Beam elements in instability problems
This paper deals with the formulation of beam elements for the numerical analysis of instability phenomena in frame-type structures. Total versus co-rotational approaches are discussed comparatively, for both two-dimensional and three-dimensional problems, and the similarities between the two types are outlined. In the context of three-dimensional beam elements, special attention is given to the parameterization of the orthogonal transformation used to define the rotational field of the beam. The technique is based on the so-called rotational vector. This leads to symmetric stiffness matrices and avoids the need for special updating procedures for the rotational variables. A set of test problems, for which the critical behaviour is governed by fold, cusp and butterfly catastrophes, is used to assess the performances of the considered element types.
parameterization of orthogonal transformation
scientific article; zbMATH DE number 1079169
scientific article