The Discrete Singular Convolution Algorithm-Basic Principle And Applications

The discrete singular convolution (DSC) is a relatively new numerical method. The methodpossesses both the accuracy of the global method and the flexibility of the local method, and has beenproved efficient for analyzing many engineering problems. The DSC can handle complex geometry,and has been successfully used in solving some challenge problems, such as the free vibration ofplates with irregular internal supports, and vibrating at higher-order modes.One of the key issues for successfully applying the DSC algorithm is the elimination of thefictitious points outside the real structural domains by using the boundary conditions. It is observed,however, that there still exist some difficulties in using DSC if the free boundary is encountered.Therefore, most reported research work in using DSC only involved the simply supported or/andclamped edges. The main objectives of this dissertation are to investigate an efficient way forapplying the free boundary conditions, use the developed DSC algorithm for solutions of linear andnonlinear problems with various boundary conditions, including the free boundary conditions, andextend the application range of the DSC algorithm in engineering analysis.The contents of the dissertation are as follows. Firstly, the research development on the DSCalgorithm and its applications is summarized. Based on the existing shortage in applications of theDSC algorithm, the research contents are presented. Then the basic principle of the DSC algorithm isbriefly presented for completeness considerations. A new way to applying the free boundaryconditions, called Taylor series expansion based method, is proposed. Comparisons are made with thedifferential quadrature method (DQM). After that, various applications in using the DSC algorithmare presented, including static and buckling analysis, free vibration and wave propagation analysis,and nonlinear analysis. Emphasize has been paid to the structural components with stress boundaryconditions or free boundary conditions, with geometric discontinuity, as well as load discontinuity.Detained formulations and solution procedures are presented. The DSC results are compared to eithertheoretical solutions, or existing numerical results or results obtained by using finite element methodor by the DQM. Finally, the research work is briefly summarized. A few conclusions are drawn andthe innovations are pointed out. Some research topics are given for future investigations.