Elsevier S & T

Non-Linear Theory of Elasticity and Optimal Design

Ratner, L.W.

In stock
No reviews
68.500 KD inc. VAT
License
Table of contents
  • Cover
  • Non-linear Theory of Elasticity and Optimal Designiii
  • Copyright Pageiv
  • Contentsvii
  • Prefacev
  • Introduction1
  • Prologue7
  • Part I: Principles and Methods of NLTE11
  • Chapter 1. Practical problems11
  • Chapter 2. Foundations of the non-linear theory of elasticity12
  • 2.1. Summary20
  • 2.2. Recapture21
  • Chapter 3. Devising the non-linear theory of elasticity22
  • 3.1. Summary28
  • Chapter 4. Principles of logic in NLTE29
  • Chapter 5. Method of optimal structural design44
  • 5.1. Summary48
  • 5.2. Example of beam design49
  • Chapter 6. Optimal structural design (examples)50
  • 6.1. Tension/compression and bending50
  • 6.2. Beams with multiple supports50
  • 6.3. Deformation of plates50
  • Chapter 7. Optimal simple beam51
  • Chapter 8. On mathematics in physics52
  • 8.1. Summary58
  • Chapter 9. On the nature of the limit of elasticity59
  • 9.1. Summary61
  • Chapter 10. The stress-strain diagram61
  • Chapter 11. On the nature of proof in physical theory62
  • 11.1. Summary64
  • Chapter 12. History of the theory of elasticity64
  • Chapter 13. On the principles of the theory of elasticity69
  • 13.1. Summary72
  • United States Patent 5,654,900 (August 5, 1997) Method of and Apparatus for Optimization of Structur75
  • Chapter 1. Background of the invention75
  • 1.1. Field of the Invention75
  • 1.2. Description of the Prior Art76
  • Chapter 2. Summary of the invention84
  • Chapter 3. Description of illustrated exemplary teaching85
  • Part II: Linear Theory of Infinitesimal Deformations91
  • Chapter 1. Principles of LTE91
  • Chapter 2. Stress94
  • Chapter 3. Deformation97
  • Chapter 4. Hooke's Law99
  • Chapter 5. Geometric characteristics of plane areas101
  • Chapter 6. Combination of stresses103
  • 6.1. Load and Resistance Factor Design (LRFD)105
  • Part III: Optimization of typical structures107
  • Chapter 1. Introduction107
  • Chapter 2. Tension/compression113
  • Chapter 3. Torsion116
  • 3.1. Recapture120
  • Chapter 4. Bending121
  • 4.1. Calculation of deflections using the unit load method125
  • Chapter 5. Combined stresses126
  • Chapter 6. Continuous beam128
  • Chapter 7. Stability of thin shells129
  • 7.1. Calculation for symmetrical thin shells130
  • Chapter 8. Elastic stability of plates132
  • Chapter 9. Dynamic stresses and the non-linear theory of elasticity135
  • Chapter 10. Impact stresses136
  • 10.1. Tension impact on a bar137
  • 10.2. Bending impact137
  • Chapter 11. Testing of materials138
  • Appendix I. Optimal design of typical beams138
  • Appendix II140
  • Tension-compression141
  • Bending141
  • Circular cylindrical shells (membrane theory)141
  • Appendix III. Table for shaft calculation143
  • Part IV: Further Discussions in the Theory of Elasticity145
  • Chapter 1. Graph analysis145
  • 1.1. Commentary to Illustration 1 of Part I149
  • Chapter 2. Geometrical models of physical functions150
  • Chapter 3. The equation for the elastic line and the non-linear theory of elasticity152
  • Part V: Philosophy and Logic of Physical Theory155
  • Chapter 1. Philosophical background of the non-linear theory of elasticity155
  • Chapter 2. Logic and physical theory163
  • 2.1. Role of logic in science163
  • 2.2. General argument166
  • Chapter 3. The rules of logic169
  • Chapter 4. Logic of construction in NLTE174
  • Chapter 5. The definitive logic177
  • 5.1. Recapture182
  • Chapter 6. It is possible to prove physical theory186
  • Chapter 7. Notes on logic189
  • 7.1. Commentaries to "Preface to Logic" by Morris R. Cohen189
  • 7.2. Commentaries to "An Introduction to the Philosophy of Science" by Rudolf Carnap194
  • 7.3. Notes on methodology of science207
  • 7.4. On the nature of a scientific theory213
  • 7.5. The theory of elasticity as an organized knowledge214
  • 7.6. Logic in mathematics. Commentaries to Bertrand Russell and Kurt Gödel222
  • 7.7. On explanation of a physical theory226
  • 7.8. Theory and observation234
  • 7.9. Validation of scientific theory238
  • 7.10. On the logic of truth-function253
  • 7.11. On the logic of classes254
  • Chapter 8. Conclusion256
  • Chapter 9. Recapture of the central ideas259
  • Bibliography263
  • Subject Index267
Book details
  • Vendor Elsevier S & T
  • SKU 9780444514271
  • ISBN-13 9780080537603
  • Author Ratner, L.W.
  • Category Science
  • Subject General

Do you have questions about this book?

Ask an expert!

Description eBook delivery & access Reviews
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.