Three-dimensional nonlinear analysis of elastic arches

This paper presents a curved finite element model for the three-dimensional nonlinear analysis of elastic arches. The model includes higher-order curvatures which make the order of the bending strains consistent with that of the membrane strains, and the same low-order polynomials are used for all the displacements, No approximations are made for the twist rotations, and the nonlinear strains and the incremental stiffness matrix include the exact coupling due to the twist rotations. All significant terms of strains are retained. Without these terms, superimposed rigid body motions may lead to overstiff solutions. The model also includes warping of the cross-section and the Wagner effect. Application of the model to several numerical examples and comparison with the existing experimental and analytical results demonstrate that the model is much more effective and efficient than other methods in terms of accuracy, the number of elements needed for convergence, and the ability to pass maximum load points. The model is also used to investigate the elastic flexural-torsional buckling and the elastic postbuckling behaviour of arches.