There is a class of problems in elasticity which, due to geometry and boundary conditions, have solution stress, strain, and displacement fields that are independent of one of the coordinate variables. The equations of elasticity for this class of problem reduce to a simplified form of the general equations. Recognizing that a body with given boundary conditions is a member of this class, in advance of solving the attendant boundary value problem, enables one to take advantage of these simplified equations. Members of this class of problem are subdivided into three types known as antiplane strain, plane strain, and plane stress, as discussed below. It will be seen that the reduced form of the equations of elasticity for the later two are functionally equivalent.
KeywordsPlane Strain Plane Stress Displacement Boundary Condition Airy Stress Function Traction Boundary Condition
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