Compatibility conditions of structural mechanics

The theory of elasticity has camouflaged a glitch in the compatibility form ulation since 1860. In structures the ad hoc compatibility conditions throu gh virtual 'cuts' and closing 'gaps' is not parallel to the strain formulat ion in elasticity. The deficiency in the compatibility condition has preven ted the development of direct stress determination method in structures and in elasticity. We have addressed and attempted to unify the theory of comp atibility. This has lead to the development of the Integrated Force Method for structures and the Completed Beltrami-Michell's Formulation in elastici ty. The utilization of the compatibility conditions allows mapping of varia bles and facile movement among different structural analysis formulations. This paper reviews and illustrates the requirement of compatibility in stru ctures and in elasticity. Addresses the generation of the conditions and qu antifies the benefit of their use. The traditional analysis methods and ava ilable solutions should be verified for compliance of the compatibility con ditions. Published in 2000 by John Wiley & Sons, Ltd.