Lumped‐Parameter Approach to Stability Analysis

Abstract

A structural stability modeling technique based on representing the in‐plane forces as discretized or lumped parameters is developed and applied to various structural members. Elastic critical loads on structures such as frames, curved beams, circular plates, and shells of revolution are calculated and compared with solutions obtained using other methods. This modeling procedure leads to a diagonal geometric stiffness matrix that provides the same advantages as lumped‐mass modeling in a dynamic analysis (including simplicity of formulation, relative accuracy, efficiency in computer time), and it usually yields eigenvalues that are less than the exact values. As in vibration problems, this modeling procedure can be easily adopted to provide a guaranteed lower bound for the critical buckling load of the system using Dunkerley's method.