Download or read book Solving the Second Boundary Value Problem of Elasticity written by Ronald O. Hultgren and published by . This book was released on 1965 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality.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 Some Basic Problems of the Mathematical Theory of Elasticity written by N.I. Muskhelishvili and published by Springer Science & Business Media. This book was released on 1977-04-30 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: TO THE FIRST ENGLISH EDITION. In preparing this translation, I have taken the liberty of including footnotes in the main text or inserting them in small type at the appropriate places. I have also corrected minor misprints without special mention .. The Chapters and Sections of the original text have been called Parts and Chapters respectively, where the latter have been numbered consecutively. The subject index was not contained in the Russian original and the authors' index represents an extension of the original list of references. In this way the reader should be able to find quickly the pages on which anyone reference is discussed. The transliteration problem has been overcome by printing the names of Russian authors and journals also in Russian type. While preparing this translation in the first place for my own informa tion, the knowledge that it would also become accessible to a large circle of readers has made the effort doubly worthwhile. I feel sure that the reader will share with me in my admiration for the simplicity and lucidity of presentation.
Download or read book An Inverse Boundary Value Problem in Linear Elasticity written by Robert L. Robertson and published by . This book was released on 1996 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Uniqueness Problem in the Second Boundary Value Problem in Elasticity written by James H. Bramble and published by . This book was released on 1961 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kirchhoff's uniqueness proof shows that, if the shear modulus is different from zero and Poisson's ratio T lies in the interval ( -1, 1/2), the second boundary value problem in elasticity (surface tractions prescribed) has a unique solution (up to a rigid body motion). A demonstration is given that for general domains uniqueness holds provided T lies in the interval ( -1, 1-K/2(1 + K)), where K is a constant depending on the geometry of the region. If the bounding surface is star shaped, K is equal to zero.
Download or read book Topics in Finite Elasticity written by Morton E. Gurtin and published by SIAM. This book was released on 1981-09-01 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a derivation of the basic equations of the theory of finite elasticity.
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 Selected Problems of Solid Mechanics and Solving Methods written by Holm Altenbach and published by Springer Nature. This book was released on with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Solution of a Boundary Value Problem in the Mathematical Theory of Elasticity by Means of Complex Potentials written by Jess Dale Armstrong and published by . This book was released on 1953 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mixed Boundary Problems in Solid Mechanics written by Natalya Vaysfeld and published by Springer Nature. This book was released on 2023-09-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers a wide range of subjects and techniques related to mixed boundary problems of elasticity from basic concepts to special techniques that are unlikely to appear in traditional university graduate courses. This book may also be of interest to industrial researchers who encounter defects such as cracks and inclusions of different materials in mechanisms under different localization and type of loading. So the topics present the application of mathematical mechanics of solid bodies notably in elasticity, showing the interconnection of elasticity and temperature that would normally treated independently. Theoretical and experimental results are expected to be useful for researchers investigating a wide range of materials including metals, composites, ceramics, polymers, biomaterials and nanomaterials under different mechanical and temperature loading. The aim of the book is to introduce an interdisciplinary audience to a variety of stress state phenomena occurring in elasticity near defects and edges of the bodies. The book is aimed at researchers, primarily but not exclusively graduate students, postdoctoral researchers, specialists from Aerospace and Civil Engineering, Materials Science, and Engineering Mechanics and should naturally also be of interest to specialists of Physics and Applied Mathematics.
Download or read book Mathematical Theory of Elasticity written by Ivan Stephen Sokolnikoff and published by . This book was released on 1941 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Mixed Boundary Value Problems in the Linear Theory of Elasticity written by Ian Naismith Sneddon and published by . This book was released on 1979 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Solution of the Two dimensional Theory of Elasticity for an Orthotropic Rectangular Plate written by Yu P. Kochanov and published by . This book was released on 1969 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A single form of the solution of the two-dimensional problem of stresses for orthotropic rectangular plates is constructed. Unlike other solutions, it is applicable under general boundary conditions at the contour of the plate. It is assumed that body forces are absent and that the principal directions of the plate coincide with the Ox and Oy axes. The usual equations are used for the two-dimensional stressed state. The solution of the first boundary value problem of elasticity theory is used as an illustration. Formulas are obtained that allow the unknown coefficients to be determined as functions of the known coefficients of Fourier series for the external forces at the contour of the plate. The formulas allow complete solution of the first boundary value problem. The second boundary problem and diverse mixed problems can be reduced to solution of infinite systems of linear algebraic equations. (Author).
Download or read book Applications of Doubly Quasi periodic Boundary Value Problems in Elasticity Theory written by Li Xing and published by . This book was released on 2001-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Ordinary and Partial Boundary Value Problems in Science and Engineering written by Karel Rektorys and published by CRC Press. This book was released on 1998-10-20 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.
Download or read book Some Basic Problems of the Mathematical Theory of Elasticity written by Nikolaĭ Ivanovich Muskhelishvili and published by . This book was released on 1953 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vibrations of Hollow Elastic Bodies written by Magomed F. Mekhtiev and published by Springer. This book was released on 2018-02-02 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the justification and refinement of highly diverse approximate dynamic models for engineering structures arising in modern technology, including high-tech domains involving nano- and meta-materials. It proposes a classification for vibration spectra over a broad frequency domain and evaluates the range of validity of various existing 2D theories for thin-walled shells by comparing them with 3D benchmark solutions. The dynamic equations in 3D elasticity are applied to the analysis of harmonic vibrations in hollow bodies with canonical shapes. New exact homogeneous and inhomogeneous solutions are derived for cylinders, spheres and cones (including spherical and conical layers), as well as for plates of variable thickness. The book includes a wealth of numerical examples, as well as refined versions of 2D dynamic formulations. Boundary value problems for hollow bodies are also addressed.
