Nonlinear Stability Analysis of Frame-Type Structures with Random Geometric Imperfections Using a Total-Lagrangian Finite Element Formulation

Abstract

With the increasing use of lightweight frame-type structures that span long distances, there is a need for a method to determine the probability that a structure having random initial geometric imperfections will become unstable at a load less than a specified fraction of the perfect critical load. The overall objective of this dissertation is to present such a method for frame-type structures that become unstable at limit points.

The overall objective may be broken into three parts. The first part concerns the development of a three-dimensional total Lagrangian beam finite element that is used to determine the critical load for the structure. The second part deals with a least squares method for modeling the random initial imperfections using the mo de shapes from a linear buckling analysis, and a specified maximum allowable magnitude for the imperfection at any imperfect node in the structure. The third part deals with the calculation of the probability of failure using a combined response surface/ first-order second-moment method. Numerical results are presented for two example problems, and indicate that the proposed method is reasonably accurate. Several problems with the proposed method were noted during the course of this work and are discussed in the final chapter.