4.6 Article

A non-singular method of fundamental solutions for two-dimensional steady-state isotropic thermoelasticity problems

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 75, Issue -, Pages 89-102

Publisher

ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2016.11.010

Keywords

Isotropic thermoelasticity; Meshless method; Non-singular method of fundamental solutions; Collocation; Efficient desingularisation

Funding

  1. Slovenian Grant Agency (ARRS) - company IMPOL [L2-6775]
  2. Slovenian Grant Agency (ARRS) - company Store Steel [L2-6775]
  3. [P2-0379]

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We consider a boundary meshless numerical solution for two-dimensional linear static thermoelastic problems. The formulation of the problem is based on the approach of Marin and Karageorghis, where the Laplace equation for the temperature field is solved first, followed by a particular solution of the non-homogenous term in the Navier-Lame system for the displacement, the solution of the homogenous equilibrium equations, and finally the application of the superposition principle. The solution of the problem is based on the method of fundamental solutions (MFS) with source points on the boundary. This is, by complying with the Dirichlet boundary conditions, achieved by the replacement of the concentrated point sources with distributed sources over the disk around the singularity, and for complying with the Neumann boundary conditions by assuming a balance of the heat fluxes and the forces. The derived non-singular MFS is assessed by a comparison with analytical solutions and the MFS for problems that can include different materials in thermal and mechanical contact. The method is easy to code, accurate, efficient and represents a pioneering attempt to solve thermoelastic problems with a MFS-type method without an artificial boundary. The procedure makes it possible to solve a broad spectra of thermomechanical problems.

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