Abstract
There are vast constraint equations in conventional dynamics analysis of deployable structures, which lead to differential-algebraic equations (DAEs) solved hard. To reduce the difficulty of solving and the amount of equations, a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements (SLEs) is presented. Firstly, a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation (ANCF), and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations. Secondly, according to features of deployable structures, the specification matrix method (SMM) is proposed to eliminate the constraint equations among SLEs in the frame of ANCF. With this method, the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently, especially on condition that there are vast nodal coordinates. So the element characteristic matrices can be added end to end circularly. Thus, the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation. Next, a new iteration procedure for the generalized-α algorithm is presented to solve the ordinary differential equations (ODEs) of deployable structure. Finally, the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements. The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure. The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.
Highlights
1 Introduction Due to their good characteristics such as simple structure, high loading capacity and excellent equilibrium stability [1], deployable structures comprised of scissor-like elements (SLEs) are widely used in many fields, such as architecture [2], antivibration [3] and astronautics [4]
A great many literatures about configuration design [5, 6], kinematic analysis [7,8,9] and static analysis [10] of deployable structures with SLEs are published in recent years
Shan et al [30] investigated the deployment dynamics of the tethered-net based on absolute nodal coordinate formulation
Summary
Due to their good characteristics such as simple structure, high loading capacity and excellent equilibrium stability [1], deployable structures comprised of SLEs are widely used in many fields, such as architecture [2], antivibration [3] and astronautics [4]. Since the locations at the arbitrary point of the finite element in the formulation are defined in the global coordinate system by using the shape function and nodal coordinates, a constant mass matrix is produced and the Coriolis and centrifugal forces vanish. Shan et al [30] investigated the deployment dynamics of the tethered-net based on absolute nodal coordinate formulation, . In their model the dynamics equations are differential-algebraic equations, which are solved hard. Utilizing the higher order shear deformable element based on ANCF, a more exact flexible model of a SLE, in which the constraint equations vanish with the master/slave freedom method, is first established. The master/slave freedom method is introduced to remove the constraint equation
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