A Review on the Discrete Singular Convolution Algorithm and Its Applications in Structural Mechanics and Engineering
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ORIGINAL PAPER
A Review on the Discrete Singular Convolution Algorithm and Its Applications in Structural Mechanics and Engineering Xinwei Wang1 · Zhangxian Yuan2 · Jian Deng1 Received: 27 February 2019 / Accepted: 30 September 2019 © CIMNE, Barcelona, Spain 2019
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.
1 Introduction Since test setups and studies are usually costly and the experimental reliability strongly depends on the expertise of the experiment performer as well as the test environment, therefore, nowadays numerical approaches have drawn much more interest among researchers and engineers and the computing is increasingly employed as a key component in mathematical problem-solving. The development of new methods for numerical solutions of problems in engineering and physical sciences is an ongoing parallel activity with the advancement of faster computers [1], since no single method is versatile and can be efficiently used for solutions of all problems in science and engineering [2]. Two types of methods, one is called the global method and the other is called the local method, have been developed. It is well known that global methods have the advantage of high accuracy and the * Zhangxian Yuan [email protected] 1
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332‑0150, USA
2
local ones have the advantage of flexibility. A chronological scheme of various numerical methods is given by Tornabene et al. [3]. According to the formulations, existing numerical methods can be also categorized into the strong form method, the weak form method, and the combination of strong and weak form methods [2–5]. The differential q
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