A methodology for modeling a rotating paraboloidal thin-shell structure attached to a spacecraft body is proposed considering its geometric nonlinear effect. Instead of using conventional shell elements to discretize the paraboloidal thin-shell in the Cartesian coordinate, the paraboloidal coordinates in the meridional, circumferential and normal directions are employed to completely express the deformations of the curved thin-shell. Then, explicit expressions for the generalized elastic forces and stiffness varying matrices are deduced on the basis of exact strain-displacement relations. And, the rigid-flexible coupled dynamic model for the flexible multibody system is derived by the principle of virtual work. In contrast with the previous modeling approaches, the present method shows an advantage in avoiding large calculation quantity of nonlinear stiffness matrix due to more formalized. Furthermore, a full analysis with specific numerical simulation is achieved by using the present model and conventional shell model, respectively. All simulation results obtained by the two modeling methods verify the correctness and better convergence of the proposed methodology.
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This material is partially based upon Project (No. 51575126) supported by the National Natural Science Foundation of China, and projects (Nos. 2013 M541358 and 2015 T80358) funded by China Postdoctoral Science Foundation, and Project (No. WH20150108) supported by Discipline Construction Guide Foundation in Harbin Institute of Technology at Weihai.
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