Using Only Elastic Stiffness in Nonlinear and Postbuckling Analysis of Structures

This paper presents a new attempt for geometric nonlinear and postbuckling analysis of structures using only elastic stiffness. This can be achieved not without reasons. Aside from a correct updating of the structural geometry in the incremental sense, there are two concerns for iterations: (i) The local strategy is that the element forces recovered in each iteration should not violate the rigid body rule, in order not to induce any fictitious forces. (ii) The global strategy is that the path-tracing scheme should be able to deal with multi critical points, such as limit and snap-back points. Both strategies will be explained via the mechanism of iterations, which seems not new, but can shed some new lights. The results obtained using only the elastic stiffness will be compared with the normal case including the geometric stiffness, with the level of approximation assessed by the general stiffness parameter (GSP). Through the study of a number of trusses, beams and shell structures, it is confirmed that the elastic stiffness alone can be used to solve the nonlinear and postbuckling responses of a wide range of structures, with only an increase in the number of iterations. This paper represents a limit application of the elastic stiffness to nonlinear structural analysis.