Three Dimensional Nonlinear Analysis of Elastic Arches

摘要

This paper presents a curved finite element model for the three dimensionalnonlinear analysis of elastic arches. The model can be used in a structural analysis computer program in conjunction with the total Lagrange or the updated Lagrange procedure for the three dimensional large deflection and twist rotation analysis. 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. As a result, membranes locking problems are avoided. All significant terms, some of which might be lost when improper approximations are made, are retained. Without these terms, superimposed rigid body motions may lead to overstiff solutions due to the development of internal strains. 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 proposed model is also used to investigate the elastic flexural-torsional buckling and the elastic post-buckling behavior of arches with different support conditions.