Abstract
A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.
Highlights
IntroductionGraded Materials (FGMs), a new type of composite material developed in recent years, are obtained by mixing two (such as metal and ceramic) or several materials in a certain volume ratio [1]
Graded Materials (FGMs), a new type of composite material developed in recent years, are obtained by mixing two or several materials in a certain volume ratio [1]
There are a number of research studies on the deformation of FG plates and shells based on different theories, including the classical laminated plate theory (CLPT), the first-order shear deformation plate theory (FSDT), the higher-order shear deformation plate theory (HSDT), and the three-dimensional elasticity theory
Summary
Graded Materials (FGMs), a new type of composite material developed in recent years, are obtained by mixing two (such as metal and ceramic) or several materials in a certain volume ratio [1]. Based on a novel integral first order shear deformation theory, Bousahla et al [7] studied buckling and vibrational behavior of the composite beam armed with single-walled carbon nanotubes resting on Winkler-Pasternak elastic foundation. Rahmani et al [9] investigated bending and free vibration behavior of elastically supported functionally graded sandwich plates with different boundary conditions by an original novel high order shear theory. By employing a new type of quasi-3D hyperbolic shear deformation theory, Kaddari et al [10] discussed statics and free vibration of functionally graded porous plates resting on elastic foundations, Zarga et al [11] analyzed thermomechanical bending of FGM sandwich plates, and Mahmoudi et al [12] studied the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate subjected to thermomechanical loading
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