Approximate elasticity solutions for functionally graded circular plates subject to a concentrated force at the center

The axisymmetric bending of a functionally graded circular plate, which is subjected to a concentrated transverse force at the center, is investigated based on a generalization of England’s method. The complex variable function method adopted in this paper involves four analytic functions of the complex variable, in which the unknown constants can be determined from cylindrical boundary conditions, similar to that in classical plate theory. The axisymmetric bending problem of a functionally graded circular plate concentrically loaded at the center can be converted into a bending problem of a functionally graded annular plate subject to shear forces uniformly distributed over the inner boundary. The elasticity solutions of a transversely isotropic and functionally graded circular plate subject to a concentrated force at the center are then derived, from which elasticity solutions for a transversely isotropic (or isotropic) and homogeneous circular plate can be obtained from the analysis as a special case. Finally, numerical examples are presented to compare the proposed analytical solutions with those of a finite-element method. The results show that the proposed elasticity solutions are very simple and usable.