Implementation of HAM and meshless method for torsion of functionally graded orthotropic bars

The aim of this study is implementation of the Homotopy Analysis Method (HAM) and the Method of Fundamental Solution (MFS) for solving a torsion problem of functionally graded orthotropic bars.The boundary value problem is formulated for the Prandtl's stress function, described by partial differential equation of second order with variable coefficients and appropriate boundary conditions.In the solving process the HAM is used to convert nonlinear equation into a linear one with known fundamental solutions.The Method of Fundamental Solutions supported by Radial Basis Functions and Monomials is suggested for calculate this linear boundary value problem.The numerical experiment has been performed to check the accuracy and the convergence of the presented method.