EN224: Linear Elasticity
Division of Engineering
1.4 Summary of the Field Equations of Linear Elasticity
Displacement field u(t): ; assume
Define infinitesimal strain tensorStress 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
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