Treatment of initial deformations in the Integrated Force Method Original Research Article

A new force finite element formulation, termed the Integrated Force Method, has been developed in recent years for the structural analysis. In the Integrated Force Method all independent forces are treated as unknown variables which are calculated by simultaneously imposing the force equilibrium and strain compatibility. The Integrated Force Method is extended in this study for the treatment of initial strains. Initial strains are incorporated into compatibility conditions through the vector of initial deformations. A general expression for the vector of initial deformations is derived by discretizing the expression for the complementary potential energy of the structure. Two special cases of initial strains are analyzed in detail: (i) thermal strains and (ii) support settlements. The vector of initial deformations due to thermal loadings is derived by introducing expressions for thermal strains into the general expression, and that due to support settlements is derived directly by equating the work done by external and internal forces, respectively. Two example problems with available analytical solutions are solved using the present developments. A good agreement of results with analytical solutions is observed.