Abstract
This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.
Highlights
Thin-walled members found in multibody systems are often modelled as thin-walled beams
This article presents the development of a new finite torsion beam element, based on the generalized strain beam formulation, that allows for the buckling and post-buckling behaviour of thin-walled beams in multibody systems
Integrating the interpolated second order curvature and strain–displacement equations over the length of the beam element using the moment-area method [19], a set of modified deformations is obtained in which second order approximations for the axial elongation and bending curvatures are represented by additional quadratic terms in the expressions of the basic deformations
Summary
Thin-walled members found in multibody systems are often modelled as thin-walled beams. This article presents the development of a new finite torsion beam element, based on the generalized strain beam formulation, that allows for the buckling and post-buckling behaviour of thin-walled beams in multibody systems To this end a second order stiffness formulation is proposed which will be derived in two-steps: 1. Integrating the interpolated second order curvature and strain–displacement equations over the length of the beam element using the moment-area method [19], a set of modified deformations is obtained in which second order approximations for the axial elongation and bending curvatures are represented by additional quadratic terms in the expressions of the basic deformations This formulation combines the advantages of the co-rotational formulation with the consistency of the inertial frame approach, viz derivation of the inertia forces in terms of absolute nodal velocities and accelerations.
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