Dynamic Analysis of Spatial Truss Structures Including Sliding Joint Based on the Geometrically Exact Beam Theory and Isogeometric Analysis

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.

Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams

“…A similar model was examined by Wu. 39 The initial configuration of the system is shown in Figure 9(a). The unfolded configuration for the model is clearly shown in Figure 9(b).…”

Modeling, Design and Optimization of Flexible Mechanical Systems

“…Wu et al [47] Dynamic analysis of spatial truss structures including sliding joint based on the geometrically exact beam theory and isogeometric analysis introduces a NURBS-based isogeometric analysis for flexible multibody simulation and applies this to a high-speed flexible slider-crank, a sliding beam, and a spatial truss structure.…”

Nonlinear statics of three‐dimensional curved geometrically exact beams by a hierarchal quadrature element method

“…Recently, Yang and Liu 5 presented an invariant isogeometric formulation for the geometric stiffness matrix of spatial curved GEBT Kirchhoff rods considering various end moments. Wu et al 6 studied the dynamics of spatial truss structures, including sliding joint, based on the geometrically exact beam theory and isogeometric analysis. Tasora et al 7 presented an efficient formulation of a geometrically exact three‐dimensional beam that can be used in dynamical simulations involving large displacements, collisions, and non‐linear materials.…”