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Author:   F. Hartmann
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Weight:   0.820kg
ISBN:  

9783540150022

ISBN 10:   3540150021
Pages:   383
Publication Date:   01 May 1985
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

1 Fundamentals.- 1.1 Vectors and Matrices.- 1.2 Differentiation.- 1.3 Domains.- 1.4 Integrals.- 1.5 Integration by Parts.- 1.6 Gateaux Differentials.- 1.7 Functionals.- 1.8 Sobolev Spaces.- 1.9 The Differential Equations.- 1.9.1 The Straight Slender Frame Element.- 1.9.1.1 The Axial Displacement u (x).- 1.9.1.2 The Rotation ? (x) of a (circular) bar.- 1.9.1.3 The Lateral and Vertical Deflections v and w.- 1.9.1.4 Shear Deformations.- 1.9.2 The Kirchhoff Plate.- 1.9.3 The Elastic Body.- 1.9.4 Elastic Plates.- 1.9.5 The Membrane.- 1.9.6 Reissner's Plate.- 2 Work and Energy.- 2.1 Integral Identities.- 2.1.1 The Beam.- 2.1.2 The Kirchhoff Plate.- 2.1.3 The Elastic Plate and Body.- 2.2 Summary.- 2.3 Three Corollaries.- 2.4 A Beam.- 2.4.1 Principle of Virtual Displacements.- 2.4.2 Principle of Virtual Forces.- 2.4.3 Betti's Principle.- 2.5 Eigenwork = Internal Energy.- 2.6 Equilibrium.- 2.7 Summation of Work and Energy.- 2.8 Rigid Supports and free Boundaries.- 2.9 Elastic Supports.- 2.10 The Mathematical Basis of Structural Mechanics.- 2.11 The Space $${C^{2m}}(\bar \Omega)$$ and its Limitations.- 3 Continuous Beams, Trusses and Frames.- 3.1 Continuous Beams.- 3.2 Trusses.- 3.3 Frames.- 3.3.1 The Method of Reduction.- 3.4 Stiffness Matrices.- 3.4.1 The Axial Displacement.- 3.4.2 Shear Deformations.- 3.4.3 Rotation.- 3.4.4 Deflections v and w.- 4 Energy Principles.- 4.1 The Basic Principle.- 4.2 Examples.- 4.2.1 An Elastic Plate.- 4.2.2 A Bar.- 4.2.3 A Cantilever Beam.- 4.2.4 A Beam on a Spring.- 4.2.5 A Kirchhoff Plate.- 4.3 The Principle of Minimum Potential Energy.- 4.4 The Complementary Principle.- 4.5 The Formulation of ?1 (u) and ?2 (u).- 4.6 The Sign of the Total Energy.- 4.7 The Point ? (w) and the Classes R1 and R2.- 4.8 Displacement Method and Force Method.- 4.9 Energy Principles for Cont. Beams, Trusses and Frames.- 4.10 The Formulation of the Functional by hand .- 4.11 Lagrange Multipliers.- 4.12 The Algebra of Structural Mechanics.- 5 Concentrated Forces.- 5.1 Fundamental Solutions.- 5.1.1 The Bar, - EAd2/dy2.- 5.1.2 The Beam, EId4/dy4.- 5.1.3 The Kirchhoff Plate, K??w.- 5.1.4 The Elastic Plate and the Elastic Body.- 5.1.5 Summary.- 5.2 Fundamental Solutions and Integral Identities.- 5.3 Results.- 5.3.1 Bars.- 5.3.2 Beams.- 5.3.3 The Kirchhoff Plate.- 5.3.4 Elastic Plates and Bodies.- 5.4 Summary.- 5.5 An Extension.- 5.6 Theorems eigenwork = int. energy .- 5.7 The Characteristic Functions.- 5.7.1 Their Origin.- 5.7.2 A Mechanical Interpretation.- 5.7.3 Integral Representation of c(x).- 5.8 An Alternative.- 5.9 Castigliano's Theorem.- 5.10 Castigliano's Generalized Theorem.- 5.11 Concentrated Forces or Disturbances on the Boundary.- 6 Influence Functions.- 6.1 Integral Representations.- 6.1.1 The Bar, - EAd2/dy2.- 6.1.2 The Beam, Eld4/dy4.- 6.1.3 The Kirchhoff Plate.- 6.1.4 Elastic Plates and Bodies.- 6.1.5 The Integral Representation of ?w(x)/?n.- 6.2 Green's function.- 6.3 Compatibility on the Boundary.- 6.3.1 The Order of the Integral Operators.- 6.3.2 The Essential Compatibility Conditions.- 6.4 Summary.- 6.4.1 Bars.- 6.4.2 Beams.- 6.4.3 Kirchhoff Plates.- 6.4.4 Elastic Plates and Bodies.- 6.5 An Example.- 6.6 Stiffness Matrices and Compatibility Conditions.- 6.7 The Boundary Element Method.- 6.8 The Trace Theorem.- 6.9 Elastic Potentials.- 7 The Operators A.- 7.1 The Systems.- 7.1.1 Bars.- 7.1.2 Elastic Plates and Bodies.- 7.1.3 Beams.- 7.1.4 Kirchhoff Plates.- 7.2 Identities.- 7.2.1 Elastic Plates and Bodies.- 7.2.2 Kirchhoff Plates.- 7.2.3 Bars.- 7.2.4 Beams.- 7.3 Energy Principles.- 7.3.1 Elastic Plates and Bodies.- 7.4 Sufficient Conditions.- 7.5 Other Mixed Formulations.- 7.6 The Babuska-Brezzi Condition.- 8 Shells.- 8.1 Shells as Surfaces.- 8.2 Statics.- 8.3 Koiter's Model.- 8.4 The first Identity.- 9 Second-Order Analysis.- 9.1 Beams.- 9.2 Stability.- 9.3 Lateral Buckling of Beams.- 9.4 The Kirchhoff Plate.- 9.5 Nonconservative Problems.- 9.6 Initial Value Problems.- 9.7 Vibrations.- 9.8 Hamilton's Principle.- 10 Nonlinear Theory of Elasticity.- 10.1 The Differential Equations.- 10.2 The first Identity.- 10.3 Energy Principles.- 10.4 Incremental Procedures.- 10.5 Large Displacement Analysis of Beams.- 10.6 Large Displacement Analysis of Plates.- 10.7 The Principle eigenwork = int. energy .- 10.8 Influence Functions.- 11 Finite Elements.- 11.1 Shape Functions.- 11.2 The Error in Finite Elements.- 11.3 Nonconforming Shape Functions.- 11.4 The Patch Test.- 11.5 Hybrid Energy Principles.- 11.6 Hybrid Energy Principles for Operators A.- 12 References.- 13 Subject Index.

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