Atanackovic T.M., Guran A. Theory of Elasticity for Scientists and Engineers

Springer Science+Business Media New York, 2000. XII, 374 p. — ISBN: 978-1-4612-7097-3.This text offers an introduction from a modern point of view, to elasticity theory and its applications in science and engineering. The approach used is oriented toward the formulation and solution of problems.Analysis of StressStress vector. Cauchy's theorem
Equilibrium equations in terms of stress components
The basic lemma of stress analysis
Equilibrium equations in coordinate systems
Transformation of stress matrix. Stress tensor
Extreme properties of principal stresses
Invariants of the stress tensor
Extreme values of shear stresses
Spherical and deviatoric part of stress tensor
Mohr's stress circles
Plane state of stress
Normal and tangential stresses in the plane state of stress
Mohr's circle for plane state of stress
Stresses at the outer surfaces of a body 1.16 Linear state of stress
ProblemsAnalysis of StrainMeasures of deformations. Strain tensor
Extension and shear angle for arbitrary directions
Infinitesimal rotation
Principal directions of strain tensor
Strain tensor in coordinate systems
Compatibility conditions for linear and nonlinear strain tensor
Plane state of strain
Linear strain tensor. Cubical dilatation
Measurement of strain. Strain gauges
ProblemsHooke's LawTransformation of the elasticity tensor by rotation of coordinate system
Anisotropic, orthotropic, and isotropic elastic body
Lame constants. Modulus of elasticity. Poisson ratio
Influence of temperature on the stress-strain relation 3.6 Hooke's law in cylindrical and spherical coordinate systems
Beltrami-Michell compatibility conditions
Finite deformations in linear state of stress ProblemsBoundary Value Problems of Elasticity TheoryClassification of problems
Lame equations coordinate systems
Uniqueness of solution
Assumptions about solution of equilibrium equations
Methods of solution
Saint-Venant principle
ProblemsSolutions for Some Problems of Elasticity TheoryHeavy rod
Rotating rod
Spherical shell under inner and outer pressure
Torsion of a prismatic rod with an arbitrary cross-section
Torsion of a rod with variable circular cross-section
Bending by couples (pure bending)
Bending of a rod by a terminal load
Elementary singular solutions
The Boussinesq problem
Tangential force on t~e elastic half space
Equilibrium of a cir¢'ular cone
Thermal stresses in a sphere and in a cylinder
Plane harmonic waves in an elastic and thermoelastic body ProblemsPlane State of Strain and Plane State of StressStress function method for the solution of plane problems
Some solutions of the plane problems
Complex variable method for plane problems ProblemsEnergy Method in Elasticity TheoryWork and inner energy
Betti's theorem
Maxwell's theorem
Principle of virtual work
Principle of virtual displacements
Principle of virtual forces
Minimum of potential and complementary energy theorems
Castigliano's theorems
Hu-Washizy and Reissner variational principles Problems
Elementary Theory of Plates
ntroduction
Basic equations of von Karman's theory of plates
Boundary conditions
Small deformations: An example
The influence of shear stresses: Reisner-Mindlin theory ProblemsPressure Between Two Bodies in ContactHertz's Problem and Its Solution
Examples of Contact Stresses
Theory of Elastic Impact
ProblemsElastic StabilityDefinitions of stability
Basic theorems of the dynamic method
Examples
Problems