Elasticity solutions for functionally graded annular plates subject to biharmonic loads

• Published in: Archive of applied mechanics (1991) Vol. 84; no. 1; pp. 51 - 65
• Main Authors: Yang, B., Chen, W. Q., Ding, H. J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2014
• Subjects: Analytic functions; Annular plates; Boundary conditions; Classical Mechanics; Elasticity; Engineering; Functionally gradient materials; Mathematical analysis; Mathematical models; Original; Plate theory; Theoretical and Applied Mechanics; Annular plates; Elasticity solutions; Transversely isotropic; Biharmonic load; Functionally graded materials
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-013-0782-1

Based on England’s expansion formula for displacements, the elastic field in a transversely isotropic functionally graded annular plate subjected to biharmonic transverse forces on its top surface is investigated using the complex variables method. The material parameters are assumed to vary along the thickness direction in an arbitrary fashion. The problem is converted to determine the expressions of four analytic functions α ( ζ ), β ( ζ ), ϕ ( ζ ) and ψ ( ζ ) under certain boundary conditions. A series of simple and practical biharmonic loads are presented. The four analytic functions are constructed carefully in a biconnected annular region corresponding to the presented loads, which guarantee the single-valuedness of the mid-plane displacements of the plate. The unknown constants contained in the analytic functions can be determined from the boundary conditions that are similar to those in the plane elasticity as well as those in the classical plate theory. Numerical examples show that the material gradient index and boundary conditions have a significant influence on the elastic field.