Thermoelastic Body Research Articles

Coupled Flight Dynamics and Thermoelasticity Model of Maneuvering Aircraft

The stress and strain tensors in maneuvering aircraft are affected not only by the aerodynamic and propulsive forces but also by the body translational and angular velocities and high rate temperature distributions. The structural design of flexible aircraft requires the elastic fields to be evaluated at high accuracy. For this, new models that couple the aeroelasticity equations with the heat and translational and rotational equations of flight dynamics are essential. In this paper, the governing equations are derived by describing the motion of a thermoelastic body in an undeformed body frame by means of the variational principle applied to four invariants: the kinetic energy, the gravitational potential energy, the thermoelastic potential, and the dissipation function. Particular cases of longitudinal and lateral flight dynamics of a thermoelastic body including longitudinal flight of a thermoelastic beam are considered. Also, a discrete system for the translational and rotational velocities, the structural modes, and nodal temperature is derived. These equations may advance control design of hypersonic platforms, flexible aircraft, and missiles.

On Some Non-existence Results in a Semilinear Theory of the Dipolar Thermoelastic Bodies

We consider a thermoelastic theory in which the equations that govern the evolution are linear with respect to the thermal displacement and nonlinear with regards to gradients of displacements and temperature. Our results refer to the non-existence of solutions for some mixed problems, considered in this context. We also address the instability of solutions of the considered problems. We will treat separately the case where the mechanical effects are neglected, taking into account only the thermal effect. In this case our problem has a nonlinear structure.

Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

The Generalized Thermodynamical Beltrami – Michell Tensorial Equations for the general Thermodynamical State of the Hooke Body

موضوع البحث هو النموذج الرياضي التقليدي لجسم مرن متماثل المناحي ) Isotropic ( ومتجانس Homogeneous) (، وغير معتبر البنية الجزيئية ويخضع لانفعالات مرنة، لامتناهية في الصغر، وذلك في إطار المرونة الخطية الديناميكية، المترابطة مع حرارة، والمناقشة بدايةً من قبل الباحث هوك لأجل الحالة متساوية الحرارة، والذي يُرمز له اختصاراً بــالرمز (H). في البحث. في البداية سنعرض النموذج الرياضي التقليدي، التنسوري الصامد، ونموذج لامي الرياضي، التنسوري الصامد لجسم هوك المرن (H)، المتجانس، والمتماثل المناحي، في حالته الترموديناميكية التقليدية العامة. أما جديد البحث فهو مناقشة معادلات بيلترامي- ميشيل، التنسورية الصامدة، المعممة إلى الحالة الترموديناميكية )العامة( للجسم المرن (H). وبالنهاية تم اقتراح مسألة للمناقشة، إضافةً إلى مسألة مفتوحة.

Some Backward in Time Results for Thermoelastic Dipolar Structures

In our study we define the linear problem of backward in time for a thermoelastic body having a dipolar structure. In our first main result we prove the uniqueness of solution for this problem. Then, we approach the question of the impossibility to locate in time for the solution of this problem.

Compatibility Condition of Thermoelastic Body in Plane Strain State using Thermal Stress Analysis for the Concrete

Compatibility Condition of Thermoelastic Body in Plane Strain State using Thermal Stress Analysis for the Concrete

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Inverse design based on nonlinear thermoelastic material models applied to injection molding

This paper describes an inverse shape design method for thermoelastic bodies. With a known equilibrium shape as input, the focus of this paper is the determination of the corresponding initial shape of a body undergoing thermal expansion or contraction, as well as nonlinear elastic deformations. A distinguishing feature of the described method lies in its capability to approximately prescribe an initial heterogeneous temperature distribution as well as an initial stress field even though the initial shape is unknown. At the core of the method, there is a system of nonlinear partial differential equations. They are discretized and solved with the finite element method or isogeometric analysis. In order to better integrate the method with application-oriented simulations, an iterative procedure is described that allows fine-tuning of the results. The method was motivated by an inverse cavity design problem in injection molding applications. Its use in this field is specifically highlighted, but the general description is kept independent of the application to simplify its adaptation to a wider range of use cases.

On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.

Effect of a general body force on a 2D generalized thermoelastic body with a cylindrical cavity

We consider a 2D problem for an infinite body with a cylindrical cavity formed of a thermoelastic substance. The body is under the action of a nonsolenoidal body force. The theory used is that of Generalized Thermoelasticity. The surface is assumed to be traction free and subjected to an asymmetrical thermal shock. Laplace transform is used. The inversion process is carried out numerically. All the relevant functions are represented graphically.

Analysis of a Contact Problem Problem Involving an Elastic Body with Dual-Phase-Lag

In this work we study a contact problem between a thermoelastic body with dual-phase-lag and a deformable obstacle. The contact is modelled using a modification of the well-known normal compliance contact condition. An existence and uniqueness result is proved applying the Faedo–Galerkin method and Gronwall’s inequality. The exponential stability is also shown. Then, we introduce a fully discrete approximation by using the implicit Euler scheme and the finite element method. A discrete stability property and a priori error estimates are obtained, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some numerical examples are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.

Some estimates on solutions of mixed problems for mixtures

Our study is dedicated to a composite, which, in fact, is a mixture of two thermoelastic micropolar bodies. We formulate the mixed initial boundary value problem in this context and define the domain of influence for given data. For any solution of the mixed problem we associate a measure and prove a second-order differential inequality for it. Based on the maximum principle for the heat equation and on the second-order differential inequality, we establish an estimate which proves that the thermal and the mechanical effects, at large distance from the domain of influence, are dominated by an exponential decay.

A thermoelastic problem with diffusion, microtemperatures, and microconcentrations

In this paper, we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic body with diffusion, whose microelements are assumed to possess microtemperatures and microconcentrations. Using the linear theory, the mechanical problem is written as a coupled system of hyperbolic and parabolic partial differential equations for the displacement, temperature, chemical potential, microconcentrations, and microtemperatures fields. The variational formulation is derived, and it leads to a coupled system of parabolic linear variational equations, for which an existence and uniqueness result is stated. Then, using the finite element method and the implicit Euler scheme, fully discrete approximations are introduced. Stability properties and a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the accuracy of the approximation and the behaviour of the solution.

Optimal control of a thermoelastic body with missing initial conditions

ABSTRACT This paper aims to control the deformation and the temperature of a thermoelastic body by acting on him by an exterior force applied on a part of the body. In this case, all the initial data in the main model are missing values. The incomplete data in the considered model requires the use of the notion of no-regret control introduced by J. L. Lions for optimal control of distributed systems with missing data. An optimality system formed of coupled equations and adjoint coupled equations characterises the optimal pair (control state).

Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models

ABSTRACTIn this article an optimal sensor placement problem for a thermo-elastic solid body model is considered. Temperature sensors are placed in a near-optimal way so that their measurements allow an accurate prediction of the thermally induced displacement of a point of interest (POI). Low-dimensional approximations of the transient thermal field are used which allows for efficient calculations. Four model order reduction (MOR) methods are applied and subsequently compared with respect to the accuracy of the estimated POI displacement and the location of the sensors obtained.

Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model

PurposeThe purpose of this paper is to obtain a general solution to the field equations of generalized thermo-diffusion in an infinite thermoelastic body under the effect of gravity in the context of the dual-phase-lag (DPL) model. The half space is considered made of an isotropic homogeneous thermoelastic material. The boundary plane surface is heated by a non-Gaussian laser beam.Design/methodology/approachAn exact solution to the problem is obtained using the normal mode analysis.FindingsThe derived expressions are computed numerically for copper and the results are presented in graphical form.Originality/valueComparisons are made with the results predicted by Lord-Shulman theory and DPL model for different values of time and in the presence and absence of gravity as well as diffusion.

A time-dependent wave-thermoelastic solid interaction

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a generalization of the coupling procedure employed by the authors for the treatment of the time-dependent fluid-structure interaction problem. Using an integral representation of the solution in the infinite exterior domain occupied by the fluid, the problem is reduced to one defined only over the finite region occupied by the solid, with nonlocal boundary conditions. The nonlocal boundary problem is analyzed with Lubich's approach for time-dependent boundary integral equations. Existence and uniqueness results are established in terms of time-domain data with the aid of Laplace-domain techniques. Galerkin semi-discretization approximations are derived and error estimates are obtained. A full discretization based on the Convolution Quadrature method is also outlined. Some numerical experiments in 2D are also included in order to demonstrate the accuracy and efficiency of the procedure.

A dipolar structure in the heat-flux dependent thermoelasticity

Our study is concerned with the mixed initial-boundary value problem for a dipolar body in the context of a heat-flux dependent theory for the dipolar thermoelastic bodies. We take into account a set of independent constitutive variables including the heat flux vector. Also, the set of basic equations which govern the behavior of such a body is completed by including an equation of evolution for the components of this vector. The uniqueness result, regarding the solution of the mixed problem, which concludes our study assures the consistency of the constructed theory.

On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

Abstract A mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body by using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory of thermoelasticity which is a coupled system of the elastic wave and heat equations. A new version of the enclosure method in the time domain which is originally developed for the classical wave equation is established. For a comparison, the results in the decoupled case are also given.

On a theory of thermoelasticity without energy dissipation for solids with microtemperatures

AbstractIn the first part of this paper we present a strain gradient theory of thermoelastic bodies with microtemperatures which permits the transmission of heat as thermal waves at finite speed. The results are based on the Green‐Naghdi theory of thermomechanics of continua. The work is motivated by increasing use of materials which posses thermal variation at a microstructure level. In the second part of the paper we establish a uniqueness result and present some applications. We study the propagation of the time‐harmonic plane waves and investigate the effects of a concentrated heat source. A study of the discontinuities produced by a suddenly applied heat source is also presented.