Vol. 11, No. 1, 2016

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

Anita Uściłowska and Agnieszka Fraska

Vol. 11 (2016), No. 1, 61–77

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.

homotopy analysis method, mesh-free methods, method of fundamental solutions, functionally graded materials, orthotropic symmetry, torsion of a prismatic bar
Received: 20 December 2014
Revised: 27 August 2015
Accepted: 11 October 2015
Published: 13 January 2016
Anita Uściłowska
Institute of Materials Technology
Poznan University of Technology
ul. Piotrowo 3
60-965 Poznań
Agnieszka Fraska
Institute of Applied Mechanics
Poznan University of Technology
ul. Jana Pawła II 24
60-695 Poznań