Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk

By X. Y. Li, H. Ding, Wenteng Chen. 2008

113 citations recorded by the source corpus.

Abstract This paper considers the bending of transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate, subject to a transverse load in the form of qr k ( k is zero or a finite even number). The differential equations satisfied by stress functions for the particular problem are derived. An elaborate analysis procedure is then presented to derive these stress functions, from which the analytical expressions for the axial force, bending moment and displacements are obtained through integration. The method is then applied to the problem of transversely isotropic functionally graded circular plate subject to a uniform load, illustrating the procedure to determine the integral constants from the boundary conditions. Analytical elasticity solutions are presented for simply-supported and clamped plates, and, when degenerated, they coincide with the available solutions for an isotropic homogenous plate. Two numerical examples are finally presented to show the effect of material inhomogeneity on the elastic field in FGM plates.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2841918eb9a019347f77435a95d7f42d7a804d46

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates (2011, methodology): “A method of solution for stresses and displacements within a transversely isotropic functionally graded circular plate, whose elastic constants are arbitrary functions of the thickness coordinate, was described by Li et al. (2008).”
Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported (2012, background): “[8] obtained elasticity solutions for transversely isotropic FGM circular plates subject to a load in form of qr (k is zero or a finite even integer).”
Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates (2014, methodology): “A good agreement with HSDT based IGA [15], elasticity solutions [36] and semi-analytical”
Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review (2015, methodology): “[12] used the same approach to derive a set of solutions for the axisymmetric problem”