Postbuckling Analysis of Continuous, Elastic Systems Under Multiple Loads—Part 1: Theory

Abstract

The stability of continuous, elastic systems subjected to multiple independent loads is considered. The analysis includes nonconservative loads as well as conservative loads, provided that instability is of the static, type. Systems exhibiting prebuckling deformations are included. A multiple-parameter perturbation technique is applied to the nonlinear equilibrium equation in the neighborhood of a critical point, and the postbuckling behavior and imperfection-sensitivity of the system are investigated. Critical points are classified as “general” or “special”, in analogy with Huseyin’s definitions for finite-degree-of-freedom, conservative systems. The results can be applied to study the interaction effects of the independent loads on stability. The theory is given in the present paper, while applications to columns and arches will be presented in the sequel.