Showing papers on "Thermoelastic damping published in 1998"
TL;DR: In this paper, the dynamic thermoelastic response of functionally graded cylinders and plates is studied, and a finite element model of the formulation is developed, where the heat conduction and the thermo-elastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading.
Abstract: The dynamic thermoelastic response of functionally graded cylinders and plates is studied. Thermomechanical coupling is included in the formulation, and a finite element model of the formulation is developed. The heat conduction and the thermoelastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading. In addition, a thermoelastic boundary value problem using the first-order shear deformation plate theory (FSDT) that accounts for the transverse shear strains and the rotations, coupled with a three-dimensional heat conduction equation, is formulated for a functionally graded plate. Both problems are studied by varying the volume fraction of a ceramic and a metal using a power law distribution.
1,196 citations
TL;DR: In this paper, the static and dynamic response of the functionally graded material (fgm) plates are investigated by varying the volume fraction of the ceramic and metallic constituents using a simple power law distribution.
1,026 citations
TL;DR: The theory of thermoelastic stress analysis is reviewed and the implications of some theoretical developments are assessed in this article, where available instrumentation is described and techniques available for separation of individual stress values are summarized.
Abstract: The theory of thermoelastic stress analysis is reviewed and the implications of some theoretical developments are assessed. Available instrumentation is described and techniques available for separation of individual stress values are summarized. The scope of the technique is illustrated with reference to a number of applications covering crack-tip stress studies, stress analysis and damage assessment in composite materials, and ‘field’ work on a traffic-loaded road bridge.
217 citations
TL;DR: In this article, it is argued that adiabatic decompression of the lower mantle is best effected by a strategy in which consistent third-order finite-strain expressions are required simultaneously to fit the strain dependence of both the seismic parameter and the density.
Abstract: The interpretation of seismological models for the Earth’s lower mantle in terms of chemical composition and temperature is sensitive both to the details of the methodology employed and also to uncertainties in key thermoelastic parameters, especially for the dominant (Mg, Fe)SiO3 perovskite phase. Here the alternative approaches—adiabatic decompression of the lower mantle for comparison at zero pressure with laboratory data, and the projection of laboratory data to lower-mantle P–T conditions for direct comparison with seismological observations—are assessed, along with the equations of state on which they are based. It is argued that adiabatic decompression of the lower mantle is best effected by a strategy in which consistent third-order finite-strain expressions are required simultaneously to fit the strain dependence of both the seismic parameter and the density. This procedure accords due weight to the most robust seismological observations, namely the wave speeds, and reduces to an acceptable level the otherwise very strong covariance among the fitted coefficients. It is demonstrated that this approach can readily be adapted to include the effects of relaxation, from the Hill average to the Reuss lower bound, of the aggregate bulk modulus which governs the radial variation of density. For the projection of laboratory thermoelastic data to lower-mantle P–T conditions, the preferred equation of state is of the Mie–Gruneisen type, involving the addition at constant volume of the pressure along a finite-strain principal (300 K) isotherm and the thermal pressure calculated from the Debye approximation to the lattice vibrational energy. A high degree of consistency is demonstrated between these alternative equations of state. Possible departures of the lower mantle from conditions of adiabaticity and large-scale homogeneity are assessed; these are negligible for the PREM model (Bullen parameter ηB = 0.99 ± 0.01) but significant for ak135 (ηB ∼ 0.94 ± 0.02), reviving the possibility of a substantially superadiabatic temperature gradient. Experimentally determined thermoelastic properties of the major (Mg, Fe)SiO3 perovskite and (Mg, Fe)O magnesiowustite phases are used to constrain the equation-of-state parameters employed in the analysis of seismological information, although the scarcity of information concerning the pressure and temperature dependence of the elastic moduli for the perovskite phase remains a serious impediment. Nevertheless, it is demonstrated that the combination of a pyrolite composition simplified to the three-component system (SiO2–MgO–FeO) with molar XPv = 0.67 and XMg = 0.89, and a lower-mantle adiabat with a potential temperature of 1600 K—consistent with the preferred geotherm for the upper mantle and transition zone—is compatible with the PREM seismological model, within the residual uncertainties of the thermoelastic parameters for the perovskite phase. In particular, such consistency requires values for the perovskite phase of KS′ = (∂KS /∂P)T and q = (∂ ln γ/∂ ln V )T of approximately 3.8 and 2, and ∂G/∂T near −0.022 GPa K−1 for the lower-mantle assemblage. More silicic models, which have sometimes been advocated, can also be reconciled with the seismological data, but require lower-mantle temperatures which are much higher—by about 700 K for pyroxene stoichiometry. However, the absence of seismological and rheological evidence for the pair of thermal boundary layers separating convection above and below, which is implied by such models, remains a formidable difficulty. Under these circumstances, the simplest possible model, that of grossly uniform chemical composition throughout the mantle, is preferred.
170 citations
TL;DR: In this article, analytical solutions for the effect of squeeze film damping on a MEMS torsion mirror were derived under the assumption of small displacements, and the damping torques based on both the analytical modeling and the numerical modeling were then used in the equation of motion of the torsions mirror which is solved by the Runge-Kutta numerical method.
Abstract: This paper presents analytical solutions for the effect of squeeze film damping on a MEMS torsion mirror. Both the Fourier series solution and the double sine series solution are derived for the linearized Reynold equation which is obtained under the assumption of small displacements. Analytical formulae for the squeeze film pressure variation and the squeeze film damping torque on the torsion mirror are derived. They are functions of the rotation angle and the angular velocity of the mirror. On the other hand, to verify the analytical modeling, the implicit finite difference method is applied to solve the nonlinear isothermal Reynold equation, and thus numerically determine the squeeze film damping torque on the mirror. The damping torques based on both the analytical modeling and the numerical modeling are then used in the equation of motion of the torsion mirror which is solved by the Runge-Kutta numerical method. We find that the dynamic angular response of the mirror based on the analytical damping model matches very well with that based on the numerical damping model. We also perform experimental measurements and obtain results which are consistent with those obtained from the analytical and numerical damping models. Although the analytical damping model is derived under the assumption of harmonic response of the torsion mirror, it is shown that with the air spring effect neglected, this damping model is still valid for the case of nonharmonic response. The dependence of the damping torque on the ambient pressure is also considered and found to be insignificant in a certain regime of the ambient pressure. Finally, the convergence of the series solutions is discussed, and an approximate one term formula is presented for the squeeze film damping torque on the torsion mirror.
167 citations
TL;DR: In this article, the authors deal with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium (CEFIT), which offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid.
Abstract: This paper deals with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium (CEFIT). This special variant of a finite difference time domain (FDTD) scheme offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid. In order to test the accuracy of the numerical CEFIT code, problems for which analytical solutions are available are presented. These solutions involve wave propagation in an elastic plate, the scattering of a plane longitudinal wave by a spherical obstacle, and ultrasound generation by a thermoelastic laser source. For the latter problem experimental results are included. The CEFIT code also allows the treatment of more complicated problems. Further possible applications are the investigation of elastic waves generated in an acoustic microscope, the simulation of impact-echo measurements in multi-layer systems, axisymmetric wave propagation in arbitrary bodies of revo...
98 citations
TL;DR: In this article, the linear theory of thermoelasticity without energy dissipation is employed to study the thermal interactions due to a continuous point heat source in a homogeneous and isotropic unbounded solid.
Abstract: The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions due to a continuous point heat source in a homogeneous and isotropic unbounded solid. The Laplace transform method is employed to solve the problem. Exact expressions, in closed form, for the displacement, temperature and stress fields are obtained. Numerical results for a copper-like material are presented.
88 citations
TL;DR: In this paper, an axisymmetric concentric cylinder model and a flat laminate model, each based on Reissner's variational principle with equilibrium stress fields, are compared and the results for the elastic stress fields and energy release rates in composite laminates with free edge and/or internal delaminations and transverse cracking are presented.
83 citations
TL;DR: In this article, Liu and Heng showed uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary and used a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates.
Abstract: We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. Lagnese, Boundary Stabilization of Thin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case---where rotational forces are neglected---in [Z. Liu and S. Z. Heng, Quarterly Appl. Math., 55 (1997), pp. 551-564]). The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for related work. Moreover, the particular choice of our multiplier becomes clear only after recasting the PDE model into an associated abstract evolution equation.
80 citations
TL;DR: Rittel et al. as discussed by the authors investigated transient thermoelastic eAects in dynamic fracture and found that they react quite differently from the baseline temperature, and that the crack-tip temperature of the PC specimen rises significantly as evidenced from the failure mode at both macroscopic and microscopic scales.
78 citations
TL;DR: In this article, the reflection coefficients of various reflected waves with the angle of incidence as well as with the thermoelastic coupling coefficients for Green-Lindsay and Lord-Shulman theories have been obtained.
TL;DR: In this article, the authors considered a right cylinder composed of a physically micropolar thermoelastic material for which one plane end is subjected to an excitation harmonic in time.
Abstract: In this study, the authors consider a right cylinder composed of a physically micropolar thermoelastic material for which one plane end is subjected to an excitation harmonic in time. By using a measure of Toupin type associated with the corresponding steady-state vibration and assuming that the exciting frequency is lower to a certain critical frequency, the authors obtain a spatial decay estimate, similar to that of the Saint-Venant type.
Patent•
18 Dec 1998
TL;DR: In this article, a non-destructive bond testing system is implemented using a pulse laser that sends a single or multiple pulse(s) of controlled magnitude and bombards an object of interest causing a thermoelastic excitation response.
Abstract: A nondestructive bond testing system is implemented using a pulse laser that sends a single or multiple pulse(s) of controlled magnitude and bombards an object of interest causing a thermoelastic excitation response. This excitation in turn induces an ultrasonic propagation along or through the surface material. By detecting, capturing and interpreting these thermoelastic propagation signatures, the attachment condition of the joining materials is determined. The technique is a significant improvement over traditional mechanical pull, shear or contact type techniques. The techniques are implemented in automated high speed inspection systems suitable for real time manufacturing application. Particular applications include evaluating material joining in microelectronics manufacture (such as ball bonds) and thin coating processes.
TL;DR: In this paper, a system of singular integral equations applicable under both the mechanical and transient thermal loading conditions is derived for collinear cracks embedded in a layered half-plane, where the medium consists of a surface layer and a semi-infinite substrate bonded through an interfacial zone with graded properties.
Abstract: The problem of collinear cracks embedded in a layered half-plane is investigated. The medium consists of a surface layer and a semi-infinite substrate bonded through an interfacial zone with graded properties. The interfacial zone is treated as a nonhomogeneous layer and its elastic modulus is assumed to vary continuously in thickness direction. Three collinear cracks of different length exist, one in each one of the constituent materials perpendicular to the nominal interfaces. A system of singular integral equations applicable under both the mechanical and transient thermal loading conditions is derived. Part I of the paper addresses the details that lead to the derivation of the integral equations and the cracking behavior in the layered medium subjected to mechanical loading. As a result, the values of stress intensity factors are presented as functions of geometric and material parameters of the problem. In Part II, under the uncoupled, quasi-static thermoelastic condition, the response of collinear cracks to thermal shock loading is considered.
TL;DR: In this article, the authors describe the formulation and numerical implementation of the three-dimensional dual boundary element method (DBEM) for the thermoelastic analysis of mixed-mode crack problems in linear elastic fracture mechanics.
Abstract: This paper describes the formulation and numerical implementation of the three-dimensional dual boundary element method (DBEM) for the thermoelastic analysis of mixed-mode crack problems in linear elastic fracture mechanics. The DBEM incorporates two pairs of independent boundary integral equations; namely the temperature and displacement, and the flux and traction equations. In this technique, one pair is applied on one of the crack faces and the other pair on the opposite one. On non-crack boundaries, the temperature and displacement equations are applied.
TL;DR: In this article, the authors used a polymer coating as a strain witness in thermoelasticity and found that thicknesses of more than 0.5 mm and frequencies greater than 5 Hz provide adequate results.
Abstract: The work described in this paper offers the possibility of using a polymer coating as a strain witness in thermoelasticity. In particular, the efficacy of a polymer coating for making thermoelastic measurements is investigated by experiment and the supporting theory is presented. It was found that the thermoelastic response is greatest with thick coatings at high frequencies. However, thicknesses of more than 0.5 mm and frequencies greater than 5 Hz provide adequate results.
TL;DR: In this paper, the problem of exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is considered, and it is shown that the energy in the system decays to zero exponentially.
Abstract: The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is
considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to
increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to
a related open question raised by Alabau and Komornik for the Lame system. Via Russell's “Controllability via Stabilizability" principle, we then
prove that the thermoelastic system is partially controllable with boundary controls without smallness restrictions on the coupling parameters.
TL;DR: In this article, a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic infinite medium with a spherical cavity subjected to a sudden change in the temperature of its internal boundary which is assumed to be traction free is studied.
TL;DR: In this article, the problem of collinear cracks in a layered halfplane with a graded nonhomogeneous interfacial zone was investigated under mechanical loading and the cracking behavior was addressed by evaluating the stress intensity factors as functions of various geometric and material parameters.
Abstract: In Part I of the paper, the problem of collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone was investigated under mechanical loading and the cracking behavior was addressed by evaluating the stress intensity factors as functions of various geometric and material parameters In Part II, the solution framework is extended to the problem of thermal shock on the basis of uncoupled, quasi-static thermoelasticity The interfacial zone, in this case, is assumed to have the graded thermoelastic properties Using the principle of superposition, a system of singular integral equations is solved subjected to equivalent crack surface tractions obtained form the transient thermoelasticity solution for a uncracked medium Main results presented are the transient thermal stress intensity factors of collinear cracks to illustrate the parametric effects of geometric and material combinations of the layered medium with the thermoelastically graded interfacial zone
TL;DR: In this article, a more primitive treatment of internal constraints for thermoelastic materials is presented, where the properties of the constrained material are inherited from the unconstrained materials belonging to its corresponding equivalence class.
Abstract: A new and more primitive treatment of internal constraints for thermoelastic materials is presented. Integrable strain-temperature constraints are considered and are used to define an equivalence relation on the set of unconstrained thermoelastic materials. A unique constrained material is associated with each equivalence class of unconstrained materials. The properties of the constrained material are inherited from the unconstrained materials belonging to its corresponding equivalence class.
TL;DR: In this article, it was shown that the global existence of a smooth solution for small data can be guaranteed when the boundary is either traction-free and at a constant temperature or rigidly clamped and thermally insulated.
Abstract: It is well known that in the absence of dissipation, smooth solution of nonlinear elastic materials develop singularities in finite time, while for thermoelastic materials the conduction of the heat equation provides dissipation that competes with the destabilizing effect of nonlinearity in the elastic response. The level of subtlety of this dissipation depends on the boundary condition that the displacement and the thermal difference are supporting. Slemrod [I] showed the global existence of smooth solution for small data when the boundary is either traction-free and at a constant temperature or rigidly clamped and thermally insulated. A similar result was obtained by Zheng [2]. These boundary conditions get a simpler damping mechanism because they imply additional boundary conditions for u and the thermal difference 8, that is, if an end is clamped then the displacement u and the thermal difference 0 satisfy u,, = 0 and 0,, = 0 there respectively. So we can make additional partial integrations which led to the desire a priori L2-estimate. In case of Dirichlet boundary condition for which the boundary is rigidly clamped and held at a constant temperature we lost the value of u,, in that point and instead of it we get u, + of& = 0. So this case leads ill behaved boundary terms and it is not possible to apply directly the multiplicative techniques to secure global estimate. Recently Racke and Shibata [3] proved Global existence of a smooth solution for these boundary conditions. To do this the authors showed the algebraic decay of the energy for the linear equation by studying the spectral properties of the stationary linearized problem. The rate of decay depends on higher regularity of the initial data and therefore the global existence result depends on the initial data to be small in Hm(O, L) with m large. One of the authors of this paper proved in [4] (see also the work of Kim [5]) that the solution of the linearized thermoelastic system decays exponentially as time goes to infinity. This fact allows us to get simpler existence result for the corresponding nonlinear equation as was shown in [6] for small data (uO, ul) in H3(0, L) x H2(0, L). The system in question is written as follows
TL;DR: In this article, a numerical algorithm is developed to determine the residual moment due to a prescribed axisymmetric thermal history, and it is shown that susceptibility to buckling depends on a dimensionless geometric shape factor, the material properties, and the magnitude of the largest thermal excursion.
Abstract: The plates of multidisk automatic transmission are known to buckle under extreme operating conditions. Axisymmetric (coning) and nonaxisymmetric (potato chip) modes can be obtained. It is shown that these modes result from in-plane axisymmetric residual bending moments in the disk and the critical value for each mode is found. A numerical algorithm is then developed to determine the residual moment due to a prescribed axisymmetric thermal history. Allowance is made for the temperature dependence of yield stress, elastic modulus, and coefficient of thermal expansion. The results show that susceptibility to buckling depends on a dimensionless geometric shape factor, the material properties, and the magnitude of the largest thermal excursion. With steel disks and typical design values for the shape parameter, buckling is predicted for temperature differences of about 600°C between inner and outer radii
TL;DR: In this article, a method to convert a parent discrete time control into a multi-pulse-width modulated equivalent is presented, which can be established by matching the system state response at each sampling interval and that, provided asufe cient number ofpulsespersamplingintervalareused,thedegree of approximation can be as high as desired even if a relatively slow sampling frequency is adopted.
Abstract: A method is presented to convert a parent discrete time control into a multi-pulse-width modulated equivalent. It is shown that such an equivalence can be established by matching the system state response at each sampling intervalandthat,providedasufe cientnumberofpulsespersamplingintervalareused,thedegreeofapproximation can be as high as desired even if a relatively slow sampling frequency is adopted. A numerical example on a simple fourth-order system provides the basis for understanding the pros and cons of the method, which is then applied to a more complex aerospace problem: the stabilization of coupled thermoelastic vibrations of a space structure.
TL;DR: Dynamical and quasi-static thermoelastic contact problems in $\hbox{{\bbb R}}^n$ modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation are considered.
Abstract: We consider dynamical and quasi-static thermoelastic contact problems in $\hbox{{\bbb R}}^n$ modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-static case are also discussed.
TL;DR: In this article, a single vertical heat exchanger tube with multiple spans was excited by random vibration, and the frequency response spectra and resonant peak-fitted damping ratios were calculated for all tests.
Abstract: Heat exchanger tubes can be damaged or fail if subjected to excessive flow-induced vibration, either from fatigue or fretting-wear. Good heat exchanger design requires that the designer understands and accounts for the vibration mechanisms that might occur, such as vortex shedding, turbulent excitation or fluidelastic instability. To incorporate these phenomena into a flow-induced vibration analysis of a heat exchanger requires information about damping. Damping in multispan heat exchanger tubes largely consists of three components: viscous damping along the tube, and friction and squeeze-film damping at the supports. Unlike viscous damping, squeeze-film damping and friction damage are poorly understood and difficult to measure. In addition, the effect of temperature-dependent fluid viscosity on tube damping has not been verified. To investigate these problems, a single vertical heat exchanger tube with multiple spans was excited by random vibration. Tests were conducted in air and in water at three different temperatures (25, 60, and 90 C). At room temperature, tests were carried out at five different preloads. Frequency response spectra and resonant peak-fitted damping ratios were calculated for all tests. Energy dissipation rates at the supports and the rate of excitation energy input were also measured. Results indicate that damping does not change overmore » the range of temperatures tested and friction damping is very dependent on preload.« less
TL;DR: In this paper, the authors present solutions for the behavior of a layered porous space which contains a decaying heat source, where high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins.
Abstract: Solutions are presented for the behaviour of a layered porous space which contains a decaying heat source. Such a problem arises when high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins. The geometry of the problem is one dimensional and the porous space is constituted by two layers: a deep low permeability layer which contains the nuclear waste disposal and a superficial layer. The solution is used to examine the effects of contrasts of permeability, thermal conductivity and specific heat capacities between the two layers on the large-scale behaviour of the porous space. Results are presented, using realistic data, for the pore pressure and temperature evolution at the heat source centre, and for the vertical displacement of the ground level. The superficial layer has no significant effects on pore pressure, temperature and stress evolution near the heat source centre. The vertical displacement of the ground level is mainly due to the thermal dilatation of the pore water, so it decreases with an increasing of permeability of the superficial layer. The solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical methods to invert the transformed solutions. Comparisons with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass are presented. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this paper, a generalized micromechanics constitutive model was developed to describe thermoelastic martensitic transformation in shape memory alloys (SMA), and uniaxial and baoxial loading tests under different combined loads at a constant temperature were performed on cruciform specimens of a SMA CuAlNi single crystal.
TL;DR: In this paper, the effect of wave propagation in an interacting random infinite magneto-thermo- visco-elastic medium has been studied formulating a generalised theory of thermoelasticity that combines both the generalised theories developed by Lord and Shulman (2) as well as by Green and Lindsay (3).
Abstract: The problem of wave propagation in an interacting random infinite magneto-thermo- visco-elastic medium has been studied formulating a generalised theory of thermoelasticity recently proposed by Noda, Furuk-Awa and Ashida (1) that combines both the generalised theories developed by Lord and Shulman (2) as well as by Green and Lindsay (3). The perturbation technique relevant to stochastic differential equations has been employed to obtain the relation connecting displacement amplitudes of waves propagating in the interacting media. The appropriate Green's tensor essential for the discussion has been obtained in the course of analysis. A more general coupled dispersion relation for longitudinal and transverse waves has been deduced to determine the effect of visco- elasticity, relaxation times, and rotation on the phase velocity of the coupled waves. The equations have been analysed for a particular form of thermo-mechanical coupling and autocorrelation function to show that the effect (of the order of e 2 only) of the thermal field is to attenuate the longitudinal type waves and to alter the phase-speed depending upon the values of the visco-elastic parameters, relaxation times, and rotation. Cases of low and high frequencies have also been studied, and numer- ical calculations have been done to determine the effect of visco-elastic parameters, relaxation times, rotation, and thermoelastic coupling on the phase velocity and attenuation coefficient of the waves. (~) 1998 Elsevier Science Ltd. All rights reserved.
TL;DR: In this paper, an experimental methodology is proposed to evaluate the thermal shock resistance of ceramics and a technique based on infrared heating has been developed to perform systematic and well controlled thermal shock experiments.
Abstract: An experimental methodology is proposed to evaluate the thermal shock resistance of ceramics. A technique based on infrared heating has been developed to perform systematic and well controlled thermal shock experiments. This novel technique was used to evaluate the resistance of yttria-stabilized zirconia–alumina foams to thermal loads. Foams of varying cell sizes were subjected to thermal shock and the damage was evaluated using retained strength and non-destructive elastic modulus measurements. The transient thermal gradients and the resulting thermoelastic stresses in the foams were predicted using finite element analysis and the extent of damage was correlated to the maximum thermal strains generated in foams.
TL;DR: In this paper, an exact separation of variables is constructed for boundary value and boundary contact problems of thermoelastic equilibrium of one and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coor- dinates o, a, z.
Abstract: Using the method of separation of variables, an exact so- lution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coor- dinates o, a, z. o, a are the orthogonal coordinates on the plane and z is the linear coordinate. The body, occupying the domain S = fo0 < o < o1; a0 < a < a1; 0 < z < z1g, is subjected to the action of a stationary thermal Þeld and surface disturbances (such as stresses, displacements, or their combinations) for z = 0 and z = z1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy z = const and nonhomogeneous along z. The same assumption is made for the layers of the multilayer body which contact along z = const.