Discrete singular convolution element method for static, buckling and free vibration analysis of beam structures

A new version of discrete singular convolution (DSC) algorithm, called the DSC element method, is proposed. The new method combines the high computational efficiency and accuracy of the original DSC algorithm with the convenience and generality of the finite element method in application to structural analysis. The shortage existing in the original DSC algorithm has been overcome. Besides, the proposed method provides a unique way to apply various boundary conditions in using DSC algorithm. Two types of DSC beam element are presented and a variety of problems, such as static, buckling and free vibrations with discontinuities in geometry or load, have been successfully solved by the proposed method. Numerical results show that the proposed DSC element method is an accurate and efficient method for analyzing beam structures.