Nonlinear Curved‐Beam Element for Arch Structures

Abstract

A nonlinear curved-beam finite element is developed for three-dimensional space systems by using the principle of potential energy and polynomial functions. It is limited to elastic material with linear stress-strain relation. Warping is not considered. A major improvement in the accuracy of the element is obtained by averaging the nonlinear part of the axial strain. The method of solution used is that of the fixed Lagrange coordinates and the Newton-Raphson procedure. Comparisons of numerical results with those of various other methods indicate that, in terms of the number of elements or degrees of freedom needed for convergence, the method seems significantly more effective than most. None of the others was seen to be more effective. The problems considered included shallow and deep arches, extremely thin arches, and arches of various profiles. An application to an arch structure subjected to dynamic or cyclic (earthquake) loading is also illustrated.