Optimization of shallow arches against instability using sensitivity derivatives (Q1090160)

In this paper, the problem of optimization of shallow frame structures, which involves coupling of axial and bending responses, is discussed. A shallow arch of given shape and given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x), and the moment of inertia, I(x), of the arch obey the relationship \(I(x)=p[A(x)]^ n\), where \(n=1,2,3\) and p is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a co-rotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm, and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentiation. Results are presented for an arch of a specified rise to span under two different loadings, and the limitations of the approach for the intermediate rise arches are addressed.