NON-LINEAR THEORY OF ELASTICITY AND OPTIMAL DESIGN
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By L.W. Ratner, Chicago, IL, USA
Description 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.
Contents Introduction.
Prologue.
PART I.
Developing the reliable theory for optimal structure.
The practical problems.
Foundation of Non-Linear Theory of Elasticity.
Comparative analysis
of the linear and non-linear theories.
Devising Non-linear Theory of Elasticity.
Principles of Logic in
NLTE.
Method of Optimal Structural Design.
On Mathematics
in Physics.
On The Nature of Limit of Elasticity.
On The Nature of Proof in Physical Theory.
History of Theory of Elasticity.
On The Principles of Non-Linear Theory.
Appendix I.
Method of and Apparatus for Optimization of Structures (US Patent Specification).
Notations.
PART II.
Linear theory of infinitesimal deformations.
The
principles of LTE.
Stress.
Deformation.
Hooke's law.
Geometric characteristics.
Combination of stresses.
PART III.
Optimization of the typical
structures.
Introduction.
Tension/Compression.
Torsion.
Bending.
Combined Stresses.
Continuous Beams.
Elastic
Stability of Thin Shells.
Elastic Stability of Plates.
Dynamic Stresses.
Testing Materials.
Appendix II.
Tables for Optimal Design of the Typical Beams.
Tables for Optimal Design of Shafts.
Tables for Optimal Design of Plates.
PART IV.
Further discussions
in the theory of elasticity.
Graph Analysis.
Geometrical
Models of Physical Functions.
The Equation of Elastic Line and NLTE.
Part V.
Philosophy and
Logic of Physical Theory.
Philosophical Background of the Non-Linear Theory of Elasticity.
Logic and Physical Theory.
Role of logic in science.
General argument.
The rules of logic.
Logic of construction Non-Linear
Theory of Elasticity.
The definitive logic.
It is possible to prove a physical theory.
Notes on Logic.
The commentaries
on "Preface to Logic" by Morris R. Cohen.
The commentaries on "An Introduction to the Philosophy of Science" by Rudolf Carnap.
Definition of Scientific Law.
Induction.
Concepts in Science.
Measurement.
Geometry and a theory.
Kant's synthetic
a priori.
Notes on methodology of science.
On nature of a scientific theory.
The theory of elasticity as an organized knowledge.
Flow-Chart Diagram.
Logical structure of Non-Linear Theory of Elasticity.
Logic in mathematics.
On explanation of a physical
theory.
Inferential conception of explanation.
The causal conception of scientific explanation.
Theory and observation.
Validation of scientific theory.
Justificationism.
Falsificationism.
Conventionalism.
The testing paradigm of scientific
inference.
In summary.
On the logic of truth-function.
On the logic of classes.
Conclusion.
Bibliography.
Subject
Index.
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