Temporal and spatial-domain DFT-based spectral element model for the dynamic analysis of a rectangular Mindlin plate

초록

A temporal and spatial-domain spectral element model for the dynamics of a rectangular Mindlin plate based on the discrete Fourier transform was developed as an extension of the authors' previous work. The following procedure was implemented to derive the spectral element model. First, the general solutions of a rectangular Mindlin plate element were derived in spectral forms in both the temporal and spatial domains. Second, the boundary functions that describe the boundary conditions were then expressed in spectral forms. Third, using the orthogonality properties of the trigonometric functions, the relationships between the spectral components of the general solutions and boundary functions were derived in the square-matrix-equation form. Finally, the spectral matrix was formulated for the entire plate element using the force-displacement relationships. The proposed spectral element method could provide accurate dynamic responses and waves in a plate structure using the fast Fourier transform algorithm owing to the spectral form representations of the general solutions and boundary functions in both the temporal and spatial domains. The high accuracy and computational efficiency of the proposed SEM were investigated by comparing the results with those of the exact theory, modal analysis method, Rayleigh Ritz method, dynamic stiffness method, and commercial finite element analysis software ANSYS. (c) 2021 Elsevier Ltd. All rights reserved.

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