Finite element analysis of dynamic stability of skeletal structures under periodic loading

INTRODUCTION Some structures fail geometrically before thestrength failure because of lack of stability and such afailure is known as instability failure or bucklingfailure. Determination of buckling load is importantin order to ensure the stability of a structure. If thestructure under consideration is subjected to a dy-namic load then this problem comes under the pur-view of dynamic stability problems. Examples areslender offshore structures subjected to periodic ex-citations and colum…

Finite element analysis of dynamic stability of skeletal structures under periodic loading

This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose. The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C⁺⁺ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of numerical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark’s method to verify the results.