Elasticity/Kinematic admissibility

Kinematically admissible displacement field

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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.  .
  •  .

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.