3D elasticity solutions for stress field analysis of FGM circular plates subject to concentrated edge forces and couples

Abstract

In this paper, the complex variable method is applied to study three-dimensional problems of transversely isotropic functionally graded circular plates subjected to concentrated edge forces and couples. To that end, the extended England–Spencer plate theory is adopted to obtain the general solutions of the governing equations in which four analytic functions $$\alpha (\zeta )$$ , $$\beta (\zeta )$$ , $$\phi (\zeta )$$ and $$\psi (\zeta )$$ are involved. The material properties can vary along the thickness direction in an arbitrary fashion. The cylindrical boundary of the plate is considered to be free which is well known as the first kind basic problem in plane elasticity. Four analytic functions can be determined by the Cauchy’s integral formula and conformal mapping technology. As a result, the 3D stress field is investigated for a transversely isotropic FGM circular plate whose cylindrical boundary is subjected to concentrated forces and couples. The proposed elasticity solutions can be used as benchmarks to validate solutions obtained based on various simplified plate theories or numerical methods.