Basic Principles of Plate Theory - Brossura

Lowe, P. G.

Brossura

ISBN 10: 0903384256 ISBN 13: 9780903384254

Casa editrice: Springer, 2013

Riassunto

My interest in plate theory extends back many years to the energetic and stimulating discussions with my supervisor, Professor R.

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Contenuti

1. Preliminaries.- 1.0 Motivation.- 1.1 Vectors—algebra.- 1.2 Vectors—calculus.- 1.3 Matrices.- 1.4 Statics—equilibrium.- 1.5 Summation convention and index notation.- 1.6 Elements of beam theory.- 1.7 Conclusions.- 2. Statics and Kinematics of Plate Bending.- 2.0 Introduction.- 2.1 The stress resultants.- 2.2 Principal values.- 2.3 The moment circle.- 2.4 Equilibrium equations—rectangular coordinates.- 2.5 Plate bending kinematics—rectangular coordinates.- 2.6 Equilibrium equations—polar coordinates—radial symmetry.- 2.7 Plate bending kinematics—polar coordinates—radial symmetry.- 2.8 Conclusions.- 3. Elastic Plates.- 3.0 Introduction.- 3.1 Elastic theory of plate bending—moment/curvature relations.- 3.2 Elastic theory of plate bending—governing equation.- 3.3 Circular plates—radial symmetry.- 3.4 Some simple solutions for circular plates.- 3.5 Simple solutions for problems in rectangular coordinates.- 3.6 Further separation of variable features—rectangular plates.- 3.7 Solution by finite differences.- 3.8 Some other aspects of plate theory.- 3.9 Stability of plates.- 3.10 Conclusions.- 4. Plastic Plates.- 4.0 Introduction.- A. Solid metal plates.- 4.1 Yield criteria.- 4.2 The bound theorems.- 4.3 The normality rule.- 4.4 Circular plates—square yield locus.- 4.5 Circular plates—Tresca yield locus.- 4.6 Plates of other shapes—square and regular shapes.- B. Reinforced concrete plates.- 4.7 Yield line theory—I. Fundamentals.- 4.8 Yield line theory—II. Further isotropic examples.- 4.9 Yield line theory—III. Orthotropic problems.- 4.10 Hillerborg strip theory.- 4.11 Conclusions.- 5. Optimal Plates.- 5.0 Introduction.- 5.1 Problem formulation.- 5.2 Constant curvature surfaces and principal directions.- 5.3 Basic results—corners.- 5.4 Some complete results.- 5.5 Moment volumes.- 5.6 Some theory.- 5.7 Conclusions.- 5.8 Exercises.- 6. Bibliography and Exercises.- 6.0 Bibliography.- 6.1 Exercises.- Appendix Geometry of Surfaces.- A.0 The need for geometry.- A.1 Geometry of a plane curve—curvature.- A.2 Length measurement on a surface—first fundamental form.- A.3 The normal to a surface.- A.4 Normal curvature—second fundamental form.- A.5 The derivatives of n—the Weingarten equations.- A.6 Directions on a surface.- A.7 The principal curvatures.- A.8 Principal directions.- A.9 Curvature and twist along the coordinate lines.- A.10 The curvature matrix.- A.11 The curvature circle.- A.12 Continuity requirements.- A.13 Special surfaces.- A.14 Summary—the geometrical quantities required for the construction of a plate theory.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 0903384256
• ISBN 13: 9780903384254
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 192
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania