Numerical Methods for the Analysis of Buckling and Postbuckling Behavior of Arch Structures

摘要

The object of this study is to develop numerical methods for the analysis of structures having prebuckling configurations which are nonlinear functions of the loading parameter. A set of numerical procedures is presented for the simultaneous improvement of an approximate eigenvector and of an approximate location of a bifurcation point on the load-deflection curve. These methods include a technique for determining accurately the changes in the prebuckling configuration near bifurcation points. Multiple eigenvalues may be treated by a minor extension of the procedures. The new techniques may be regarded as modifications of the standard Newton-Raphson procedure. Experience indicates that the proposed methods are rapidly convergent and are economical of computational effort. The numerical procedures developed in this study are applied to buckling and postbuckling of arch members. Numerical results are presented for both in-plane and out-of-plane buckling of an initially planar arch. The results of these various analyses are in good agreement with certain of the previous solutions presented in the literature. (Author)