The variational energy formulation for the integrated force method

Abstract

The integrated force method (IFM) is one of the five formulations of mechanics, the others being the flexibility, stiffness, mixed, and total methods. To date, all but the IFM have been associated with variational functionals. A variational functional (VF) has been developed for the IFM. The stationary condition of the VF for the IFM yields the equilibrium and compatibility equations as well as the force and displacement boundary conditions. The stationary condition also yields a new set of boundary equations identified as the boundary compatibility conditions. This paper presents the theory of the variational functional for the IFM. It is illustrated by examples from discrete structures, the plane stress problem of elasticity, and Kirchhoff s plate bending problem. The properties of the VF and its relationship to the potential and complementary energy functionals are shown for discrete analysis.