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# An RMVT-Based Finite Rectangular Prism Method for the 3D Analysis of Sandwich FGM Plates with Various Boundary Conditions

Chih-Ping Wu1,2, Hao-Yuan Li1

Department of Civil Engineering, National Cheng Kung University, Tainan 70101, Taiwan, ROC
Corresponding author. E-mail: cpwu@mail.ncku.edu.tw

Computers, Materials & Continua 2013, 34(1), 27-62. https://doi.org/10.3970/cmc.2013.034.027

## Abstract

A Reissner's mixed variational theorem (RMVT)-based finite rectangular prism method (FRPM) is developed for the three-dimensional (3D) analysis of sandwich functionally graded material (FGM) plates subjected to mechanical loads, in which the edge conditions of the plates are such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The sandwich FGM plate considered consists of two thin and stiff homogeneous material face sheets combined with an embedded thick and soft FGM core, the material properties of which are assumed to obey the powerlaw distributions of the volume fractions of the constituents. In this formulation, the plate is divided into a number of finite rectangular prisms, in which the trigonometric functions and Lagrange polynomials are used to interpolate the y-direction and x-ζ plane variations of the primary field variables of each individual prism, respectively. Because an h-refinement process is adopted to yield the convergent solutions in this analysis, the prism-wise either linear or quadratic function distribution through the x-ζ plane is assumed for the related field variables. A unified formulation of these FRPMs with freely-chosen orders for assorted field variables is presented. It is shown that these quadratic FRPM solutions of simply supported, multilayered composite plates and sandwich FGM ones are in excellent agreement with the exact 3D solutions available in the literature, and those of multilayered composite plates with various boundary conditions closely agree with the solutions obtained using the ANSYS commercial software.

## Keywords

APA Style
Wu, C., Li, H. (2013). An rmvt-based finite rectangular prism method for the 3D analysis of sandwich FGM plates with various boundary conditions. Computers, Materials & Continua, 34(1), 27-62. https://doi.org/10.3970/cmc.2013.034.027
Vancouver Style
Wu C, Li H. An rmvt-based finite rectangular prism method for the 3D analysis of sandwich FGM plates with various boundary conditions. Comput Mater Contin. 2013;34(1):27-62 https://doi.org/10.3970/cmc.2013.034.027
IEEE Style
C. Wu and H. Li, "An RMVT-Based Finite Rectangular Prism Method for the 3D Analysis of Sandwich FGM Plates with Various Boundary Conditions," Comput. Mater. Contin., vol. 34, no. 1, pp. 27-62. 2013. https://doi.org/10.3970/cmc.2013.034.027

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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