Modelling of Generalised Thermoelastic Wave Propagation of Multilayer Material under Thermal Shock Behaviour

Abstract

This paper describes a time-discontinuous Galerkin finite element method (DGFEM-) for the generalised thermoelastic problem of multilayer materials subjected to a transient high-frequency heat source. The governing and constitutive relations are presented on the basis of the well-known Lord-Shulman (L-S) theory. A DGFEM-method is developed to allow the general temperaturedisplacement vector and its temporal gradient to be discontinuous at a fixed time . A stiffness proportional artificial damping term is added to the final DG discretisation form to filter out the spurious numerical oscillations in the wave-after stage and at adjacentlayer interfaces. The numerical results show that the present DGFEM-provides much more accurate solutions for generalised thermoelastic coupled behaviour of multilayer structures. Compared with widely used traditional numerical methods (e.g., the Newmark method), the present DGFEM-can effectively capture the discontinuities behaviours of impulsive waves in space in the simulation of high modes and sharp gradients.

A Time-Discontinuous Galerkin Finite Element Method for the Solution of Impact Problem of Gas-Saturated Coal

“…e main features of the discontinuous Galerkin integration method in time domain have been described in our previous articles [13,15]. Different from the continuous Galerkin method, the DGFEM permits the discontinuity of functions at discrete-time sequence, 0…”

“…It should be noted that the global nodal displacement vector of solid and fluid is continuous at any time level and the global nodal velocity vector is still discontinuous at any time level [10][11][12][13][14][15]. To demonstrate the advantage of the present DGFEM, we have to solve several problems in our previous work [10][11][12][13][14][15]. For the elastic-plastic dynamic problems, the Newton-Raphson process is used [10,14].…”

“…When simulating problems of structure dynamics and wave propagation under impulse load, the modified time-continuous Galerkin finite element method shows better ability to filter out the effects of spurious numerical oscillations. Having demonstrated the applicability and advantage of the MDGFEM as indicated in our articles [13][14][15], we apply and discuss the method to solve the problem of gas-saturated coal based on Biot's model subjected to impulse load.…”

“…From equation 27, we can see that the value of stiffness proportional damping constant β is complex to calculate. As discussed in our articles [13][14][15], the value should be less than or equal to the time step. Using the stiffness proportional artificial damping matrix equation 27, (25) can be written in matrix form as…”