Thermoelastic coupling problems caused by thermal contact resistance:A discontinuous Galerkin finite element approach

A discontinuous Galerkin (DG) finite element method is presented to solve the thermoelastic coupling problems caused by temperature and pressure dependent thermal contact resistance (TCR).The whole analysis is made up of two parts,thermal and mechanical analysis.In thermal analysis,the DG method is employed to simulate the temperature jump phenomenon,which satisfies the imperfect thermal contact condition in a straightforward manner.In mechanical analysis,the impenetrability condition is fulfilled through a DG approach with penalty functions.The Picard iteration procedure with a relaxation technique is also adopted to accelerate the rate of convergence and avoid numerical instability.Numerical examples show that the present method is an attractive approach for solving thermoelastic coupling problems caused by TCR.The methodology can also be expanded to solve problems with friction finite deformation contact,node-to-segment contact and node-to-surface contact,etc.in a straightforward manner.

DYNAMIC RESPONSE OF TWO-DIMENSIONAL GENERALIZED THERMOELASTIC COUPLING PROBLEM SUBJECTED TO A MOVING HEAT SOURCE

Based on the Lord and Shulman generalized thermoelasticity theory with one relaxation time, an isotropic semi-infinite plate subjected to a moving heat source has been studied by employing the finite element method directly in time domain, whose distributions of nora dimensional temperature, displacement and stress are illustrated graphically. The results show that the present method is an effective and exact numerical one for solving the thermoelastic coupling problem and is capable of overcoming the defects of traditional integrated transformation and inverse integrated transformation methods. At the same time, the temperature step of the thermal wave front is obtained exactly in contrast with conventional numerical transformation methods.

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model.This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic,composite and sandwich structures.Cylindrical and spherical panels,cylinders and plates are analyzed in orthogonal mixed curved reference coordinates.The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels.The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate.The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature.The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses.As a consequence,the sovra-temperature description is assumed to be an unknown variable of themodel and it is calculated in the sameway as the three displacements.The final systemis based on a set of coupled homogeneous differential relations of second order in the thickness coordinate.This system is reduced in a first order differential relation system by redoubling the number of unknowns.Therefore,the exponential matrix methodology is applied to calculate the solution.The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components.After an appropriate preliminary validation,new benchmarks are discussed for several thickness ratios,geometrical data,lamination sequences,materials and sovra-temperature values imposed at the outer faces.Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation.Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.

GENERAL SOLUTIONS OF COUPLED THERMOELASTIC PROBLEM

A new type of general solution of thermoelasticity is derived from the linearized basic equations for coupled thermoelastic problem. In the case of quasi-static problem, the present general solution is simpler since it involves one less potential function than Blot's solution.

MD simulation of a copper rod under thermal shock

In this paper, thermoelastic problem of onedimensional copper rod under thermal shock is simulated using molecular dynamics method by adopting embedded atom method potential. The rod is on axis x, the left outermost surface of which is traction free and the right outermost surface is fixed. Free boundary condition is imposed on the outermost surfaces in direction y and z. The left and right ends of the rod are subjected to hot and cold baths, respectively. Temperature, displacement and stress distributions are obtained along the rod at different moments, which are shown to be limited in the mobile region, indicating that the heat propagation speed is limited rather than infinite. This is consistent with the prediction given by generalized thermoelastic theory. From simulation results we find that the speed of heat conduction is the same as the speed of thermal stress wave. In the present paper, the simulations are conducted using the large-scale atomic/molecular massively parallel simulator and completed visualization software.

Coupled thermoelastic theory and associated variational principles based on decomposition of internal energy

A new framework of coupled thermoelasticity is constructed in this paper based on a decomposition of internal energy into free internal energy and dissipative energy.Fundamental equations(i.e.divergence and gradient equations,constitutive equations including evolving laws)along with proper boundary conditions are all included in this framework,from which two novel dual-complementary variational principles with explicit functionals are proposed.Unlike the conventional thermoelastic theory,the proposed variational principles for thermoelasticity are established without the approximate assumption of small temperature changes.To verify the usefulness of the proposed variational principles in simulating coupled thermoelastic problems,a coupled thermoelastic example is numerically implemented.