Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm

This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are const...

Full description

Saved in:
Bibliographic Details
Main Authors: WEI, G. W., ZHAO, Yibao, XIANG, Y.
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2002
Subjects:
Online Access:https://ink.library.smu.edu.sg/lkcsb_research/931
https://ink.library.smu.edu.sg/context/lkcsb_research/article/1930/viewcontent/Discrete_singular_convolution_pt1_pv.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Singapore Management University
Language: English
id sg-smu-ink.lkcsb_research-1930
record_format dspace
spelling sg-smu-ink.lkcsb_research-19302018-08-28T00:29:18Z Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm WEI, G. W. ZHAO, Yibao XIANG, Y. This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet. 2002-11-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/lkcsb_research/931 info:doi/10.1002/nme.526 https://ink.library.smu.edu.sg/context/lkcsb_research/article/1930/viewcontent/Discrete_singular_convolution_pt1_pv.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection Lee Kong Chian School Of Business eng Institutional Knowledge at Singapore Management University square plates vibration analysis wavelets discrete singular convolution Physical Sciences and Mathematics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic square plates
vibration analysis
wavelets
discrete singular convolution
Physical Sciences and Mathematics
spellingShingle square plates
vibration analysis
wavelets
discrete singular convolution
Physical Sciences and Mathematics
WEI, G. W.
ZHAO, Yibao
XIANG, Y.
Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
description This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet.
format text
author WEI, G. W.
ZHAO, Yibao
XIANG, Y.
author_facet WEI, G. W.
ZHAO, Yibao
XIANG, Y.
author_sort WEI, G. W.
title Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
title_short Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
title_full Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
title_fullStr Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
title_full_unstemmed Discrete Singular Convolution and Its Application to the Analysis of Plates with Internal Supports. Part 1: Theory and Algorithm
title_sort discrete singular convolution and its application to the analysis of plates with internal supports. part 1: theory and algorithm
publisher Institutional Knowledge at Singapore Management University
publishDate 2002
url https://ink.library.smu.edu.sg/lkcsb_research/931
https://ink.library.smu.edu.sg/context/lkcsb_research/article/1930/viewcontent/Discrete_singular_convolution_pt1_pv.pdf
_version_ 1770569736410628096