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Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

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Applied Mathematics and Mechanics(English Edition) 2015年第4期36卷 417-426页

作者： Bo YANG Weiqiu CHEN Hao jiang DING Department of Civil Engineering Zhejiang Sci-Tech University Department of Engineering Mechanics Zhejiang University Department of Civil Engineering Zhejiang University

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α（ζ）, β（ζ）, φ（ζ）, and ψ（ζ） when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func- tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional （3D） elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.

关键词： functionally graded plate elastic circular inclusion elasticity solution

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

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Applied Mathematics and Mechanics(English Edition) 2018年第10期39卷 1485-1498页

作者： Libiao XIN Yanbin LI Dongmei PAN Guansuo DUI Chengjian JU Shanxi Key Laboratory of Material Strength & Structural Impact College of MechanicsTaiyuan University of Technology National Demonstration Center for Experimental Mechanics Education College of Mechanics Taiyuan University of Technology Applied Mechanics of Materials Laboratory Department of Mechanical EngineeringTemple University Department of Civil and Environmental Engineering University of Houston Institute of Mechanics Beijing Jiaotong University

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material(FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

关键词： functionally graded material(FGM) thick-walled tube elasticity solution magnetic field perturbation of magnetic field vector

On asymmetric bending of functionally graded solid circular plates

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Applied Mathematics and Mechanics(English Edition) 2018年第6期39卷 767-782页

作者： Yingwu YANG Ying ZHANG Weiqiu CHEN Bo YANG Department of Civil Engineering Zhejiang Agriculture and Forestry University Department of Civil Engineering Zhejiang Sci-Tech University Department of Engineering Mechanics Yuquan CampusZhejiang University

Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.

关键词： functionally graded material circular plate transversely isotropic bihar-monic load elasticity solution