In this paper, a scheme of shape optimization is proposed for obtaining the maximum strength of free-form steel reticulated shells. In order to discuss the effectiveness of objective functions with respect to the strength, several different optimizations using GA are applied to two roof structures. Both examples are shallow steel single layer reticulated shell structures consisting of rigidly jointed tubular members. One of the examples has a square plan with a side length of 50m. All nodes on the outer periphery are pin-supported. Another example has a free edge at the peripheries and two surfaces which are concave down. The objective functions to be searched and compared are, respectively, strain energy minimization, linear buckling load maximization, initial yield load maximization, and buckling strength maximization. The buckling strength as a target for the fourth optimization is evaluated based on Modified Dunkerley Formula. With respect to the obtained free-forms based on the four optimization schemes, elasto-plastic buckling behaviour is investigated and compared.
The conclusions are as follows in the present study.
1) The ratio of bending strain energy Ub to total strain energy U of the shape which is obtained from strain energy minimization is the smallest of all. On the other hand, there is a tendency that the value of Ub/U of the shape which is obtained from linear buckling load maximization, buckling strength maximization and, initial yield load maximization is larger than initial shape.
2) The elasto-plastic buckling strength of Opt1 indicates relatively good results in all configurations. However, the ratio λelplcr(imp)/estλelplcr showing the accuracy of estimation of the elasto-plastic buckling strength fluctuates a little around 1.0 but almost independent generalized slenderness Λe(m) (Fig. 12(b)). For this reason, the elasto-plastic strength of Opt1 isn't necessarily the largest of all model.
3) Because of the displacement-to-load factor shows the load factor still increasing even after initial yielding of the structure, maximizing the initial yielding load factor is effective to obtain the configuration which has higher buckling strength. However, if generalized slenderness Λe(m) becomes larger, the discrepancy between λy(FEM) which denotes the initial yield load which is obtained by elasto-plastic buckling analysis, and λy estimated from linear acting force gets bigger. Therefore, it is preferable to impose a limitation of Λe(m), when the initial load maximization is conducted.
4) The knockdown factor α0 takes the value within a range of 0.4 to 0.7 in this paper. This tendency is same with the classical reticulated shell structures which are dealt in the previous research.
5) The buckling strength of free-form shells which are investigated in this study can be evaluated by generalized slenderness ratio Λe(m). However, the magnitude of Λe(m) will change by optimization schemes. Therefore, multiple objective functions have to be considered for maximizing the buckling strength. And then, it is necessary to evaluate the generalized slenderness ratio of obtained shape to judge the validity for buckling strength.
