Introduction to Elasticity/Kinematic admissibility
Kinematically admissible displacement field
Consider a body with a boundary with an applied body force field .
Suppose that displacement BCs are prescribed on the part of the boundary .
Suppose also that traction BCs are applied on the portion of the boundary .
A displacement field is kinematically admissible if
- satisfies the displacement boundary conditions on .
- is continuously differentiable, i.e., and .
A kinematically admissible displacement field needs only to satisfy compatibility condition and the displacement boundary conditions - but not the traction boundary conditions or equilibrium.
Recall that a kinematically admissible displacement field is used to define the principle of minimum potential energy.