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

• 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
• DOI: 10.1007/s00419-018-1407-5

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.