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Implementation of
HAM and meshless method for torsion of functionally graded
orthotropic bars
Anita Uściłowska and Agnieszka Fraska |
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Vol. 11 (2016), No. 1, 61–77
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Abstract |
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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. |
Keywords
homotopy analysis method, mesh-free methods, method of
fundamental solutions, functionally graded materials,
orthotropic symmetry, torsion of a prismatic bar
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Milestones
Received: 20 December 2014
Revised: 27 August 2015
Accepted: 11 October 2015
Published: 13 January 2016
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Authors |
| Anita Uściłowska | |
| Institute of Materials
Technology Poznan University of Technology ul. Piotrowo 3 60-965 Poznań Poland |
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| Agnieszka Fraska | |
| Institute of Applied Mechanics Poznan University of Technology ul. Jana Pawła II 24 60-695 Poznań Poland |
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