Elasticity solutions for a uniformly loaded rectangular plate of functionally graded materials with two opposite edges simply supported

• Published in: Acta mechanica Vol. 207; no. 3-4; pp. 245 - 258
• Main Authors: Yang, B., Ding, H. J., Chen, W. Q.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.10.2009; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Control; Dynamical Systems; Elasticity; Engineering; Engineering Thermodynamics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mathematics; Mechanical engineering; Physics; Solid Mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Theoretical and Applied Mechanics; Theory; Vibration; Opposite Edge; Elasticity Solution; Annular Plate; Uniform Load; Rectangular Plate; Uniform load; Functionnally graded material; Tridimensional elasticity; Transverse isotropy; Rectangular plate; Simple support; Modeling; Exact solution
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-008-0122-7

While the expansion formula for displacements and the hypothesis that the material parameters can vary along the thickness direction in an arbitrary fashion are retained, the plate theory of functionally graded materials suggested by Mian and Spencer is extended in this paper in two aspects. First, the material is assumed to be transversely isotropic, rather than isotropic. Second, the tractions-free conditions on the top and bottom surfaces are replaced by the conditions of uniform loads applied on the surfaces. The governing equations are derived rigorously, which are expressed in terms of three components of the mid-plane displacement. The mid-plane deflection satisfies a fourth-order partial differential equation, which is similar to that in the classical plate theory (CPT). The two in-plane displacements satisfy two second-order partial differential equations and are coupled with the mid-plane deflection. Boundary conditions are expressed in the form of those adopted in the CPT. Three-dimensional elasticity solutions are presented for a uniformly loaded rectangular plate with two opposite edges simply supported and six different types of supports at the other two edges. Numerical results are given for a simply supported functionally graded plate, and good agreement with exact solutions is obtained.