A comparative study of beam element formulations for nonlinear analysis: corotatinal vs. geometrically exact formulations

Abstract

In this work the geometrically exact three-dimensional beam theory has been used as basis for development of a family of isoparametric higher order large deformation curved beam elements. Geometrically exact three-dimensional beam theory has no restrictions with respect to the magnitude of displacements, rotations and deformations. While reduced integration may be used to alleviate transverse shear and membrane locking in linear and quadratic C0-continuous Lagrange elements, this does not automatically extend to higher order elements. In this study we demonstrate that uniform reduced numerical quadrature rules may be used to obtain locking-free isoparametric large deformation geometrically exact curved beam elements of arbitrary order. A set of carefully selected numerical examples serves to illustrate and assess the performance of the various geometrically exact elements and compare them with one of the most popular finite element formulations for solving nonlinear beam problems based on the corotational formulation.