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matrix and tensor analysis of elastic continua
1 online resource (v, 203 pages) : illustrations.
This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approachUses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis.
Front Cover; About the Author; Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua; Copyright Page; Table of Contents; Chapter 1. Matrix methods; 1.1 Summary of matrix properties; 1.2 Vector representation; 1.3 Coordinate transformation; 1.4 Differential operators; 1.5 The strain matrix; 1.6 The stress matrix; 1.7 Isotropic elasticity; 1.8 Linear anisotropic behaviour; 1.9 Engineering theory of beams; 1.10 Engineering theory of plates; 1.11 Applications and worked examples; Problems; Chapter 2. Cartesian tensors; 2.1 Vector and matrix representation.
2.2 Coordinate transformation2.3 Differentiation; 2.4 Representation of strain; 2.5 Representation of stress; 2.6 Thermoelastic behaviour; 2.7 Isotropic materials; 2.8 Applications and worked examples; Problems; Chapter 3. Curvilinear tensors; 3.1 Base vectors; 3.2 Metric tensors; 3.3 Higher order tensors; 3.4 Vector products; 3.5 Orthogonal coordinate systems; 3.6 Covariant differentiation; 3.7 Strain and stress tensors; 3.8 Elastic behaviour; 3.9 Membrane theory of thin shells; 3.10 Applications and worked examples; Problems; Chapter 4. Large deformation theory.
4.1 Lagrangean and Eulerian strain4.2 Material coordinates; 4.3 The state of stress; 4.4 Elementary solutions; 4.5 Incompressible materials; 4.6 Stability of continua; Problems; Appendix A1: Formulae for orthogonal coordinate systems; A1.1 Cylindrical coordinates; A1.2 Spherical coordinates; A1.3 Curvilinear anisotropy; Appendix A2: Harmonic and biharmonic functions; A2.1 The two-dimensional case; A2.2 The three-dimensional case; Appendix A3: Equations in vector form; A3.1 The Papkovich-Neuber functions; A3.2 The wave equations; A3.3 Gradient, divergence and curl for curvilinear coordinates.
A3.4 The cone problemAppendix A4: Direct tensor notation; Appendix A5: Polar decomposition; Appendix A6: Cosserat continua and micropolar elasticity; Appendix A7: Minimal curves and geodesics; A7.1 Minimal curves; A7.2 Geodesics; A7.3 Relativity; Answers to problems; Further reading and references; Index.
Includes bibliographical references (pages 198-200) and index.
With bibliographical references and index.
Applied Elasticity : Matrix And Tensor Analysis Of Elastic Continua
Woodhead Publishing series in civil and structural engineering