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

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 governi...

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Vydané v:Applied mathematical modelling Ročník 36; číslo 1; s. 488 - 503
Hlavní autori: Yang, B., Ding, H.J., Chen, W.Q.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 2012
Predmet:
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
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Shrnutí: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.
Bibliografia:ObjectType-Article-2
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ISSN:0307-904X
DOI:10.1016/j.apm.2011.07.020