Stability of a reticulated dome under multiple independent loads

Abstract

The primary purpose of this thesis is to investigate stability boundaries, or load interaction curves, of a reticulated dome. An elastic, geometrically nonlinear model with 21 degrees of freedom is considered.

The nonlinear response of the model to imposed loads is determined using two separate computer programs as a check on each other. One program is based on the static perturbation technique and the other is based on an energy minimization technique. Program.solutions are compared with each other and with other published solutions. Various characteristics of the two programs are discussed.

Five stability boundaries for two independent loads and one for three independent loads are presented. These stability boundaries are all found to exhibit convexity or piecewise convexity toward the origin. Characteristics of points composing the stability boundaries are noted and discussed with emphasis placed on ways that point characteristics affect boundary shape. Three observations are noted:

1. Critical points classified as limit points consistently form smooth boundaries, those classified as bifurcation points do not.

2. It is possible to predict the occurrence of a cusp in the stability boundary in certain load planes.

3. The occurrence of load maxima at cusps in stability boundaries is due to the higher degree of balance achieved in the stress distribution throughout the structure at that critical point.

In addition, a method of estimating lower bounds and a theorem dealing with convexity of stability boundaries are briefly discussed.