Geometric and material nonlinear analyses of elastically restrained arches

An arch is often connected with other structural members and may be supported by elastic foundations that provide elastic-like restraints to the arch. These elastic restraints participate in the structural response of the arch, and may significantly influence its structural behaviour. A curved-beam element for the structural analysis of arches should therefore consider the effects of these elastic restraints. It is known that the elasto-plastic properties of materials also affect the behaviour of a structure significantly, and so the nonlinearities of the materials need to be included in the curved element for elasto-plastic analysis of an arch. An elastic curved-beam element for the in-plane nonlinear analysis of arches is extended here to an elasto-plastic curved-beam element by formulating the elastic restraints and the material nonlinearities into the element. Geometric nonlinearities in the element are based on an accurate rotation matrix of the two dimensional special orthogonal group that satisfies the desired orthogonality and unimodular conditions. Comparisons of results from the curved element with test results and with analytical solutions demonstrate that the curved-beam element can provide accurate predictions for elastic behaviour, and acceptablly accurate predictions for the elasto-plastic behaviour of elastically restrained arches.