Continuum Mechanics

7.

Linear Elasticity

7.1.

Governing Equations

7.1.1.

Navier-Cauchy Equations

7.1.2.

Displacement Formulation

7.1.3.

Stress Formulation

7.1.4.

Mixed Formulations

7.2.

Boundary Value Problems

7.2.1.

Types of Boundary Conditions

7.2.1.1.

Displacement Boundary Conditions

7.2.1.2.

Traction Boundary Conditions

7.2.1.3.

Mixed Boundary Conditions

7.2.2.

Uniqueness and Existence

7.2.3.

Superposition Principle

7.3.

Two-Dimensional Problems

7.3.1.

7.3.2.

7.3.3.

Generalized Plane Stress

7.3.4.

Airy Stress Function

7.4.

Torsion Problems

7.4.1.

Saint-Venant Torsion

7.4.2.

Prandtl Stress Function

7.4.3.

Warping Function

7.4.4.

Circular Shafts

7.4.5.

Non-Circular Cross-Sections

7.5.

7.5.1.

Euler-Bernoulli Theory

7.5.2.

Timoshenko Theory

7.5.3.

Composite Beams

7.5.4.

7.6.

7.6.1.

7.6.2.

Complementary Energy

7.6.3.

Virtual Work Principles

7.6.4.

Variational Formulations

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8. Fluid Mechanics Applications