Nonlinear dynamic formulation for flexible origami-based deployable structures considering self-contact and friction

Abstract

Compared with the conventional rigid origami, the flexible origami has larger deformation and more complicated mechanical property and nonlinear problems due to self-contact and friction. In this paper, the nonlinear dynamic formulation for flexible origami-based deployable structures considering selfcontact and friction is investigated. Firstly, a symmetric rigid origami model is presented based on the forward recursive formulation without the inclusion of contact, and then, a discretized dynamic model for flexible origami structures is established by using thin plate element of absolute nodal coordinate formulation. To consider the normal contact, the penalty method is adopted to enforce the nonpenetration condition. In order to improve the precision and applicability, a modified mixed contact method considering the friction effect is developed by integrating the advantages of node-to-surface, edge-to-surface and surface-to-surface contact elements. This proposed method can effectively avoid the mutual penetration of different corner nodes, element edges and contact element surfaces. Moreover, the tangential friction model considering the stick-slip transition and large sliding is established by the regularized Coulomb friction law. A series of numerical examples validate the effectiveness of the proposed mixed contact method considering the friction and show the advantage of the flexible model compared with the rigid origami model. Furthermore, the nonlinear performance of the flexible origami-based deployable structures due to the contact and friction is revealed.

Rigid–flexible–thermal coupling dynamics of a hub and multiplate system considering frictional contact

“…The normal contact is formulated using the penalty method [41,45], and the tangential contact is modeled by the Coulomb friction law with a penalty regularization considering the stick-slip transition [42]. The virtual work of the contact force is…”

“…Lei et al [40] presented a strong coupling modelling method for the rigid bodies and the large deformed beams in contact interaction with the granular matter to simulate the flexible brush sampling process. To avoid mutual penetration of plate element with large deformation, a mixed method combining the node-to-surface, edge-to-surface and surface-to-surface contact elements based on ANCF was proposed by the authors [41,42]. Nevertheless, few studies have considered the frictional contact in the rigid-flexible-thermal coupling modeling.…”

Simulation of membrane deployment accounting for the nonlinear crease effect based on absolute nodal coordinate formulation

“…Due to its consistency with strain and stress measures from general continuum mechanics, the ANCF method has been widely applied in various nonlinear static/dynamic problems [27,28,11,12]. Luo et al [15] and Yuan et al [34,35] analyzed a spinning deployable solar sail, a leaf-in origami membrane, and a leafout origami membrane respectively using the thin ANCF shell/membrane element. These researches did not consider the anti-deployment effect of the crease.…”