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Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis

J. Sladek1, V. Sladek1, Ch. Zhang2, C.L. Tan3
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany
Department of Mechanical & Aerospace Engineering, Carleton University, Ottawa, Canada

Computer Modeling in Engineering & Sciences 2006, 16(1), 57-68. https://doi.org/10.3970/cmes.2006.016.057

Abstract

The Meshless Local Petrov-Galerkin (MLPG) method for linear transient coupled thermoelastic analysis is presented. Orthotropic material properties are considered here. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two-dimensional (2-D) problems. In transient coupled thermoelasticity an inertial term appears in the equations of motion. The second governing equation derived from the energy balance in coupled thermoelasticity has a diffusive character. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied to both of them. Local integral equations are written on small sub-domains with a circular shape. They surround nodal points which are distributed over the analyzed domain. The spatial variation of the displacements and temperature are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, a system of linear algebraic equations for unknown nodal values is obtained. The boundary conditions on the global boundary are satisfied by the collocation of the MLS-approximation expressions for the displacements and temperature at the boundary nodal points. The Stehfest's inversion method is then applied to obtain the final time-dependent solutions.

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Cite This Article

Sladek, J., Sladek, V., Zhang, C., Tan, C. (2006). Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis. CMES-Computer Modeling in Engineering & Sciences, 16(1), 57–68.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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