** EN224: Linear
Elasticity **
** **

** Division of Engineering**

1.4 Summary of the Field Equations of Linear Elasticity

Displacement fieldu(t): ; assume

Define infinitesimal strain tensor

Stress measure

Linear Momentum

Angular Momentum:

Constitutive Law(or) with

Special case: isotropy

Boundary value problems:

Initial BVP:

Given a region and a time interval ; given the mass density and the elastic constants on , and given the time variation of body force field

bonfind displacements, strains and stresses satisfying the field equations listed above, with

Initial Conditions:

and one of the following boundary conditions:

1.

Displacement boundary value problemon

2. **Traction boundary value problem**** on**

3. **Mixed boundary value problem**

**Static Boundary Value Problem**

Given a region ; given the elastic constants on
, and given a time independent body force field **b **on
find displacements, strains and stressessatisfying the field
equations listed above, with one of the following boundary conditions

**1. Displacement boundary value problem ****on**

**2**. **Traction boundary value problem ****on**

**3**. **Mixed boundary value problem**