EN224: Linear Elasticity

Division of Engineering

1.4 Summary of the Field Equations of Linear Elasticity

Displacement field u(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 b onfind displacements, strains and stresses satisfying the field equations listed above, with

Initial Conditions:

and one of the following boundary conditions:

1. Displacement boundary value problem on

2. Traction boundary value problem on

3. Mixed boundary value problem

on

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

on