Boundary compatibility condition and rotation in elasticity

Abstract

The boundary compatibility condition in elasticity that was missed for more than one century has been
formulated. The new condition has completed the Beltrami-Michell formulation in elasticity. The completed
formulation can solve stress, displacement, and mixed boundary value problems. The boundary compatibility
condition, which is not a rotation, should be imposed on an indeterminate boundary. The use of the new
condition is illustrated through the solution of a mixed boundary value problem.