Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Abstract

SUMMARYPart 2 of this series of two papers presents the applications of the discrete singular convolution (DSC) algorithm. The main purpose of this paper is to explore the utility, test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports. Both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions. The e ects of di erent size, shape and topology of the internal supports and di erent boundary conditions on the vibration response of plates are investigated. The partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports. Several closed-loop supports, such as ring, square and rhombus, and their combinations are studied for complex internal supports. Convergence and comparison studies are carried out to establish the correctness and accuracy of the DSC algorithm. The DSC results are compared with those in the available literature obtained by using other methods. Numerical results indicate that the DSC algorithm exhibits controllable accuracy for plate analysis and shows excellent exibility in handling complex geometries, boundary conditions and support conditions.

DSC solution for flow in a staggered double lid driven cavity

“…Conventional methods have encountered great di culty of numerical instability for such analyses. The DSC algorithm found its success in resolving these problems [33,34]. The DSC solution of the Navier-Stokes equations is of primary interest to the present study.…”

Numerical solution of the Helmholtz equation with high wavenumbers

“…The unified feature of the DSC formalism was discussed and it was demonstrated that computational methods of Galerkin, collocation, global, local and finite difference types can be derived from a single starting point in the framework of the DSC algorithm [24]. The DSC algorithm may be regarded as a local spectral method [25] and it has been used for the treatment of complex boundary conditions in structural analysis [26,27] and applied to computational hydrodynamics [28]. Certain aspects of the convergence of the DSC algorithm have been discussed [25].…”

Free vibration analysis of Timoshenko beams by DSC method

“…The method of DSC was proposed to solve linear and nonlinear differential equations by Wei [35,36], and later it was introduced to solid and fluid [37][38][39][40][41][42][43][44][45][46]. It has also been successfully employed for different vibration problems of structural members such as plates and shells [47][48][49][50]. It is shown from these studies that the method of DSC has high level of accuracy and reliability.…”