Chapter 1

3D Elasticity Formulations

Displacement formulations (Navier's equations)

medium • 1 min read

Stress formulations (Beltrami-Michell equations)

medium • 2 min read

Boundary value problems in elasticity

medium • 3 min read

Uniqueness theorem and St. Venant's principle

medium • 4 min read

Papkovich-Neuber and Galerkin vector solutions

medium • 5 min read

Chapter 2

Energy Methods in Elasticity

Principle of virtual work and potential energy

medium • 1 min read

Castigliano's theorems

medium • 2 min read

Theorem of minimum complementary energy

medium • 3 min read

Rayleigh-Ritz and Galerkin techniques

medium • 4 min read

Applications to torsion and bending problems

medium • 5 min read

Chapter 3

Fundamentals of Plasticity

Physical foundations of plastic deformation

medium • 1 min read

Yield criteria: Tresca and Von Mises

medium • 2 min read

Experimental verification of yield criteria

medium • 3 min read

Flow rules and normality principle

medium • 4 min read

Isotropic and kinematic hardening models

medium • 5 min read

Chapter 4

Constitutive Equations in Plasticity

Prandtl-Reuss equations

medium • 1 min read

Levy-Mises equations

medium • 2 min read

Stress-strain relations in plastic range

medium • 3 min read

Deformation theory of plasticity (Hencky theory)

medium • 4 min read

Elasto-plastic bending and torsion

medium • 5 min read

Chapter 5

Limit Analysis and Plastic Design

Upper and lower bound theorems

medium • 1 min read

Calculation of plastic hinge and plastic moment capacity

medium • 2 min read

Collapse load analysis of beams and frames

medium • 3 min read

Mechanism method and statical method

medium • 4 min read

Shakedown analysis and repeated loading

medium • 5 min read