A Koiter-Type Method for Finite Element Analysis of Nonlinear Structural Behavior. Volume I. The Modified Structure Method

摘要

Koiter's method for the asymptotic analysis of post-buckling behavior is reformulted in finite element notation for application to structures idealized by finite element models. Koiter's method is herein adapted to a general class of structures exhibiting the common snap-through (limit point) type of buckling. This is referred to as the Modified Structure method. It is accomplished by modification of the actual energy functional to create a hypothetical modified structure having a strictly linear pre-buckling path along which buckling must be of the bifurcation type. The analysis of the actual structure is then accomplished by application of Koiter's method through consideration of the actual structure as an imperfect version of the modified structure. The effects of pre-buckling nonlinearity are approximated asymptotically. The use of the Modified Structure method in conjunction with direct methods of nonlinear analysis is examined. A highly accurate finite element representation is employed in presenting a comprehensive numerical evaluation of the Modified Structure method of analysis on the basis of a number of planar frame problems. (Author)