Saint Venant s Problem

speaking, consists in the generalization of Saint-Venant's notion of twist so as to apply to any solution of the torsion problem.

Author: Dorin Iesan

Publisher: Springer

ISBN: 9783540479116

Category: Science

Page: 166

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This monograph is concerned with the equilibrium of linearly elastic cylinders. It gives an up-to-date and systematic treatment of extension, bending, torsion and flexure of cylinders, including the deformation of homogeneous and nonhomogeneous anisotropic elastic cylinders by loads distributed on their lateral surfaces. Minimum energy characterizations of the solutions are discussed. An analysis of Saint-Venant's principle, in the context for which it was originally intended, is also presented. Many of the results included have not appeared or been previously discussed in the literature, and illustrative applications are presented throughout.
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Saint Venant s Problem

This monograph is concerned with the equilibrium of linearly elastic cylinders.

Author: Dorin Ieşan

Publisher: Springer Verlag

ISBN: 0387183612

Category: Mathematics

Page: 161

View: 341

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Saint Venant s Problem and Semi inverse Solutions

A. Mielke : On Saint - Venant's Problem for an Elastic Strip , Arch . Rat . Mech . Anal , submitted . 14. R.G. Muncaster : Saint - Venant's Problem in ...

Author: Alexander Mielke

Publisher:

ISBN: CORNELL:31924074844212

Category:

Page: 44

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Advances in Applied Mechanics

He also considered the cross-sectional eigenvalue problems associated with ... When the issues underlying Saint-Venant's principle are examined in the ...

Author:

Publisher: Academic Press

ISBN: 0080564011

Category: Technology & Engineering

Page: 453

View: 343

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Advances in Applied Mechanics
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The Elastical Researches of Barr de Saint Venant

This particular problem in torsion has been termed by Clebsch : Das de Saint - Venantsche Problem ( Theorie der Elasticität , S. 74 ) , and following him we ...

Author: Isaac Todhunter

Publisher:

ISBN: WISC:89046271375

Category: Elasticity

Page: 296

View: 667

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Classical and Generalized Models of Elastic Rods

The importance of Saint-Venant's celebrated memoirs [291,292] on what has long since become known as Saint-Venant's problem requires no emphasis.

Author: D. Iesan

Publisher: CRC Press

ISBN: 1420086502

Category: Science

Page: 380

View: 768

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Reflecting new developments in the study of Saint-Venant’s problem, Classical and Generalized Models of Elastic Rods focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material. The author presents a method to construct Saint-Venant’s solutions, minimum energy characterizations of these solutions, and a proof of Saint-Venant’s principle. He then discusses the deformation of nonhomogenous and isotropic cylinders as well as the problem of loaded anisotropic elastic cylinders. The book also deals with the deformation of cylinders within the linearized theory of homogeneous Cosserat elastic solids, the deformation of nonhomogeneous Cosserat cylinders, and the extension, bending, and torsion of porous elastic cylinders. With numerous results not found in related texts, this book provides a unique, unified point of view in the theory of the deformation of elastic cylinders.
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Nonlinear Analysis and Continuum Mechanics

[29] Maisonneuve, O. Sur le Principe de Saint-Venant. These d'Etat, Université de Poitiers, March 1971. [30] Mielke, A. Saint-Venant's problem and ...

Author: Giuseppe Butazzo

Publisher: Springer Science & Business Media

ISBN: 9781461221968

Category: Technology & Engineering

Page: 148

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The chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations.
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Analysis and Design of Elastic Beams

The elasticity problem of torsion as formulated by Saint-Venant is the subject of this chapter. A finite element formulation, which defines a numerical ...

Author: Walter D. Pilkey

Publisher: John Wiley & Sons

ISBN: 0471423211

Category: Technology & Engineering

Page: 480

View: 539

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State-of-the-art coverage of modern computational methods for the analysis and design of beams Analysis and Design of Elastic Beams presents computer models and applications related to thin-walled beams such as those used in mechanical and aerospace designs, where thin, lightweight structures with high strength are needed. This book will enable readers to compute the cross-sectional properties of individual beams with arbitrary cross-sectional shapes, to apply a general-purpose computer analysis of a complete structure to determine the forces and moments in the individual members, and to use a unified approach for calculating the normal and shear stresses, as well as deflections, for those members' cross sections. In addition, this book augments a solid foundation in the basic structural design theory of beams by: * Providing coverage of thin-wall structure analysis and optimization techniques * Applying computer numerical methods to classical design methods * Developing computational solutions for cross-sectional properties and stresses using finite element analyses Including access to an associated Web site with software for the analysis and design of any cross-sectional shape, Analysis and Design of Elastic Beams: Computational Methods is an essential reference for mechanical, aerospace, and civil engineers and designers working in the automotive, ship, and aerospace industries in product and process design, machine design, structural design, and design optimization, as well as students and researchers in these areas.
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Mechanics of Micropolar Media

18 ) Iesan , D. , " On Saint - Venant's Problem in Micropolar Elasticity , " Int . J. Engng . Sci . , 9 ( 1971 ) 879 . 19 ) Iesan , D. , " Flexure of ...

Author: Olof Brulin

Publisher: World Scientific

ISBN: 9971950022

Category: Science

Page: 478

View: 649

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This book is essentially made up of the lecture notes delivered by seven authors at the International Centre for Mechanical Sciences in Udine in June 1979. It attempts to provide an up-to-date and concise summary of the authors' understanding of micropolar materials. Both asymmetric elasticity and fluids are covered. The chapters range from the discussion of micropolar molecular models to the analysis of structure models, from linear to nonlinear theories and from electromagnetic, thermal, viscous effects to lattice defects. The subjects are treated from both theoretical and experimental points of view. Students with physics, mathematics and mechanical backgrounds as well as professionals will find this treatise useful for study and reference.
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Theory of Elasticity

402 6 Saint-Venant's problem 409 6.1 The state of stress . ... 411 6.1.4 Normal stress a 2 in Saint-Venant's problem . . . . . 412 6.1.5 Shear stresses Tr2 ...

Author: A.I. Lurie

Publisher: Springer Science & Business Media

ISBN: 3540264558

Category: Technology & Engineering

Page: 1050

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The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.
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III European Conference on Computational Mechanics

Solids, Structures and Coupled Problems in Engineering: Book of Abstracts ... the relaxed SaintVenant's problem in the linear theory of elastic shells made ...

Author: C. A. Mota Soares

Publisher: Springer Science & Business Media

ISBN: 9781402053702

Category: Technology & Engineering

Page: 788

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III European Conference on Computational Mechanics: Solids, Structures and Coupled Problem in Engineering Computational Mechanics in Solid, Structures and Coupled Problems in Engineering is today a mature science with applications to major industrial projects. This book contains the edited version of the Abstracts of Plenary and Keynote Lectures and Papers, and a companion CD-ROM with the full-length papers, presented at the III European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering (ECCM-2006), held in the National Laboratory of Civil Engineering, Lisbon, Portugal 5th - 8th June 2006. The book reflects the state-of-art of Computation Mechanics in Solids, Structures and Coupled Problems in Engineering and it includes contributions by the world most active researchers in this field.
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Mathematical Theory of Elasticity

With respect to ( a ) torsion , Saint - Venant's problem ( see later ) was treated not by the semi - inverse method , but by considering a mathematical ...

Author: Richa Hetnarski

Publisher: CRC Press

ISBN: 0203502485

Category: Mathematics

Page: 800

View: 540

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The purpose of this book is to present Mathematical Theory of Elasticity and its applications to a wide range of readers, including graduate students and researchers in modern theory of continuum mechanics. The book provides classical results on elasticity as well as the new findings of classical type obtained in recent years by various researchers
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Structural Analysis

3.2 Saint-Venant 1855, 1856, 1864 Navier has not, of course, ... The first deals with what has come to be known as 'Saint-Venant's problem', ...

Author: Jacques Heyman

Publisher: Cambridge University Press

ISBN: 0521622492

Category: Technology & Engineering

Page: 174

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A concise, historical review of the methods of structural analysis and design - from Galileo in the seventeenth century, to the present day.
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Non Classical Elastic Solids

5.4 Saint - Venant's problem . Over an ( a ) Preliminaries . Saint - Venant's problem in classical elasticity consists in determining the equilibrium of an ...

Author: Michele Ciarletta

Publisher: CRC Press

ISBN: 9781000115260

Category: Mathematics

Page: 360

View: 961

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Problems concerning non-classical elastic solids continue to attract the attention of mathematicians, scientists and engineers. Research in this area addresses problems concerning many substances, such as crystals, polymers, composites, ceramics and blood. This comprehensive, accessible work brings together recent research in this field, and will be of great interest to mathematicians, physicists and other specialists working in this area.
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