Download or read book Uniqueness Theorems in Linear Elasticity written by Robin J. Knops and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.
Download or read book Uniqueness Theorems in Linear Elasticity by R J Knops and L E Payne written by Robin John Knops and published by . This book was released on 1971 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Uniqueness Theorems in the Theory of Elasticity written by James H. Bramble and published by . This book was released on 1961 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that in the first boundary value problem of classical elasticity the range of values of Poisson's ratio for which the solution is unique may be extended to include values outside the range of physical interest. It is shown that certain other interesting boundary value problems in classical elasticity have unique solutions for an extended range of values of Poisson's ratio. Such results may prove useful in non-linear elasticity.
Download or read book Boundary Value Problems of Finite Elasticity written by Tullio Valent and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub sequent developments.
Download or read book Qualitative Estimates For Partial Differential Equations written by J N Flavin and published by CRC Press. This book was released on 2020-12-17 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry. The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research. Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.
Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elasticity and Geomechanics written by R. O. Davis and published by Cambridge University Press. This book was released on 1996-04-26 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise examination of the use of elasticity in solving geotechnical engineering problems.
Download or read book Weighted Energy Methods in Fluid Dynamics and Elasticity written by Giovanni P. Galdi and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second book of a three-volume set, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. Theory of Plates also illustrates how asymptotic methods allow for justification of the Kirchhoff–Love theory of nonlinear elastic plates and presents a detailed mathematical analysis of the von Kármán equations. 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.
Download or read book Mathematical Elasticity written by and published by Elsevier. This book was released on 1997-07-22 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Mathematical Elasticity written by Michael J. Cloud and published by World Scientific. This book was released on 2009 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability. Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems. Sample Chapter(s). Foreword (46 KB). Chapter 1: Models and Ideas of Classical Mechanics (634 KB). Contents: Models and Ideas of Classical Mechanics; Simple Elastic Models; Theory of Elasticity: Statics and Dynamics. Readership: Academic and industry: mathematicians, engineers, physicists, students advanced undergraduates in the field of engineering mechanics.
Download or read book Nonlinear Functional Analysis and its Applications written by E. Zeidler and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 1007 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
Download or read book Uniqueness Theorems in Linear Elastostatics for Unbounded Bodies written by Kenneth Bruce Howell and published by . This book was released on 1978 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thermoelastic Models of Continua written by D. Iesan and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with the basic problems of the theory of thermoelasticity for three models of continuous bodies: materials with voids, micropolar solids and nonsimple bodies. Beginning with the basic laws of thermodynamics, the theory of thermoelastic materials with voids is treated. Two subsequent chapters cover the analysis of the linear theory of micropolar thermoelastic bodies. The book concludes with a study of nonsimple thermoelastic materials, which are characterised by the inclusion of higher gradients of displacement in the basic postulates. Relevant examples and exercises which illustrate the theory are given throughout the text. The book should be of interest to mathematicians and specialists working in the fields of elasticity, thermoelasticity, civil engineering and geophysics.
Download or read book Mechanics Today written by S. Nemat-Nasser and published by Elsevier. This book was released on 2014-05-09 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics Today, Volume 5 contains some of the papers presented at a symposium to honor Eric Reissner, held at the University of California in San Diego, on June 23, 1978, under the sponsorship of the Office of Naval Research. The symposium provided a forum for discussing various topics related to mechanics, from the pseudo-elasticity of living tissues and compression of spherical cells to kinematically unstable space frameworks. Reissner's equations for sandwich plates are also considered. Comprised of 36 chapters, this volume begins with an analysis of the state of stress near the boundary of a thick plate by means of "end solutions" obtained from Reissner's sheaf deformation plate theory. A deformable primary reflecting surface composed of an array of relatively small diameter circular elements is then described. The discussion then turns to the "Taylor instability" of the surface of an elastic-plastic plate; free vibration spectrum structure of a shell of revolution; and the momentum-balance method in earthquake engineering. Subsequent chapters focus on the intrinsic equations of shell theory with some applications; stress analysis in plasticity; density-wave theory of the spiral structure of galaxies; and a mixture theory for wave propagation in anisotropic angle-ply laminates. This book will be of interest to engineers and physicists.
Download or read book Model Validation and Uncertainty Quantification Volume 3 written by Zhu Mao and published by Springer Nature. This book was released on 2020-10-27 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty
Download or read book Non Classical Elastic Solids written by Michele Ciarletta and published by CRC Press. This book was released on 1993-10-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
