Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Mark D. Snyder. / Ph.D.

The generalized theory of thermoelasticity was employed to characterize the coupled thermal and mechanical wave propagation in high performance microelectronic packages. Application of a Gaussian heat source of spectral profile similar to high performance devices was shown to induce rapid thermal and mechanical transient phenomena. The stresses and temporal gradient of stresses (power density) induced by the thermal and mechanical disturbances were analyzed using the Gabor Wavelet Transform (GWT). The arrival time of frequency components and their magnitude was studied at various locations in the package. Comparison of the results from the classical thermoelasticity theory and generalized theory was also conducted. It was found that the two theories predict vastly different results in the vicinity of the heat source but that the differences diminish within a larger time window. Results from both theories indicate that the rapid thermal-mechanical waves cause high frequency, broadband stress waves to propagate through the package for a very short period of time. The power density associated with these stress waves was found to be of significant magnitude indicating that even though the effect, titled short time scale effect, is short lived, it could have significant impact on package reliability. The high frequency and high power density associated with the stress waves indicate that the probability of sub-micron cracking and/or delamination due to short time scale effect is high. The findings demonstrate that in processes involving rapid thermal transients, there is a non-negligible transient phenomenon worthy of further investigation.

The generalized theory of thermoelasticity was employed to characterize the coupled thermal and mechanical wave propagation in high performance microelectronic packages. Application of a Gaussian heat source of spectral profile similar to high performance devices was shown to induce rapid thermal and mechanical transient phenomena. The stresses and temporal gradient of stresses (power density) induced by the thermal and mechanical disturbances were analyzed using the Gabor Wavelet Transform (GWT). The arrival time of frequency components and their magnitude was studied at various locations in the package. Comparison of the results from the classical thermoelasticity theory and generalized theory was also conducted. It was found that the two theories predict vastly different results in the vicinity of the heat source but that the differences diminish within a larger time window. Results from both theories indicate that the rapid thermal-mechanical waves cause high frequency, broadband stress waves to propagate through the package for a very short period of time. The power density associated with these stress waves was found to be of significant magnitude indicating that even though the effect, titled short time scale effect, is short lived, it could have significant impact on package reliability. The high frequency and high power density associated with the stress waves indicate that the probability of sub-micron cracking and/or delamination due to short time scale effect is high. The findings demonstrate that in processes involving rapid thermal transients, there is a non-negligible transient phenomenon worthy of further investigation.

In this preprint, we look onto the theory of linear thermoelasticity. At the beginning, this theory is shortly repeated and afterwards applied to transversely isotropic materials. Then, the corresponding weak formulation is derived, which is the starting point for a FE-discretisation. In the last part, we explain how we added this material behaviour to an adaptive Finite-Element-code and show some numerical results.

Ce travail s’inscrit dans la thématique classique en mécanique de l’endommagement de milieux polycristallin. Il a pour but d’étudier et de modéliser le comportement thermique et mécanique d’un matériau énergétique. Ce matériau, dont le comportement en compression est quasi-fragile, présente en particulier un coefficient de dilatation thermique qui diminue lors de cycles de refroidissement-réchauffement.L’étude repose sur un modèle morphologique de type Johnson-Mehl avec grains non convexes et une méthode numérique à champ complet par transformée de Fourier rapide. La précision de ces méthodes en termes de réponse effective et de champs en pointe de fissure est étudiée par comparaison avec des éléments finis. Plusieurs types de microstructures sont ensuite étudiés de façon heuristique par ordre croissant de complexité.Le comportement élastique du polycristal non endommagé, calculé par méthode FFT, surestime celui observé expérimentalement. L’ajout de liant et de porosité dans le matériau n’expliquant pas le comportement mécanique expérimental, on étudie l’influence de différentes populations de fissures.Seule l’ajout de fissures intergranulaires permet de rendre compte du comportement effectif du matériau à l’état initial. La chute du coefficient de dilatation thermique est prédite par méthode FFT dans le cas de fissures dans le plan graphitique des monocristaux, dont l’existence est confirmée par des images MEB. / This work aims to study the thermal and mechanical behavior of an energetic polycrystal. This material displays a quasi-brittle behavior and its thermal dilation coefficient decreases when it undergoes cooling-heating cycles.The study relies on the use of a Johnson-Mehl tessellation model which has non-convex grains, and a full-field numerical method based on the Fourier transform. The accuracy of such methods concerning cracked media are determined by comparison with Finite Elements computations. The numerical tool is then used to investigate different microstructural assumptions, from the simplest to the most sophisticated.The first computation is that of an undammaged polycrystal, which overestimates the overall mechanical properties. The attempt to account for porosity and the presence of binder gives interesting results, but the latter are not enough to reproduce the experimental behavior.Finally, different types of microcracks are investigated and two major conclusions are drawn. First, in its initial state, the material contains intergranular cracks, that are uncorrelated to the local microstructure. Such cracks can lower the elastic moduli and leave the thermal properties unaffected. To obtain a decrease in terms of thermal dilation coefficient, one must consider families of cracks which are correlated to the local crystal orientation, especially along the weak plane of the crystal.

Three-dimensional basic problems of statics, pseudo-oscillations, general dynamics and steady state oscillations of the thermoelasticity of isotropic bodies have been completely investigated by many authors. In particular, exterior steady state oscillation problems have been studied on the basis of Sommerfeld-Kupradze radiation conditions in the thermoelasticity, and the uniqueness theorems were proved with the help of the well-known Rellich's lemma, since the components of the displacement vector and the temperature in the isotropic case can be represented as a sum of metaharmonic functions . Unfortunately, the methods of investigation of thermoelastic steady state oscillation problems developed for the isotropic case are not applicable in the case of general anisotropy. This is stipulated by a very complicated form of the corresponding characteristic equation which plays a significant role in the study of far field behaviour of solutions to the oscillation equa- tions. We note that the basic and crack type boundary value problems (BVPs) for the pseudo-oscillation equations of the thermoelasticity theory in the anisotropic case are considered in [3,14]. To the best of the authors' knowledge the problems of thermoelastic steady oscillations for anisotropic bodies have not been treated in the scientific literature. In the present paper we will consider a wide class of basic and mixed type BVPs for the equations of thermoelastic steady state oscillations. We will formulate thermoelastic radiation conditions for an anisotropic medium (the generalized Sommerfeld-Kupradze type radiation conditions) and prove the uniqueness theorems in corresponding spaces. To derive these conditions we have essentially applied results of Vainberg. Further, using the potential method and the theory of pseudodifferential equations on manifolds we will prove existence theorems in various functional spaces and establish the smoothness properties of solutions.

Design of thermoelastic structures can be highly counterintuitive due to design-dependent loading and impact of geometric nonlinearity on the structural response. Thermal loading generates in-plane stresses in a restrained panel, but the presence of geometric nonlinearity creates an extension-bending coupling that results in considerable transverse displacement and variation in stiffness characteristics, and these affects are enhanced in post-bucking regimes. Herein a methodology for structural sizing of thermally stressed post-buckled stiffened panels is proposed and applied for optimization of the blade and hat stiffeners using a gradient-based optimizer. The stiffened panels are subjected to uniform thermal loading and optimized for minimum mass while satisfying stress and stability constraints. The stress constraints are used to avoid yielding of the structure, whereas the stability constraints are used to ensure static stability. Corrugation of the hat stiffeners is also studied through variation of its magnitude and position. A continuation solver has been validated to tackle the highly nonlinear nature of the thermoelastic problem, and formulations for the stability constraints have been derived and imposed to satisfy the static stability of the structure. The study confirms that geometric nonlinearity is an important aspect of sizing optimization and is needed for an accurate modeling of the structural behavior. The results also show that modeling of geometric nonlinearity adds extra complexity to the thermoelastic problem and requires a path-tracking solver. Finally, this work supports that corrugation enhances the stability features of the panel but requires a blending function to reduce stresses at the panel boundaries.

<p> Nonlinear flexural vibrations of simply supported rectangular plates with thermal coupling  are studied for the case when the plate is harmonically excited by the force acting normal to the  midplane of the plate. The coupled thermo-mechanical equations are derived by applying the  Galerkin procedure on the von-Karman equation and the energy equation for an element of the  plate. The thermo-mechanical equations are second order in transverse displacement and first order  in thermal dynamics. In our first study, we represent the transverse displacement, bending moment  and membrane force due to temperature by one mode approximation, and study the response of  thermoelastic plate in time and frequency domain. The analysis of forced vibration to a transverse  harmonic excitation is carried out using harmonic balance as well as direct time integration coupled  to a Fourier analysis for a range of excitation frequencies. The effects of thermal coupling, material  nonlinearity and different amplitudes of excitation on the thermoelastic plate’s transverse  displacement and thermoelastic variables are investigated. The method of averaging is applied to the one mode case to transform the nonlinear modal  equations into sets of two-dimensional dynamical systems which govern the amplitudes and phases  of the two modes. The averaged system is studied in detail by using pseudo arc-length continuation  schemes implemented in MATCONT. The physical phenomena of interest in this study arise when a plate exhibits two distinct  linear modes of vibration with nearly the same natural frequency. To analyze the dynamics of the  thermoelastic plate in this scenario, we utilize a two-mode approximation. The response of the  plate, as a function of excitation frequency, is determined for the two-mode model using  MATCONT, and several bifurcation points are identified. Our analysis reveals two types of  solutions: single-mode and coupled-mode solutions. We find that stable single-mode and coupled mode solutions can coexist over a wide range of amplitudes and excitation frequencies. Under the influence of thermal coupling, our analysis using MATCONT reveals the  identification of Neimark-Sacker bifurcation points. After a detailed study of the Neimark-Sacker  region using Fourier spectrum and Poincare section, we conclude that a pitchfork bifurcation  occurs, resulting in stable asymmetric solutions. We further investigate the effect of in-plane forces  or mechanical precompression on the thermoelastic plate, using MATCONT for a fixed value of  force, damping, and excitation frequency. We find that the in-plane forces lead to buckling, which  12 is identified as a branch point cycle (pitchfork bifurcation) in MATCONT. Consequently, the  bifurcation diagram of transverse displacement as a function of in-plane forces can be divided into  prebuckling and post buckling regions, with multistable solutions in each region. To validate our one mode model, we use ANSYS software to verify the transverse  displacement and temperature results. We validate the frequency and time domain results for both  the linear and nonlinear cases, and plot contours using ANSYS to observe the variation of  displacement and temperature over the surface of the plate. Our one mode model results closely  match with the ANSYS results, leading us to conclude that our one mode approximation is accurate  and that the coupled thermo-mechanical equations we derived are correct.  </p>

The precise and detailed characterization of the dynamic response of structures has become increasingly important in recent years. As a consequence, the accuracy of experimental data, which is often used to validate and update finite element models, has become extremely important. However, as researchers have attempted to identify and quantify sources of error in the experimental modal analysis (EMA) process, an important potential error source has been largely overlooked. Instabilities in the dynamic response of structures due to small variations in test environmental conditions may result in significant errors in experimental and analytical results, leading to erroneous and/or misleading conclusions. This thesis presents an experimental and analytical investigation of the effects of ambient temperature variations on the dynamic characteristics of a thin, square steel plate. The modal properties of the plate with two different boundary conditions and at temperatures above and below standard room temperature are examined. In addition, an analytical model is developed accounting for the effects of temperature-dependent material properties. Results indicate that natural frequencies and damping are significantly affected by changes in temperature. In the case of the natural frequency variations, the temperature-dependence of Young's modulus is the dominant factor, but boundary condition effects may also be important. Also, FRF magnitudes at spectral lines close to the resonances are very sensitive to temperature. Finally, only minor variations in the plate response shapes are observed, although significant changes in the imaginary component of the velocity field are evident. / Master of Science

Current methods for solving thennoelasticity problems involve using finite element analysis, boundary element analysis, or other meshed-type methods to determine the deflections under an imposed temperature/stress field. This thesis will detail a new approach using meshless methods to solve these types of thermoelasticity problems in which the solution is independent of boundary and internal meshing. With the rapidly increasing availability and performance of computer workstations and clusters, the major time requirement for solving a thermoelasticity model is no longer the computation time, but rather the problem setup. Defining the required mesh for a complex geometry can be extremely complicated and time consuming, and new methods are desired that can reduce this model setup time. The proposed meshless methods completely eliminate the need for a mesh, and thus, eliminate the need for complicated meshing procedures. Although the savings gain due to eliminating the meshing process would be more than sufficient to warrant further study, the localized meshless method can also be comparable in computational speed to more traditional finite element solvers when analyzing complex problems. The reduction of both setup and computational time makes the meshless approach an ideal method of solving coupled thermoelasticity problems. Through the development of these methods it can be determined whether they are feasible as potential replacements for more traditional solution methods. More specifically, two methods will be covered in depth from the development to the implementation. The first method covered will be the global meshless method and the second will be the improved localized method. Although they both produce similar results in terms of accuracy, the localized method greatly improves upon the stability and computation time of the global method.