Completed Beltrami-Michell Formulation for Analyzing Mixed Boundary Value Problems in Elasticity

摘要

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation. The Beltrami-Michell formulation can only solve stress boundary value prob- lems; it cannot handle the more prevalent displacement or mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier displacement method, which can solve all three types of boundary value problems. The restrictions of the Beltrami-Michell formulation have been alleviated by augmenting the classical formulation with a novel set of conditions identi- fied as the boundary compatibility conditions.