Optimal Shape of Shallow Circular Arches Against Snap-Buckling

Abstract

The optimal shapes of shallow circular arches against snap-buckling are obtained by a combination of perturbation method, variational calculus, and the numerical solution of integral equations. The method that is developed is applicable to the optimization against buckling of structures which undergo limit load buckling. Here, the in-plane extensional deformation of simply supported circular arches with prescribed volume of structural material is considered. The results indicates that the buckling load of arches may be increased by more than 10 percent by a redistribution of the volume of the arch material.