Introduction to Elasticity/Kinematic admissibility

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Kinematically admissible displacement field[edit | edit source]

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.