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Non-Singular Method of Fundamental Solutions for Two-dimensional Thermoelasticity
Božidar Šarle, liu qingguo, published scientific conference contribution abstract

Abstract: A framework for simulation of thermomechanical processing of microstructures by the method of fundamental solutions, free of artificial boundary, is shown. The formulation of the method for two-dimensional thermal and mechanical models is presented. In particular, the formulation for thermo-elastic problems is discussed. In the thermal and mechanical models, the concentrated point sources are replaced by the distributed sources over the sphere around the singularity to regularize the singularities and the balance of forces is used to calculate some of the otherwise singular diagonal coefficients. This procedure enables also for solving problems with internal voids and inclusions. The novel boundary meshless method has been assessed by comparison with MFS and analytical solution. The method is easy to code, accurate, and efficient.
Found in: osebi
Keywords: thermomechanics, elasticity, plasticity, non-singular method of fundamental solutions, three-dimensions, microstructures
Published: 28.06.2016; Views: 2984; Downloads: 0
.pdf Fulltext (239,40 KB)

A non-singular method of fundamental solutions for two-dimensional steady-state isotropic thermoelasticity problems
qingguo liu, Božidar Šarler, 2017, original scientific article

Abstract: 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-Lamé 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.
Found in: osebi
Keywords: Keywords: Isotropic thermoelasticity Meshless method Non-singular method of fundamental solutions Collocation Efficient desingularisation
Published: 23.12.2016; Views: 2742; Downloads: 0
.pdf Fulltext (2,54 MB)

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