TY - EJOU
AU - Sladek, J.
AU - Sladek, V.
AU - Solek, P.
AU - Tan, C.L.
AU - Zhang, Ch.
TI - Two- and Three-Dimensional Transient Thermoelastic Analysis by the MLPG Method
T2 - Computer Modeling in Engineering \& Sciences
PY - 2009
VL - 47
IS - 1
SN - 1526-1506
AB - The meshless local Petrov-Galerkin (MLPG) method for transient linear thermoelastic analysis is presented. Orthotropic material properties are considered here. In uncoupled thermoelasticity, the temperature field is not influenced by displacements. Therefore, in the first step, the heat conduction equation is solved for the temperature distribution in the domain. The equations of motion are then solved with the inertial term considered. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two- and three-dimensional problems. Local integral equations are written on small sub-domains with circular or spherical shapes. 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 ordinary differential equations for certain nodal unknowns is obtained. The backward finite difference method is applied for the approximation of the diffusive term in the heat conduction equation. Then, the system of the ordinary differential equations of the second order resulting from the equations of motion is solved by the Houbolt finite-difference scheme as a time stepping method.
KW - Transient thermoelasticity
KW - orthotropic materials
KW - moving least-squares interpolation
KW - Houbolt finite-difference scheme
KW - crack problems
KW - functionally graded materials
DO - 10.3970/cmes.2009.047.061