Dynamic Coupled Thermoelasticity Problems Research Articles

Analysis of dynamic coupled thermoelasticity problems based on element differential method

As an exploratory study for the thermodynamic response in many engineering applications, numerical methods are a powerful technique to simulate the dynamic performance of thermoelasticity coupling problems based on the classic Fourier heat conductive law. Basically, the influence of coupling terms cannot be ignored for the dynamically coupling problem subjected to shock loadings. In order to deal with this complex type of coupling problem more conveniently, the element differential method (EDM) is developed for solving thermoelasticity problems. Since EDM does not use variational principles or virtual work principles to establish a solution format, it has higher flexibility in dealing with such complex coupling problems. This work establishes the dynamical scheme of the EDM for solving some 2D and 3D thermoelastic problems. In thermoelastic problems, an energy loss is caused by the coupling effect, leading to the changes in the temperature field and displacement field. And the shock loading caused the wave propagation. The examples under shock loading prove that EDM is accurate and efficient in solving dynamic coupled thermoelasticity problems.

A boundary meshless method for dynamic coupled thermoelasticity problems

This work develops the boundary knot method (BKM) for two-dimensional (2D) coupled thermoelasticity problems in the frequency domain. By taking the non-singular general solution satisfying the governing equations as the basis function, the BKM does not require domain discretization. Nevertheless, the non-singular solution for the considered problems is absent. The Helmholtz decomposition and eigen-analysis are introduced to firstly derive the non-singular general solution, and thus the BKM can be formulated in terms of the discretized boundary points. In the final, the exponential window method (EWM) in conjunction with the BKM is employed to perform the transient analysis. The accuracy and feasibility of the proposed method are presented via numerical examples.

A novel space–time generalized FDM for dynamic coupled thermoelasticity problems in heterogeneous plates

A novel space–time generalized FDM for dynamic coupled thermoelasticity problems in heterogeneous plates

The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems

In this study, a new framework for the efficient and accurate solutions of three-dimensional (3D) dynamic coupled thermoelasticity problems is presented. In our computations, the Krylov deferred correction (KDC) method, a pseudo-spectral type collocation technique, is introduced to perform the large-scale and long-time temporal simulations. The generalized finite difference method (GFDM), a relatively new meshless method, is then adopted to solve the resulting boundary-value problems. The GFDM uses the Taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables. The method, thus, is truly meshless that can be applied for solving problems merely defined over irregular clouds of points. For problem with complicated geometries, this paper also examines a new distance criterion for adaptive selection of nodes in the GFDM simulations. Preliminary numerical experiments show that the KDC accelerated GFDM methods are very promising for accurate and efficient long-time and large-scale dynamic simulations.

Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.

A novel meshless local Petrov–Galerkin method for dynamic coupled thermoelasticity analysis under thermal and mechanical shock loading

A meshless local Petrov–Galerkin method (MLPG) based on the moving Kriging interpolation is further developed for two-dimensional linear dynamic coupled thermoelasticity problems under thermal and mechanical shock loading. In this method the moving Kriging interpolation is employed to construct the shape functions, and the Heaviside step function is applied in the local weak-form as the test functions. The equations of motion and transient heat conduction equations of the coupled thermoelasticity interact on each other. So these equations must be solved simultaneously. In this paper the backward difference method is applied to approximate the time derivatives. The main idea of treating the time-dependent problem is based on the reduction procedure of the equations of motion, in which the displacements, velocities and temperature are taken as the field variables. Then a unified explicit expression of the system of differential algebraic equations is obtained. Numerical examples are presented to illustrate the accuracy of this method.

NUMERICAL SOLUTION OF 1D AND 2D THERMOELASTIC COUPLED PROBLEMS

Study the heats propagation in a solid, liquid continuums is an actual problems. The liquid continuum may be considered as a biomaterial. The present investigation is devoted to the study of 1D and 2D dynamic coupled thermo elasticity problems. In case of coupled problems the motion and heat conduction equations are considered together. For numerical solution of thermo elasticity problems an explicit and implicit schemes are constructed. The explicit and implicit schemes by using recurrent formulas and the "consecutive" methods are solved. Comparison of two results shows a good coincidence.

Closed-form solutions of dynamic coupled thermoelasticity problems for a cylinder and a sphere

Closed-form solutions of dynamic coupled thermoelasticity problems for a cylinder and a sphere

Boundary element analysis of stress intensity factor KI in some two-dimensional dynamic thermoelastic problems

This paper presents a numerical technique for the calculation of stress intensity factor as a function of time for coupled thermoelastic problems. In this task, effect of inertia term considering coupled theory of thermoelasticity is investigated and its importance is shown. A boundary element method using Laplace transform in time-domain is developed for the analysis of fracture mechanic considering dynamic coupled thermoelasticity problems in two-dimensional finite domain. The Laplace transform method is applied to the time-domain and the resulting equations in the transformed field are discretized using boundary element method. Actual physical quantities in time-domain is obtained, using the numerical inversion of the Laplace transform method. The singular behavior of the temperature and stress fields in the vicinity of the crack tip is modeled by quarter-point elements. Thermal dynamic stress intensity factor for mode I is evaluated using J-integral method. By using J-integral method effects of inertia term and other terms such as strain energy on stress intensity factor may be investigated separately and their importance may be shown. The accuracy of the method is investigated through comparison of the results with the available data in literature.

IMPORTANCE OF INERTIA TERM IN DYNAMIC CRACK PROBLEMS CONSIDERING LORD–SHULMAN THEORY OF THERMOELASTICITY

A numerical technique is presented for the accurate calculation of stress intensity factors as a function of time for generalized coupled thermoelastic problems. In this task, the effect of the inertia term is investigated, considering different theories of thermoelasticity, and its importance is shown. A boundary element method using the Laplace transform in time domain is developed for the analysis of fracture mechanics; dynamic coupled thermoelasticity problems with relaxation time are considered in the two-dimensional finite domain. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. Actual physical quantities in the time domain are obtained using the numerical inversion of the Laplace transform method. The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. The thermal dynamic stress intensity factor for mode I is evaluated using the J-integral method. The accuracy of the method is investigated through comparison of the results with the data available in literature. The J integral, which represents the dynamic energy release rate for propagating cracks, contains a boundary integral and a domain integral. The boundary integral contains strain energy, tractions, and strains whereas the domain integral contains inertia and strains. The J-integral method allows these two terms to be calculated separately. In this way, the importance of each term may be investigated by considering different theories of dynamic thermoelasticity.

Boundary element analysis of dynamic coupled thermoelasticity problems

Some possibility of numerical analysis of coupled dynamic problems of linear elastic heat conductors on classical thermoelasticity theory by using the boundary element method is shown in this paper. The boundary integral equation formulation and its numerical implementation of the two-dimensional problem are developed in the manner by the newly derived fundamental solution for the coupled equations of elliptic type in the transformed space and the numerical inversion of Laplace transformation. The boundary element unsteady solutions of the first and second Danilovskaya problems and the Sternberg and Chakravorty problem in the half-space are demonstrated through comparison with the existing solutions.

Finite Element Analysis of Dynamic Coupled Thermoelasticity Problems With Relaxation Times

A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.