Analytic Solution to Isotropic Axisymmetric Cylinder Under Surface Loadings Problem Through Variational Principle

Abstract Analysis of cylinders under axisymmetric loading is of great interest as it finds many practical application. In this work an attempt has been made to solve this problem through variational principle. The variational statement results in a set of coupled partial governing equation and associated boundary conditions. The solution has been derived after systematic decoupling of governing equation, application of separation of variables and use of Frobenius method. The resulting solution as demonstrated is capable of satisfying all the boundary conditions in an exact sense. The accuracy and efficiency of the presented solution have been validated for problems available in the literature and against three dimensional finite element simulations for isotropic homogeneous material. It is observed that the present solution not only has excellent agreement with three dimensional finite element analysis but also is generic in nature.