Short Communication

Boundary compatibility condition and rotation in elasticity

Surya N Patnaik and Shantaram S. Pai

Ohio Aerospace Institute NASA Glenn Research Center M.S. 49-8, 21000 Brookpark Road, Cleveland, Ohio 44135.

Accepted 13 October, 2021

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.