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.
A geometric nonlinear modeling approach for strong rigid-flexible-thermal coupling dynamics of the hub and multi-plate system considering frictional contact is proposed. Based on the absolute nodal coordinate formulation (ANCF), a thermal integrated ANCF thin plate element is developed, where the temperature field is expressed with Taylor polynomials to yield two-dimensional heat conduction equations. Different from the traditional coupling formulations, the influences of the attitude motion and structural deformation on the intensity of the solar radiation, the geometric nonlinearity of the plate as well as the frictional contact are taken into account. The normal contact is formulated by the penalty method, and the tangential friction considers the stick-slip transition. To solve the strong rigid-flexible-thermal coupling equations, a novel numerical method combining the modified central difference approach and the generalized- method is proposed. Two validations are performed to verify the proposed thermal-structural coupling model, which proves the importance of the geometric nonlinearity and can capture the thermally induced vibration. Then the thermal-dynamic coupling analysis for the satellite and solar array multibody system in thermal environment is carried out. The dynamic characteristics of the thermally induced vibration can be successfully revealed by the rigid-flexible-thermal coupling model. Furthermore, it is indicated that the influence of contact and thermal load on the nonlinear behavior of the solar array deployment is essential, which demonstrates the feasibility of the proposed approach.
A geometric nonlinear modeling approach for strong rigid-flexible-thermal coupling dynamics of the hub and multi-plate system considering frictional contact is proposed. Based on the absolute nodal coordinate formulation (ANCF), a thermal integrated ANCF thin plate element is developed, where the temperature field is expressed with Taylor polynomials to yield two-dimensional heat conduction equations. Different from the traditional coupling formulations, the influences of the attitude motion and structural deformation on the intensity of the solar radiation, the geometric nonlinearity of the plate as well as the frictional contact are taken into account. The normal contact is formulated by the penalty method, and the tangential friction considers the stick–slip transition. To solve the strong rigid-flexible-thermal coupling equations, a novel numerical method combining the modified central difference approach and the generalized-a method is proposed. Two validations are performed to verify the proposed thermal-structural coupling model, which proves the importance of the geometric nonlinearity and can capture the thermally induced vibration. Then the thermal-dynamic coupling analysis for the satellite and solar array multibody system in thermal environment is carried out. The dynamic characteristics of the thermally induced vibration can be successfully revealed by the rigid-flexible-thermal coupling model. Furthermore, it is indicated that the influence of contact and thermal load on the nonlinear behavior of the solar array deployment is essential, which demonstrates the feasibility of the proposed approach.
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