Compatibility conditions of structural mechanics

The theory of elasticity has camou#aged a glitch in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual &cutsʹ and closing &gapsʹ is not parallel to the strain formulation in elasticity. The de"ciency in the compatibility condition has prevented the development of direct stress determination method in structures and in elasticity. We have addressed and attempted to unify the theory of compatibility. This has lead to the development of the Integrated Force Method for structures and the Completed Beltrami}Michellʹs Formulation in elasticity. The utilization of the compatibility conditions allows mapping of variables and facile movement among di!erent structural analysis formulations. This paper reviews and illustrates the requirement of compatibility in structures and in elasticity. Addresses the generation of the conditions and quanti"es the bene"t of their use. The traditional analysis methods and available solutions should be veri"ed for compliance of the compatibility conditions