Lectures on Three-dimensional Elasticity PDF Download
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Author: Philippe G. Ciarlet
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Author: Philippe G. Ciarlet
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Author: P. G. Ciarlet
Publisher: Springer
ISBN: 9783662009000
Category : Science
Languages : en
Pages : 0
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Book Description
Author: Philippe G. Ciarlet
Publisher: Elsevier
ISBN: 9780444817761
Category : Mathematics
Languages : en
Pages : 500
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Book Description
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.
Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 1611976782
Category : Mathematics
Languages : en
Pages : 521
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Book Description
The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Author:
Publisher: Elsevier
ISBN: 9780080875415
Category : Mathematics
Languages : en
Pages : 448
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Book Description
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.
Author: Claudio Borri
Publisher:
ISBN: 9788884538536
Category : Technology & Engineering
Languages : en
Pages : 238
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Book Description
Author: Surya N. Patnaik
Publisher:
ISBN:
Category : Boundary element methods
Languages : en
Pages : 26
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Book Description
The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary. the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation : differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function.
Author: David J. Steigmann
Publisher: Springer Nature
ISBN: 3031256743
Category : Science
Languages : en
Pages : 258
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Book Description
This book presents the theory of plates and shells on the basis of the three-dimensional parent theory. The authors explore the thinness of the structure to represent the mechanics of the actual thin three-dimensional body under consideration by a more tractable two-dimensional theory associated with an interior surface. In this way, the relatively complex three-dimensional continuum mechanics of the thin body is replaced by a far more tractable two-dimensional theory. To ensure that the resulting model is predictive, it is necessary to compensate for this ‘dimension reduction’ by assigning additional kinematical and dynamical descriptors to the surface whose deformations are modelled by the simpler two-dimensional theory. The authors avoid the various ad hoc assumptions made in the historical development of the subject, most notably the classical Kirchhoff–Love hypothesis requiring that material lines initially normal to the shell surface remain so after deformation. Instead, such conditions, when appropriate, are here derived rather than postulated.
Author: V.D. Kupradze
Publisher: Elsevier
ISBN: 0080984630
Category : Science
Languages : en
Pages : 951
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Book Description
North-Holland Series in Applied Mathematics and Mechanics, Volume 25: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity focuses on the theory of three-dimensional problems, including oscillation theory, boundary value problems, and integral equations. The publication first tackles basic concepts and axiomatization and basic singular solutions. Discussions focus on fundamental solutions of thermoelasticity, fundamental solutions of the couple-stress theory, strain energy and Hooke’s law in the couple-stress theory, and basic equations in terms of stress components. The manuscript then examines uniqueness theorems and singular integrals and integral equations. The book ponders on the potential theory and boundary value problems of elastic equilibrium and steady elastic oscillations. Topics include basic theorems of the oscillation theory, existence of solutions of boundary value problems, integral equations of the boundary value problems, and boundary properties of potential-type integrals. The publication also reviews mixed dynamic problems, couple-stress elasticity, and boundary value problems for media bounded by several surfaces. The text is a dependable source of data for mathematicians and readers interested in three-dimensional problems of the mathematical theory of elasticity and thermoelasticity.
Author: Philippe G. Ciarlet
Publisher: Society for Industrial and Applied Mathematics (SIAM)
ISBN: 9781611976779
Category : Elastic plates and shells
Languages : en
Pages : 0
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Book Description
"This textbook is appropriate for graduate level courses in pure or applied mathematics or in continuum mechanics"--
