A Review on the Discrete Singular Convolution Algorithm and Its Applications in Structural Mechanics and Engineering

Abstract

The discrete singular convolution (DSC) algorithm is a relatively new numerical method. It has not only the advantage of high accuracy of global methods but also the advantage of the flexibility of local methods, and thus has been projected by its proponents as one of the potential alternative approaches to the conventional finite element method, especially for solving problems of structures in high frequency vibrations. Although the progression on the DSC algorithm and its applications is clear from past researches, but this has been scattered over lots of published articles. This paper presents a comprehensive review on the DSC algorithm and the application of the DSC for solutions of a variety of problems in structural mechanics and engineering, which should be of general interest to the computational community. The DSC algorithm is introduced first in a concise and clear manner to help the beginners and engineers who are going to use the DSC algorithm for structural analysis. Emphasis of the review is placed on the DSC analysis of bending, buckling, free vibration and dynamic analysis of structural elements and structures, although the DSC algorithm with a proper singular kernel can solve a wide range of science and engineering problems.