustrate the workings of the dual mesh finite domain models presented in the previous sections, we consider two cases: (a) hinged and (b) clamped functionally graded circular plates, subjected to uniformly distributed load of intensity qq
Summary
Structures whose material properties are continuously varied in one or more coordinate directions are abundant in nature (e.g., sea shells, bones, etc). With increasing demand for novel materials whose properties can be tailored to suit a particular application, such natural structures provided an inspiration for the design and development of an advanced class of composite materials called functionally graded materials (FGMs) (see, e.g., [1,2]). This is usually done by providing in-depth graded compositions, microstructure and properties [3]. The variation in material properties of FGM can be expressed by a thickness function describing the spatial variation of volume fractions of FGM constituents Various such functions are proposed in the literature (see, e.g., [5] for a review).
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