A Dynamic Procedure for Time and Space Domain Based on Differential Cubature Principle
Qiang Xu; Hongjing Li; Yuchen Mei
Based on the differential cubature (DC) principle, a dynamic procedure for simultaneous discretization of time and space is developed. A spatial&ndash:temporal differential cubature analysis method for dynamic problems is established with the Timoshenko shear beam: the reliability of analysis results obtained by which is verified, and the stability of the numerical scheme is studied. This method is extended to the two-dimensional structure, and the forced vibration analysis is carried out with the thin plate as an example. The research shows that the method can acquire highly accurate numerical results, and the calculated time-history numerical solution of beam displacement is extremely consistent with the analytical solution, which can adopt to the changes in beam properties and load parameters. With fewer nodes and longer time step than the finite element method (FEM), the method in this paper can still obtain stable and accurate results when solving displacement responses of plate under forced vibration. The numerical stability of this method is closely related to the grid form and the size of time step, and the increase in the number of nodes in the time domain is conducive to increasing the stability range.
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