3D elasticity solution for uniformly loaded elliptical plates of functionally graded materials using complex variables method

Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The e...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) Vol. 88; no. 10; pp. 1829 - 1841
Main Authors: Yang, Y. W., Zhang, Y., Chen, W. Q., Yang, B., Yang, Q. Q.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2018
Springer Nature B.V
Subjects:
Analytic functions
Boundary conditions
Classical Mechanics
Complex variables
Deformation effects
Elasticity
Elliptical plates
Engineering
Functionally gradient materials
Material properties
Original
Theoretical and Applied Mechanics
Elasticity solutions
Elliptical plates
Functionally graded materials
Complex variables method
ISSN:0939-1533, 1432-0681
Online Access:Get full text
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Summary:Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The expressions of the mid-plane displacements of the plate are constructed to meet the clamped boundary conditions in which the unknown constants are determined from the governing equations. The expressions of four analytic functions α ( ζ ) , β ( ζ ) , ϕ ( ζ ) and ψ ( ζ ) corresponding to this problem are then obtained using the complex variables method. As a result, the three-dimensional elasticity solution of a functionally graded elliptical plate with clamped boundary subject to uniform load is derived. Finally, numerical examples are presented to verify the proposed method and discuss the effects of different factors on the deformation and stresses in the plate.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-018-1407-5