Theory of Plasticity

by Chakrabarty

• ISBN13: 9780750666381
• ISBN10: 0750666382
• Edition: 3rd
• Format: Paperback
• Copyright: 2006-04-18
• Publisher: Elsevier Science

Summary

Plasticity is concerned with the mechanics of materials deformed beyond their elastic limit. A strong knowledge of plasticity is essential for engineers dealing with a wide range of engineering problems, such as those encountered in the forming of metals, the design of pressure vessels, the mechanics of impact, civil and structural engineering, as well as the understanding of fatigue and the economical design of structures. Theory of Plasticity is the most comprehensive reference on the subject as well as the most up to date -- no other significant Plasticity reference has been published recently, making this of great interest to academics and professionals. This new edition presents extensive new material on the use of computational methods, plus coverage of important developments in cyclic plasticity and soil plasticity, and is accompanied by a fully worked solutions manual. * A complete plasticity reference for graduate students, researchers and practicing engineers; no other book offers such an up to date or comprehensive reference on this key continuum mechanics subject * Updates with new material on computational analysis and applications, new end of chapter exercises and a worked solutions manual * Plasticity is a key subject in all mechanical engineering disciplines, as well as in manufacturing engineering and civil engineering. Chakrabarty is one of the subject's leading figures.

Table of Contents

Preface to the third edition	ix
Preface to the first edition	xi
1 Stresses and Strains	1	(55)
1.1 Introduction	1	(2)
1.2 The Stress—Strain Behavior	3	(14)
1.3 Analysis of Stress	17	(12)
1.4 Mohr's Representation of Stress	29	(4)
1.5 Analysis of Strain Rate	33	(9)
1.6 Concepts of Stress Rate	42	(5)
Problems	47	(9)
2 Foundations of Plasticity	56	(71)
2.1 The Criterion of Yielding	56	(9)
2.2 Strain-Hardening Postulates	65	(7)
2.3 The Rule of Plastic Flow	72	(9)
2.4 Particular Stress—Strain Relations	81	(11)
2.5 The Total Strain Theory	92	(4)
2.6 Theorems of Limit Analysis	96	(7)
2.7 Uniqueness Theorems	103	(11)
2.8 Extremum Principles	114	(7)
Problems	121	(6)
3 Elastoplastic Bending and Torsion	127	(106)
3.1 Plane Strain Compression and Bending	127	(5)
3.2 Cylindrical Bars Under Torsion and Tension	132	(9)
3.3 Thin-Walled Tubes Under Combined Loading	141	(11)
3.4 Pure Bending of Prismatic Beams	152	(12)
3.5 Bending of Beams Under Transverse Loads	164	(20)
3.6 Torsion of Prismatic Bars	184	(24)
3.7 Torsion of Bars of Variable Diameter	208	(9)
3.8 Combined Bending and Twisting of Bars	217	(6)
Problems	223	(10)
4 Plastic Analysis of Beams and Frames	233	(90)
4.1 Introduction	233	(2)
4.2 Limit Analysis of Beams	235	(8)
4.3 Limit Analysis of Plane Frames	243	(15)
4.4 Displacements in Plane Frames	258	(10)
4.5 Variable Repeated Loading	268	(12)
4.6 Minimum Weight Design	280	(12)
4.7 Influence of Axial Forces	292	(12)
4.8 Limit Analysis of Space Frames	304	(9)
Problems	313	(10)
5 Further Solutions of Elastoplastic Problems	323	(96)
5.1 Expansion of a Thick Spherical Shell	323	(10)
5.2 Expansion of a Thick-Walled Tube	333	(19)
5.3 Thermal Stresses in a Thick-Walled Tube	352	(7)
5.4 Thermal Stresses in a Thick Spherical Shell	359	(9)
5.5 Pure Bending of a Curved Bar	368	(9)
5.6 Rotating Discs and Cylinders	377	(11)
5.7 Infinite Plate with a Circular Hole	388	(13)
5.8 Yielding Around a Cylindrical Cavity	401	(9)
Problems	410	(9)
6 Theory of the Slipline Field	419	(74)
6.1 Formulation of the Plane Strain Problem	419	(7)
6.2 Properties of Slipline Fields and Hodographs	426	(7)
6.3 Stress Discontinuities in Plane Strain	433	(8)
6.4 Construction of Slipline Fields and Hodographs	441	(8)
6.5 Analytical and Matrix Methods of Solution	449	(11)
6.6 Explicit Solutions for Direct Problems	460	(12)
6.7 Some Mixed Boundary-Value Problems	472	(10)
6.8 Superposition of Slipline Fields	482	(7)
Problems	489	(4)
7 Steady Problems in Plane Strain	493	(140)
7.1 Symmetrical Extrusion Through Square Dies	493	(16)
7.2 Unsymmetrical and Multihole Extrusion	509	(10)
7.3 Sheet Drawing Through Tapered Dies	519	(12)
7.4 Extrusion Through Tapered Dies	531	(9)
7.5 Extrusion Through Curved Dies	540	(6)
7.6 Ideal Die Profiles in Drawing and Extrusion	546	(7)
7.7 Limit Analysis of Plane Strain Extrusion	553	(10)
7.8 Cold Rolling of Strips	563	(24)
7.9 Analysis of Hot Rolling	587	(13)
7.10 Mechanics of Machining	600	(19)
Problems	619	(14)
8 Nonsteady Problems in Plane Strain	633	(147)
8.1 Indentation by a Flat Punch	633	(10)
8.2 Indentation by a Rigid Wedge	643	(18)
8.3 Compression of a Wedge by a Flat Die	661	(7)
8.4 Cylindrical Depression in a Large Block	668	(6)
8.5 Compression Between Smooth Platens	674	(11)
8.6 Compression Between Rough Platens	685	(19)
8.7 Yielding of Notched Bars in Tension	704	(10)
8.8 Bending of Single-Notched Bars	714	(15)
8.9 Bending of Double-Notched Bars	729	(8)
8.10 Bending of Beams and Curved Bars	737	(18)
8.11 Large Bending of Wide Sheets	755	(9)
Problems	764	(16)
9 Computational Methods	780	(59)
9.1 Numerical Mathematics	780	(16)
9.2 Finite Difference Method	796	(7)
9.3 Finite Element Discretization	803	(13)
9.4 Finite Element Procedure	816	(11)
9.5 Illustrative Examples	827	(5)
Problems	832	(7)
Appendixes	839	(30)
A Tables on Slipline Fields	839	(13)
B Orthogonal Curvilinear Coordinates	852	(4)
C Fundamentals of Soil Plasticity	856	(13)
Author Index	869	(8)
Subject Index	877