LEADER 05231nam 2200661 a 450 001 9910826606903321 005 20240404153807.0 010 $a1-282-75812-8 010 $a9786612758126 010 $a981-4273-73-2 035 $a(CKB)2490000000001656 035 $a(EBL)1681613 035 $a(OCoLC)729020097 035 $a(SSID)ssj0000421017 035 $a(PQKBManifestationID)12147331 035 $a(PQKBTitleCode)TC0000421017 035 $a(PQKBWorkID)10407879 035 $a(PQKB)10530152 035 $a(WSP)00000559 035 $a(Au-PeEL)EBL1681613 035 $a(CaPaEBR)ebr10422301 035 $a(CaONFJC)MIL275812 035 $a(MiAaPQ)EBC1681613 035 $a(EXLCZ)992490000000001656 100 $a20100517d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to mathematical elasticity /$fLeonid P. Lebedev, Michael J. Cloud 205 $a1st ed. 210 $aHackensack, N.J. $cWorld Scientific$dc2009 215 $a1 online resource (317 p.) 300 $aDescription based upon print version of record. 311 $a981-4273-72-4 320 $aIncludes bibliographical references and index. 327 $aContents; Foreword; Preface; Some Notation; 1. Models and Ideas of Classical Mechanics; 1.1 Orientation; 1.2 Some Words on the Fundamentals of Our Subject; 1.3 Metric Spaces and Spaces of Particles; 1.4 Vectors and Vector Spaces; 1.5 Normed Spaces and Inner Product Spaces; 1.6 Forces; 1.7 Equilibrium and Motion of a Rigid Body; 1.8 D'Alembert's Principle; 1.9 The Motion of a System of Particles; 1.10 The Rigid Body; 1.11 Motion of a System of Particles; Comparison of Trajectories; Notion of Operator; 1.12 Matrix Operators and Matrix Equations; 1.13 Complete Spaces; 1.14 Completion Theorem 327 $a1.15 Lebesgue Integration and the Lp Spaces1.16 Orthogonal Decomposition of Hilbert Space; 1.17 Work and Energy; 1.18 Virtual Work Principle; 1.19 Lagrange's Equations of the Second Kind; 1.20 Problem of Minimum of a Functional; 1.21 Hamilton's Principle; 1.22 Energy Conservation Revisited; 2. Simple Elastic Models; 2.1 Introduction; 2.2 Two Main Principles of Equilibrium and Motion for Bodies in Continuum Mechanics; 2.3 Equilibrium of a Spring; 2.4 Equilibrium of a String; 2.5 Equilibrium Boundary Value Problems for a String 327 $a2.6 Generalized Formulation of the Equilibrium Problem for a String2.7 Virtual Work Principle for a String; 2.8 Riesz Representation Theorem; 2.9 Generalized Setup of the Dirichlet Problem for a String; 2.10 First Theorems of Imbedding; 2.11 Generalized Setup of the Dirichlet Problem for a String, Continued; 2.12 Neumann Problem for the String; 2.13 The Generalized Solution of Linear Mechanical Problems and the Principle of Minimum Total Energy; 2.14 Nonlinear Model of a Membrane; 2.15 Linear Membrane Theory: Poisson's Equation 327 $a2.16 Generalized Setup of the Dirichlet Problem for a Linear Membrane2.17 Other Membrane Equilibrium Problems; 2.18 Banach's Contraction Mapping Principle; 3. Theory of Elasticity: Statics and Dynamics; 3.1 Introduction; 3.2 An Elastic Bar Under Stretching; 3.3 Bending of a beam; 3.4 Generalized Solutions to the Equilibrium Problem for a Beam; 3.5 Generalized Setup: Rough Qualitative Discussion; 3.6 Pressure and Stresses; 3.7 Vectors and Tensors; 3.8 The Cauchy Stress Tensor, Continued; 3.9 Basic Tensor Calculus in Curvilinear Coordinates; 3.10 Euler and Lagrange Descriptions of Continua 327 $a3.11 Strain Tensors3.12 The Virtual Work Principle; 3.13 Hooke's Law in Three Dimensions; 3.14 The Equilibrium Equations of Linear Elasticity in Displacements; 3.15 Virtual Work Principle in Linear Elasticity; 3.16 Generalized Setup of Elasticity Problems; 3.17 Existence Theorem for an Elastic Body; 3.18 Equilibrium of a Free Elastic Body; 3.19 Variational Methods for Equilibrium Problems; 3.20 A Brief but Important Remark; 3.21 Countable Sets and Separable Spaces; 3.22 Fourier Series; 3.23 Problem of Vibration for Elastic Structures; 3.24 Self-Adjointness of A and Its Consequences 327 $a3.25 Compactness of A 330 $a 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 principl 606 $aElasticity 615 0$aElasticity. 676 $a531.382 676 $a531.3820151 676 $a531/.3820151 700 $aLebedev$b L. P$01089225 701 $aCloud$b Michael J$041158 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826606903321 996 $aIntroduction to mathematical elasticity$94026048 997 $aUNINA