Microelectronics packaging has been developing rapidly due to the demands for faster, lighter and smaller products. Printed circuit boards (PCBs) provide mechanical support and electrical interconnection for electronic devices. Many types of composite PCBs have been developed to meet various needs. Recent trends in reliability analysis of PCBs have involved development of the structural integrity models for predicting lifetime under thermal environmental exposure; however the theoretical models need verification by the experiment.
The objective of the current work is the development of an optical system and testing procedure for evaluation of the thermal deformation of PCBs in the wide temperature range. Due to the special requirements of the specimen and test condition, the existing technologies and setups were updated and modified. The discussions on optical methods, thermal loading chambers, and image data processing are presented. The proposed technique and specially designed test bench were employed successfully to measure the thermal deformations of PCB in the −40°C to +160°C temperature range. The video-based moiré interferometry was used for generating, capturing and analysis of the fringe patterns. The obtained information yields the needed coefficients of thermal expansion (CTE) for tested PCBs. 相似文献
We consider three different models of linear differential equations and their isomonodromic deformations. We show that each
of the models has its own specificity, although all of them lead to the same final result. It turns out that isomonodromic
deformations are closely related to the Hamiltonian structure of both classical mechanics and quantum mechanics.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 143–151, January, 2007. 相似文献
We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on formal deformation quantization of Poisson manifolds by star products. 相似文献
The anatomy and geometry of the lung at the micro- and macroscopic level have been described briefly. A notion of lung parenchyma — a macroscopically continuous medium whose mechanical properties result from those of microstructural components — has been adapted. Simplifying assumptions propounded in the constitutive model have been discussed. Two phases have been distinguished in the medium: the solid phase — a highly deformable, nonlinearly elastic skeleton in the form of a thin-walled tissue structure on the micro-scale — and the fluid phase — perfect gas (air) filterating through the structure. General constitutive relations for both phases and their mechanical interactions have ben formulated. Further, the fundamental set of differential equations of the quasi-static coupled problem has been developed. Large deformations, material nonlinearities, and dependence of permeability on skeleton deformation have been included. Matrix formulation of the problem has been presented from the point of view of the finite element method. An implicit iterative time integration scheme has been proposed. The algorithm has been illustrated with results of simple numerical tests. 相似文献
In the present paper we consider interior and exterior mixed boundary value problems of anti-plane shear in the static theory of linear piezoelectricity. Using the boundary integral equation method we reduce the problems to systems of singular integral equations with discontinuous coefficients to which the classical Nöether’s theorems on existence of the solution can be applied. This allows us to establish well-posedness results and to obtain integral solutions of the corresponding mixed boundary value problems for a rather general class of piezoelectric materials.
Mathematics Subject Classifications (2000) 45E05, 45F15, 74F15. 相似文献
FEA calculations have been carried out for a model rubber shear spring, consisting of a block of a highly elastic material, bonded between two rigid parallel plates and sheared by displacing one of the plates parallel to the other in its own plane. The block was prevented from deforming in the perpendicular direction, and thus was deformed in plane strain. Stress distributions along the bond-line and the center-line are reported and compared with those expected from the theory of large elastic deformations. Unexpected tensile stresses were found to develop in the interior of the sheared block. They are attributed to the absence on the end surfaces of the stresses needed to maintain a simple shear, causing a pronounced change in the reference pressure—a consequence that is usually overlooked. Because the internal stresses are governed by the boundary conditions, they were strongly affected by the shape of the end surfaces. In addition, they were reduced markedly by assigning values to Poisson's ratio slightly lower than 0.5, thus allowing some volume expansion of the rubber. Strain energy release rates were also evaluated for growth of a crack along the bond-line, starting at the edges, and compared with those reported previously by Lindley and Teo [Energy for crack growth at the bonds of rubber springs, Plast. Rubber Mat. Appl. 4 (1979) 29-37], Muhr et al. [A fracture mechanics study of natural rubber-to-metal bond failure, J. Adhes. Sci. Technol. 10 (1996) 593-616], Gregory and Muhr [Stiffness and fracture analysis of bonded rubber blocks in simple shear, in: D. Boast, V.A. Coveny (Eds.), Finite Element Analysis of Elastomers, Professional Engineering Publications, Bury St. Edmunds, UK, 1999, pp. 265-274] and Gough and Muhr [Initiation of failure of rubber close to bondlines, in: Proceedings of the International Rubber Conference, Maastricht, Netherlands, June 2005, IOM Communications Ltd., London, 2005, pp. 165-174]. They confirm that a long crack at the compression edge will grow faster than one at the tension edge, but the results for short cracks were inconclusive. 相似文献
The interaction between bubbles and solid surfaces is central to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. A main challenge is to accurately and reliably control the relative motion over a wide range of hydrodynamic conditions and at the same time to determine the interaction forces, bubble–solid separation and bubble deformation. Existing experimental methods are able to focus only on one of the aspects of this problem, mostly for bubbles and particles with characteristic dimensions either below 100 μm or above 1 cm. As a result, either the interfacial deformations are measured directly with the forces being inferred from a model, or the forces are measured directly with the deformations to be deduced from the theory. The recently developed integrated thin film drainage apparatus (ITFDA) filled the gap of intermediate bubble/particle size ranges that are commonly encountered in mineral and oil recovery applications. Equipped with side-view digital cameras along with a bimorph cantilever as force sensor and speaker diaphragm as the driver for bubble to approach a solid sphere, the ITFDA has the capacity to measure simultaneously and independently the forces and interfacial deformations as a bubble approaches a solid sphere in a liquid. Coupled with the thin liquid film drainage modeling, the ITFDA measurement allows the critical role of surface tension, fluid viscosity and bubble approach speed in determining bubble deformation (profile) and hydrodynamic forces to be elucidated. Here we compare the available methods of studying bubble–solid interactions and demonstrate unique features and advantages of the ITFDA for measuring both forces and bubble deformations in systems of Reynolds numbers as high as 10. The consistency and accuracy of such measurement are tested against the well established Stokes–Reynolds–Young–Laplace model. The potential to use the design principles of the ITFDA for fundamental and developmental research is demonstrated. 相似文献
We develop a model framework for anisotropic damage coupled to crystal (visco)plasticity, which is based on the concept of a fictitious (undamaged) configuration. The theoretical setting is that of finite strains, which is natural when studying crystal inelasticity even in the case of actual small strains. It turns out that the evolution law for damage, which reflects degradation in the slip planes and which is the key new relation, bears strong resemblance with the inelastic flow rule. Some numerical results showing qualitatively the anisotropic development of damage concludes the paper. 相似文献
This work is concerned with the homogenization of solids reinforced by aligned parallel continuous fibers or weakened by aligned
parallel cylindrical pores and undergoing large deformations. By alternatively exploiting the nominal and material formulations
of the corresponding homogenization problem and by applying the implicit function theorem, it is shown that locally homogeneous
deformations can be produced in such inhomogeneous materials and form a differentiable manifold. For every macroscopic strain
associated to a locally homogeneous deformation field, the effective nominal or material stress–strain relation is exactly
determined and connections are also exactly established between the effective nominal and material elastic tangent moduli.
These results are microstructure-independent in the sense that they hold irrespectively of the transverse geometry and distribution
of the fibers or pores. A porous medium consisting of a compressible Mooney–Rivlin material with cylindrical pores is studied
in detail to illustrate the general results.
This work was the first time presented at the Euromech Colloqium 464 on “Fiber-reinforced Solids: Constitutive Laws and Instabilities”,
September 28–October 1, 2004, Cantabria, Spain. 相似文献