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Geometric nonlinear formulation and discretization method for a rectangular plate undergoing large overall motions. (English) Zbl 1192.74151

Summary: In the present paper, the geometric nonlinear formulation is developed for dynamic stiffening of a rectangular plate undergoing large overall motions. The dynamic equations, which take into account the stiffening terms, are derived based on the virtual power principle. Finite element method is employed for discretization of the plate. The simulation results of a rotating rectangular plate obtained by using such geometric nonlinear formulation are compared with those obtained by the conventional linear method without consideration of the stiffening effects. The application limit of the conventional linear method is clarified according to the frequency error. Furthermore, the accuracy of the assumed mode method is investigated by comparison of the results obtained by using the present finite element method and those obtained by using the assumed mode method.

MSC:

74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
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