Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: Geometric stiffness

The occurrence of strong deflections and major axial forces in many applications involving flexible multibodies entails including non-linear terms coupling deformation-induced axial and transverse displacements in the motion equation. The formulations, including such terms, are known as geometrically non-linear formulations. The authors have developed one such formulation that preserves higher-order terms in the strain energy function. By expressing such terms as a function of selected elastic coordinates, three stiffness matrices and two non-linear vectors of elastic forces are defined. The first matrix is the conventional constant-stiffness matrix, the second is the classical geometric stiffness matrix and the third is a second-order geometric stiffness matrix. The aim of this work is to define the third matrix and the two non-linear vectors of elastic forces by using the finite-element method. Copyright (C) 1996 Elsevier Science Ltd.