A Proposed Approach to Simulate Thin Quadrilateral Plates Using GDQM Based on Kirchhoff–Love Theory

Document Type : Research Article


Department of Aerospace Engineering and Center of Excellence in Computational Aerospace, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15875-4413, Iran



In this study, an approach to free vibration analysis of thin quadrilateral plates using the generalized differential quadrature method based on the strong version of the governing equation is proposed. To achieve this aim, the governing equation of a thin quadrilateral plate is firstly obtained using the Kirchhoff–Love theory of plates (classical theory). The well-known differential quadrature method (GDQ) is then utilized to obtain the discretized form of the equations of motion. However, simulation of any arbitrary geometry using conventional GDQM based on classical theory is impossible. This drawback can be removed by defining the additional degrees of freedom in boundaries. Moreover, the combination of the Refined Differential Quadrature Method with geometry mapping is developed to simulate thin quadrilateral plates. Also, the multi-block or elemental strategy is implemented for problems with more geometric complexities. For this aim, geometry can be divided into several subdomains. Continuity conditions make the connection between adjacent elements at each interface. By establishing the whole discretized governing equations, the free vibration analysis of a thin plate will be provided via the achieved eigenvalue problem. The obtained results are compared and validated with available results in the literature that show high accuracy and a fast rate of convergence.


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