Abstract
With increasing of the size of spatial truss structures, the beam component will be subjected to the overall motion with large deformation. Based on the local frame approach and the geometrically exact beam theory, a beam finite element, which can effectively reduce the rotational nonlinearity and is appropriate for finite motion and deformation issues, is developed. Dynamic equations are derived in the Lie group framework. To obtain the symmetric Jacobian matrix of internal forces, the linearization operation is conducted based on the previously converged configuration. The iteration matrix corresponding to the rotational parameters, including the Jacobian matrix of inertial and internal forces in the initial configuration, can be maintained in the simulation, which drastically improves the computational efficiency. Based on the Lagrangian multiplier method, the constraint equation and its Jacobian matrix of sliding joint are derived. Furthermore, the isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) basis functions, is adopted to interpolate the displacement and rotation fields separately. Finally, three dynamic numerical examples including a deployment dynamic analysis of spatial truss structure are conducted to verify the availability and the applicability of the proposed formulation.
Highlights
The deployable spatial truss structure is a typical flexible multibody system consisting of beam members
The objective of this paper is to propose a geometrically exact beam element based on the local frame approach under the concept of isogeometric analysis (IGA)
The proposed element can be applied to the cases of finite deformation and rotation in dynamic analyses of flexible multibody systems, especially for the deployable spatial truss structures with a sliding joint
Summary
The deployable spatial truss structure is a typical flexible multibody system consisting of beam members. The most common modeling methods in flexible multibody system for beams are the Absolute Nodal Coordinate Formulation (ANCF) and the Geometrically Exact Beam Theory (GEBT). Under the concept of IGA, the dynamic analysis of the beam structure with a sliding joint, based on the GEBT and Lagrangian multiplier method, has rarely been reported. The proposed element can be applied to the cases of finite deformation and rotation in dynamic analyses of flexible multibody systems, especially for the deployable spatial truss structures with a sliding joint. Deployment dynamic analysis of spatial truss structure are implemented to verify the availability paper is organized follows: The basic theory the geometrically beam theory and The the applicability of the as formulation proposed in thisof paper.
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