基于分数阶热弹性理论的含有球型空腔无限大体的热冲击动态响应

基于新近提出的分数阶广义热弹性理论,研究了含有球型空腔的无限大体受热冲击作用时的动态响应。该文给出分数阶广义热弹性理论下的控制方程,通过拉普拉斯积分变换及其数值反变换对控制方程进行了求解,得到了带有球型空腔无限大体中的无量纲温度、位移、径向应力和环向应力等物理量的分布规律。计算中重点研究了分数阶参数对各物理量的影响效应。结果表明:含有球腔的无限大体内由于热冲击而出现了热弹耦合效应;分数阶参数显著地影响各物理量的分布规律。     

超急速传热过程中热弹性响应的解析分析

考虑超急速传热过程中诱发的热冲击效应,基于L-S广义热弹性理论,建立了温度突变加热条件下热弹性响应的控制方程组。借助于Laplace正逆变换,在适当简化的条件下推导了一维超急速传热问题热弹性响应的解析表达式。通过对温度场、位移场及应力场的解析求解,给出了超急速传热过程中热波和热弹性波在弹性体内的传递规律,并指出在超急速传热条件下,由于热波和热弹性波的相互叠加作用削弱了热作用产生的热冲击效应。     

Two-dimensional problem for a half-space with axi-symmetric distribution in the theory of generalized thermoelastic diffusion

In this work, we study a two-dimensional problem of axi-symmetric distribution of temperatures in a half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The surface of the half-space is taken as traction free and subjected to axi-symmetric time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. The Laplace and Hankel transform techniques are used. The analytical solution in the transform domain is obtained by using a direct approach. The inverse of the double transform is obtained by using a numerical method based on Fourier expansion techniques. Numerical results for the temperature, displacement, stress, concentration, and chemical potential are carried out and represented graphically.     

Fractional Order Thermoelasticity Theory for a Half-Space Subjected to an Axisymmetric Heat Distribution

The present work is concerned with a traction-free thermoelastic half-space subjected to a known axisymmetric temperature distribution. The thermoelastic interactions inside the medium are investigated by employing the fractional order theory of thermoelasticity. The problem is solved by using Laplace's and Hankel's transforms. The inverse transforms are computed numerically. The variations of temperature, displacements, and stresses inside the half-space are investigated. The field variables for a particular material are graphically presented. Comparisons are made within the theory in the presence and absence of fractional order parameter.     

受移动热源作用的两端固定杆的广义热-弹耦合问题

基于带有一个热松弛时间的Lord-Shulman广义热弹性理论,研究了受移动热源作用的两端固定的均质各向同性杆的热-弹动态响应。该文给出了杆的广义热-弹耦合的控制方程,借助拉普拉斯积分变换及其数值反变换对控制方程进行了求解。计算得到了杆内温度、应力及位移的分布规律,从其分布图上可以看出,温度、应力及位移随移动热源速度的增大而减小。     

Influence of the size factor on the thermal shock resistance of ceramic samples

The cracking of brittle samples having suffered thermal shocks may be calculated by using the thermoelastic theory. This theory leads to a size effect, which is not always verified by experiments. The use of acoustic methods of characterization, for samples of various shapes and sizes, shows the size effect, but the experimental T _c values are greater than the calculated ones. This discrepancy must be due both to an overestimation of the A coefficient and an underestimation of the R parameter.     

Application of fractional order theory of thermoelasticity to 3D time-dependent thermal shock problem for a half-space

A three-dimensional model of thermoelasticity with fractional order heat transfer is established. The resulting nondimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverses of Fourier transforms and Laplace transforms are obtained numerically. Numerical results for the temperature, the stress, the strain, and the displacement distributions are represented graphically. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity.     

Asymptotic approach to transient thermal shock problem with variable material properties

In this paper, an asymptotic approach is proposed to solve the transient thermal shock problem with variable material properties. The governing equations of isotropic elastic medium with temperature-dependent properties are derived in the context of the Lord–Shulman generalized theory of thermoelasticity, where the higher-order expansion with respected to increment temperature of the Helmholtz free energy is used to describe the relation of each material parameter with real temperature. Then, the layer method is used to deal with the variation of material properties with real temperature, and a system with discrete linear equations is obtained by ignoring some higher-order quantities. This system is then solved analytically by the integral transform method, where the Laplace transform technique and its limit theorem is employed to deal with these linear partial differential equations. This asymptotic approach is applied to solve the thermoelastic response of a thin plate with variable material properties. The asymptotic solutions of the displacement, temperature and stresses, induced by a sudden temperature rise at the boundary of thin plate, are obtained. The corresponding results for each physical field are discussed, as well as the comparison with the results obtained from the case with constant properties is also conducted to evaluate the effect of temperature dependency of material properties.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

Dynamic response of a generalized piezoelectric-thermoelastic problem under fractional order theory of thermoelasticity

The dynamic response of a piezoelectric-thermoelastic rod made of piezoelectric ceramics (PZT-4) subjected to a moving heat source is dealt with in the context of the fractional order theory of thermoelasticity. The piezoelectric-thermoelastic governing equations for the problem are formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered nondimensional temperature, displacement, stress, and electric potential are obtained and illustrated graphically. The effects of fractional order parameter and the velocity of heat source on the variations of the considered variables are investigated, and the results show that they have significant influence on the variations of the considered variables. The present investigation could be helpful for better understanding the multi-field coupling effect of mechanical, electric, and thermal fields in real piezoelectric ceramics structures, and provide some guidelines in the optimal design of actuators or sensors made of piezoelectric ceramics serving in a thermoelastic environment.     

Boundary element method analyses of transient heat conduction in an unbounded solid layer containing inclusions

The boundary element method (BEM) is used to compute the three-dimensional transient heat conduction through an unbounded solid layer that may contain heterogeneities, when a pointwise heat source placed at some point in the media is excited. Analytical solutions for the steady-state response of this solid layer when subjected to a spatially sinusoidal harmonic heat line source are presented when the solid layer has no inclusions. These solutions are incorporated into a BEM formulation as Greens functions to avoid the discretization of flat media interfaces. The solution is obtained in the frequency domain, and time responses are computed by applying inverse (Fast) Fourier Transforms. Complex frequencies are used to prevent the aliasing phenomena. The results provided by the proposed Greens functions and BEM formulation are implemented and compared with those computed by a BEM code that uses the Greens functions for an unbounded media which requires the discretization of all solid interfaces with boundary elements. The proposed BEM model is then used to evaluate the temperature field evolution through an unbounded solid layer that contains cylindrical inclusions with different thermal properties, when illuminated by a plane heat source. In this model zero initial conditions are assumed. Different simulation analyses using this model are then performed to evaluate the importance of the thermal properties of the inclusions on transient heat conduction through the solid layer.     

Boundary element prediction of TBC fracture resistance

The present study investigates the transient behaviour of interfacial cracks in thermal barrier coatings. It is assumed that a TBC withstands a thermal shock in the presence of external mechanical load acting on its surface. Crack closure takes place while the thermal contact resistance as well the friction between the crack faces is considered. The dependence of the thermal resistance on the contact pressure invokes coupling between the temperature and displacement fields. An appropriate boundary element procedure based on two‐dimensional time‐dependent thermoelasticity, is utilized for the numerical solution. A series of parametric analyses examines the impact of the coefficient of friction, thermal contact resistance and coefficient of heat convection on the crack severity.     

Semi-analytical model based on generalized plane strain assumption for unidirectional composites with matrix micro cracks

Generalized plane strain state is assumed and stress-based finite strip method is formulated for analysis of unidirectional laminates with matrix microcracks. Total complementary potential energy is minimized and fourth-order Euler Lagrange governing equations are presented. This stress-based generalized plane strain approach analyzes general layup and loading conditions. It provides flexibility to control the number of finite strip nodal lines within each lamina; hence, stress behavior can be predicted across each lamina at the desired location of the structure. Along with all of the capabilities which are common with finite strip methodology based on plane strain assumption, this current work has extended the analysis of the cracked laminate. For example, by incorporating behavior of the out of the plane shear stress, boundary conditions including natural boundary conditions are imposed appropriately to solve governing Euler's equations. Results are compared with previously developed displacement-based formulation in the literature for cracked laminates. It has already been shown that a stress-based plane strain approach enhances variation-based cracked laminate analysis where only the case of cross-ply laminate under tension is considered. This current work applies generalized plane strain-based finite strip methodology to carry out analysis under different loading conditions.     

考虑热松弛的热弹耦合二维问题的有限元法

为了解决利用积分变换方法在求解Lord-Shulman (L-S)型广义热弹性耦合二维问题时由于数值反变换所引起的计算精度降低的问题,该文采用新近被应用的直接有限元方法,求解了基于L-S型广义热弹性理论的半无限大体受热冲击作用的动态响应问题,结果表明,该方法对求解L-S型广义热弹性耦合二维问题具有很高的精度。该文给出了L-S型广义热弹性理论下的热弹耦合的控制方程,建立了L-S型的广义热弹性问题的虚位移原理,推导得到了相应的有限元方程。经计算得到了半无限大体中无量纲温度、位移及应力的分布规律,从温度分布图上可以清晰地观察到热波波前的特有属性,即热波波前处存在温度突变。     

Thermal Behavior of Perfect and Imperfect Contact Composite Slabs Under the Effect of the Hyperbolic Heat Conduction Model

This work studies the heat transfer mechanisms during rapid heating of two-layer composite thin slabs from a macroscopic point of view using the hyperbolic heat conduction model. The composite slabs consist of two thin metal layers which may be in perfect or imperfect thermal contact. The effects of parameters such as the two films' thickness ratio, thermal conductivity ratio, heat capacity ratio, thermal relaxation time, and interfacial heat transfer coefficient on the thermal behavior of the composite slabs are investigated.