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Mathematical Elasticity

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Publisher: Elsevier
ISBN: 9780080535913
Size: 20.90 MB
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The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

Mathematical Elasticity

Author: Philippe G. Ciarlet
Publisher: North Holland
ISBN: 9780444825704
Size: 62.48 MB
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The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.

Mathematical Elasticity

Author: Philippe G. Ciarlet
Publisher: Elsevier
ISBN: 9780444817761
Size: 72.96 MB
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This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Multiscale Problems

Author: Alain Damlamian
Publisher: World Scientific
ISBN: 9814458120
Size: 40.78 MB
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The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier–Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated. Contents:An Introduction to Periodic Homogenization (Alain Damlamian)The Periodic Unfolding Method in Homogenization (Alain Damlamian)Deterministic Homogenization of Stationary Navier–Stokes Type Equations (Gabriel Nguetseng & Lazarus Signing)Homogenization of a Class of Imperfect Transmission Problems (Patricia Donato)Decompositions of Displacements of Thin Structures (Georges Griso)Decomposition of Rods Deformations. Asymptotic Behavior of Nonlinear Elastic Rods (Georges Griso)Junction of a Periodic Family of Rods with a Plate in Elasticity (Dominique Blanchard)Multi-scale Modelling of New Composites: Theory and Numerical Simulation (Bernadette Miara)A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle) Readership: PhD students and researchers in applied mathematics, mechanics, physics and engineering. Keywords:Multiscale Problem;Homogenization;Asymptotic Behavior;Approximation

Nonlinear Partial Differential Equations And Their Applications

Author: Doina Cioranescu
Publisher: Elsevier
ISBN: 9780080537672
Size: 59.17 MB
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This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

Numerical Methods And Analysis Of Multiscale Problems

Author: Alexandre L. Madureira
Publisher: Springer
ISBN: 3319508660
Size: 31.88 MB
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This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

Mathematical Models For Registration And Applications To Medical Imaging

Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 3540347674
Size: 54.60 MB
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This volume gives a survey on mathematical and computational methods in image registration. During the last year sophisticated numerical models for registration and efficient numerical methods have been proposed. Many of them are contained in this volume. The book also summarizes the state-of-the-art in mathematical and computational methods in image registration. In addition, it covers some practical applications and new directions with industrial relevance in data processing.

Variational Problems In Materials Science

Author: Gianni Dal Maso
Publisher: Springer Science & Business Media
ISBN: 3764375655
Size: 58.93 MB
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This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.