Analysis Of Structure With Discontinuousvariations Of Geometry By The DSC Algorithm

Over the past decade, with much effort spent on the development of the discrete singular convolution algorithm(DSC), it becomes a potential and promising numerical method in science and engineering applications. However, some difficulties exist in the applications of the DSC to structural analysis, e.g., establish a unique scheme and more accurate method to handle boundary conditions and structures with discontinuities in geometry. The main objectives of this thesis are to investigate a unique scheme and more accurate method to handle various boundary conditions and propose two novel DSC algorithms based on conventional DSC and Taylor’s series expansion, namely, the modified DSC with polynomial interpolation method and discrete singular convolution element method.For the modified discrete singular convolution method, an nth-order interpolation polynomial is established on each side of the step. Then two or three jump conditions together with two continuous conditions at steps are established and used to relate the two polynomials. Detained formulations and solution procedures are presented. For the discrete singular convolution element method, it provides a unique way to apply various boundary conditions in using DSC algorithm. Based on two forms of Taylor series expansion equations, two types of DSC beam element are formulated. Results obtained by the two methods are compared to either theoretical solutions, or existing numerical results or results obtained by using finite element method or by the DQM. Numerical results show that both methods are accurate and efficient for analyzing beams and plates with discontinuities in geometry or load. Finally, the research work is briefly summarized. A few conclusions are drawn and the innovations are pointed out. The presented research achievements extend the application range of the DSC algorithm in the area of structural mechanics.