Analysis of Two- and Three-dimensional Steady-state Thermo-mechanical Problems Including Curved Line/Surface Heat Sources Using the Method of Fundamental Solutions
Keywords:Method of fundamental solutions, Curved line heat source, Curved surface heat source, Thermo-mechanical, Meshfree.
In this work, the method of fundamental solutions (MFS) and the method of particular solutions (MPS) are used to solve two and three dimensional steady-state thermoelastic problems involving curved-shape heat sources. The geometrical shape of the heat sources can be very complicated. Each curved heat source is modelled by assembling several simple sources with quadratic shapes. The particular solutions for temperature and stress are presented in simple forms and they are used without considering any internal points or internal cells. Several examples are analysed to demonstrate the efficiency of the presented formulation. Numerical results show that the presented MFSMPSformulation is very efficient and useful. Unlike the finite element method, only a small number of collocation and source points are sufficient to achieve accurate results in the proposed MFS formulation.
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