Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported

• Published in: Applied mathematical modelling Vol. 36; no. 1; pp. 488 - 503
• Main Authors: Yang, B., Ding, H.J., Chen, W.Q.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 2012
• Subjects: Biharmonic load; Boundary conditions; Complex variables; Elasticity; Elasticity solutions; England’s method; Functionally graded materials; Functionally gradient materials; Mathematical analysis; Mathematical models; Plates; Rectangular plates; Transversely isotropic; Rectangular plates; Elasticity solutions; Transversely isotropic; Biharmonic load; Functionally graded materials; England’s method
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2011.07.020

England (2006) [13] proposed a novel method to study the bending of isotropic functionally graded plates subject to transverse biharmonic loads. His method is extended here to functionally graded plates with materials characterizing transverse isotropy. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solution may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory. The elasticity solutions of an FGM rectangular plate with opposite edges simply supported under 12 types of biharmonic polynomial loads are derived as appropriate sums of the general and particular solutions of the governing equations. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity, and thickness to length ratio on the plate deflection and stresses for the load x 2 yq are studied numerically.