A Numerical Strategy for Searching the Initial Critical Instability Point of Spati al Structures

The behaviour and the mechanism of instability of single layer reticulated shells have been investig ated widely all over the world till now. A lot of achievements have been obtained and also adopted i n actual structure design. However, techniques for identifying the initial critical instability point of a structure are still not suitable or convenient for numerical computation. Based on current investigat ions about the instability behaviour of the single layer reticulated shells, the relationship between th e instability mechanism and the stiffness parameter is explored theoretically. The inherent changing mechanism of the stiffness parameter is traced and investigated during the tracing procedure of the whole nonlinear equilibrium path of the shells. After strictly mathematical and mechanical analysis, the formulae for searching and confirming the initial critical point are obtained. Finally, a numerical method for identification and calculation of the initial critical points, including the limit point and t he bifurcation point, of the instability of the single layer reticulated shells is proposed in this paper. In order to verify the numerical method, a single-layer reticulated shell, used in many former refere nces, is adopted for instability analysis. The effectiveness and the efficiency of the method are verifi ed. The numerical method can also be used for instability analysis of the spatial structures.