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Author Kostin, Georgy V
Title Integrodifferential Relations in Linear Elasticity
Imprint Berlin/Boston : De Gruyter, Inc., 2012
©2012
book jacket
Descript 1 online resource (280 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series De Gruyter Studies in Mathematical Physics Ser. ; v.10
De Gruyter Studies in Mathematical Physics Ser
Note Intro -- Preface -- 1 Introduction -- 2 Basic concepts of the linear theory of elasticity -- 2.1 Stresses -- 2.2 Linearstrains -- 2.3 Constitutive relations -- 2.4 Boundary value problems -- 2.4.1 Static statements -- 2.4.2 Dynamic problems -- 2.5 Simplified models -- 2.5.1 Elastic rods and strings -- 2.5.2 Beam models -- 2.5.3 Membranes -- 2.5.4 Plane stress and strain states -- 3 Conventional variational principles -- 3.1 Classical variational approaches -- 3.1.1 Energy relations -- 3.1.2 Direct principles -- 3.1.3 Complementary principles -- 3.2 Variational principles in dynamics -- 3.3 Generalized variational principles -- 3.3.1 Relations among variational principles -- 3.3.2 Semi-inverse approach -- 3.4 Finite dimensional discretization -- 3.4.1 Ritz method -- 3.4.2 Galerkin method -- 3.4.3 Finite element method -- 3.4.4 Boundary element method -- 4 The method of integrodifferential relations -- 4.1 Basic ideas -- 4.1.1 Analytical solutions in linear elasticity -- 4.1.2 Integral formulation of Hooke's law -- 4.2 Family of quadratic functionals -- 4.3 Ritz method in the MIDR -- 4.3.1 Algorithm of polynomial approximations -- 4.3.2 2D clamped plate - static case -- 4.4 2D natural vibrations -- 4.4.1 Eigenvalue problem -- 4.4.2 Free vibrations of circular and elliptic membranes -- 5 Variational properties of the integrodifferential statements -- 5.1 Variational principles for quadratic functionals -- 5.2 Relations with the conventional principles -- 5.3 Bilateral energy estimates -- 5.4 Body on an elastic foundation -- 5.4.1 Variational principle for the energy error functional -- 5.4.2 Bilateral estimates -- 6 Advance finite element technique -- 6.1 Piecewise polynomial approximations -- 6.2 Smooth polynomial splains -- 6.2.1 Argyris triangle -- 6.2.2 Stiffness matrix for the Argyris triangle -- 6.2.3 C2 approximations for a triangle element
6.3 Finite element technique in linear elasticity problems -- 6.4 Mesh adaptation and mesh refinement -- 7 Semi-discretization and variational technique -- 7.1 Reduction of PDE system to ODEs -- 7.1.1 Beam-oriented notation -- 7.1.2 Semi-discretization in the displacements -- 7.1.3 Semi-discretization in the stresses -- 7.2 Analysis of beam stress-strain state -- 7.3 2D elastic beam vibrations -- 8 An asymptotic approach -- 8.1 Classical variational approach -- 8.2 Integrodifferential approach -- 8.2.1 Basic ideas of asymptotic approximations -- 8.2.2 Beam equations - general case of loading -- 8.3 Elastic beam vibrations -- 8.3.1 Statement of an eigenvalue problem -- 8.3.2 Longitudinal vibrations -- 8.3.3 Lateral vibrations -- 8.4 3D static problem -- 9 A projection approach -- 9.1 Projection formulation of linear elasticity problems -- 9.2 Projections vs. variations and asymptotics -- 10 3D static beam modeling -- 10.1 Projection algorithms -- 10.2 Cantilever beam with the triangular cross section -- 10.3 Projection beam model -- 10.4 Characteristics of a beam with the triangular cross section -- 11 3D beam vibrations -- 11.1 Integral projections in eigenvalue problems -- 11.2 Natural vibrations of a beam with the triangular cross section -- 11.3 Forced vibrations of a beam with the triangular cross section -- A Vectors and tensors -- B Sobolev spaces -- Bibliography -- Index
This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements.It also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Kostin, Georgy V. Integrodifferential Relations in Linear Elasticity Berlin/Boston : De Gruyter, Inc.,c2012 9783110270303
Subject Elasticity.;Plasticity.;Integro-differential equations
Electronic books
Alt Author Saurin, Vasily V
Efroimsky, Michael
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