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# Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis

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.

### Keywords

Transient coupled thermoelasticity, Orthotropic materials, Moving least-squares interpolation, 2-D problems, Laplace-transform, Stehfest's inversion

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.

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