Numerical analysis of branched shapes of arches in bending

Nonlinear boundary-value problems of plane bending of elastic arches under a uniformly distributed load are solved by the shooting method. The problems are formulated for a system of six first-order ordinary differential equations with a finite-rotation field independent of displacements. Simply supported and clamped cases are considered. Branching solutions of the boundary-value problems are obtained. For a simply supported arch, a set of solutions describes symmetric and nonsymmetric shapes of bending, which correspond to positive, negative, and zero loads. For a clamped arch, the set of solutions consists of symmetric shapes that occur only for positive loads.