MESHLESS METHOD BASED ON INTERPOLATING MOVING LEAST SQUARE SHAPE FUNCTIONS FOR DYNAMIC COUPLED THERMOELASTICITY ANALYSIS

The two-dimensional structural dynamic coupled thermoelastic problem is solved by meshless local Petrov-Galerkin (MLPG) method based on the interpolating moving least-squares (IMLS) method. The local weak forms are developed using the weighted residual method from the modified Fourier heat conduction equations and elastodynamic equations, in which the Heaviside step function is used as the test function in each sub-domain. Then the second-order ordinary differential equations describing the coupled thermoelasticity problem are obtained. Using the differential algebraic method, these second-order ordinary differential equations can be transformed into ordinary differential algebraic systems, in which temperature and displacement are chosen as auxiliary variables. The Newmark step-integration method is used to solve the ordinary differential system. The temperature and displacement numerical results can be obtained directly without the Laplace transform. Since the shape functions constructed from the IMLS method possess the Kronecker delta property, the essential boundary conditions can be implemented directly. Finally, two numerical examples are studied to illustrate the effectiveness of this method.