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Linear approximation
About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.
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TL;DR: In this article, the authors consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects, and they show that the geometry theory quantitatively reproduces all the results of linear approximation in the linear approximation.
Abstract: We consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects. We show that the geometric theory quantitatively reproduces all the results of elasticity theory in the linear approximation. The coincidence is achieved by introducing a postulate that the vielbein satisfying the Einstein equations must also satisfy the gauge condition, which in the linear approximation leads to the elasticity equations for the displacement vector field. The gauge condition depends on the Poisson ratio, which can be experimentally measured. This indicates the existence of a privileged reference frame, which denies the relativity principle.
39 citations
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TL;DR: In this paper, a coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended to dynamics, and the conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first or thirdorder equivalent single-layer theory.
Abstract: A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first- or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.
39 citations
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TL;DR: A rigorous formulation of the parametric yield for very large scale integration (VLSI) designs including the mismatch effect is proposed using a new model for the autocorrelation function from which the covariance matrix of parameters is derived.
Abstract: A rigorous formulation of the parametric yield for very large scale integration (VLSI) designs including the mismatch effect is proposed. The theory has been carried out starting from a general statistical model relating random variations of device parameters to the stochastic behavior of process parameters. The model predicts a dependence of correlation, between devices fabricated in the same die, on their dimensions and mutual distances so that mismatch between equally designed devices can be considered as a particular case of such a model. As an application example, a new model for the autocorrelation function is proposed from which the covariance matrix of the parameters is derived. By assuming a linear approximation, a suitable formulation of the parametric yield for VLSI circuit design is obtained in terms of the covariance matrix of parameters.
39 citations
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TL;DR: In this paper, an error bound is proved for a piecewise linear finite element approximation, using a backward-Euler time discretization, of a model for phase separation of a multi-component alloy.
Abstract: An error bound is proved for a fully practical piecewise linear finite element approximation, using a backward-Euler time discretization, of a model for phase separation of a multi-component alloy. Numerical experiments with three components in one and two space dimensions are also presented.
39 citations