Research on nonlinear, postbuckling and elasto-plastic analyses of framed structures and curved beams

Nonlinear analysis of structures is an effective way for predicting the bearing capacity or ultimate strength of a structure. This paper will review researches on the nonlinear, buckling, postbuckling and elasto-plastic analyses of three-dimensional (3D) framed structures. Also considered are curved beams since they share the problem of joint equilibrium in simulation. The following are the key issues to be covered in this paper: (a) analytical or semi-analytical approaches; (b) formulation for incremental-iterative nonlinear analysis; (c) joint equilibrium of 3D frames at the deformed configuration; (d) rigid body test for nonlinear finite elements; (e) rigid-body-qualified geometric stiffnesses and derivation; (f) simulation of buckling of curved beams; (g) elasto-plastic analysis of steel frames; (h) mechanism of iterations in incremental analysis; (i) recovery of element forces; and (j) path-tracing scheme for the postbuckling response. In this paper, the theories and methods for solving the postbuckling responses of structures involving multi-loop curves are considered. In fact, the incremental-iterative procedure for the geometric and/or inelastic nonlinear analysis can be greatly simplified if it is well rooted in physics. Namely, if the rigid body rule is fully obeyed at each stage of analysis, then the entire incremental-iterative procedure can be made simpler and more efficient. Recently, it was demonstrated that satisfactory results can be obtained for the postbuckling response of a number of structures using the elastic stiffness alone. A total of 154 references are cited in this paper.