Nonlinear time-dependent analysis of planar frames using an ‘exact’ formulation—I. Theory

Abstract The real objective underlying any structural analysis procedure is the solution of the corresponding mathematical governing equations. On this basic idea, the fundamental assumption of shape functions usually made in FEM formulations, and some limitations which can follow in practical computations, are discussed. Then the analysis of frames is considered, in which a specially favorable structure of equations permits a solution of the equilibrium equations, since they are uncoupled from the remaining (strain-displacement and material) laws. That solution is used as a fundamental assumption in a general hybrid-type formulation valid for nonlinear material and second order equilibrium analysis, which has the special property of being ‘exact’. In the particular case of linear material and first order equilibrium this formulation corresponds to the classical matrix theory of frames. Thus, it can also be considered as a generalization of that theory into the nonlinear analysis field. As practical advantages, it permits the use of long elements in the discretization, and the distributions of forces obtained always satisfy equilibrium.