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Generation of shape functions by optimization

In boundary value problems, the solution region is always discreti-zed into finite elements. The polynomial chosen to interpolate the field vari-ables over the element are called shape functions. The shape functions establish the relationship between the displacement at any point in the element with...

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Main Authors: Akeremale, O. C., Olaiju, O. A., Yeak, S. H.
Format: Article
Published: Research Publication 2020
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/93241/
http://dx.doi.org/10.37418/amsj.9.11.47
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spelling my.utm.932412021-11-19T03:23:33Z http://eprints.utm.my/id/eprint/93241/ Generation of shape functions by optimization Akeremale, O. C. Olaiju, O. A. Yeak, S. H. QA Mathematics In boundary value problems, the solution region is always discreti-zed into finite elements. The polynomial chosen to interpolate the field vari-ables over the element are called shape functions. The shape functions establish the relationship between the displacement at any point in the element with the nodal displacement of the element. However, the polynomial cannot guarantee the shape function of all the transition elements as the inverse of the matrix generated from some of the transition elements are not feasible. This paper of-fers an insight into the derivation of shape function using minimization theory. In the case of irregular elements, such as transition elements, improvements are made regarding the derivation so as to capture the peculiarities of the so-called transition elements. All the shape functions derived using minimization approach are validated according to interpolation properties. Research Publication 2020 Article PeerReviewed Akeremale, O. C. and Olaiju, O. A. and Yeak, S. H. (2020) Generation of shape functions by optimization. Advances in Mathematics: Scientific Journal, 9 (11). pp. 9429-9441. ISSN 1857-8365 http://dx.doi.org/10.37418/amsj.9.11.47
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Akeremale, O. C.
Olaiju, O. A.
Yeak, S. H.
Generation of shape functions by optimization
description In boundary value problems, the solution region is always discreti-zed into finite elements. The polynomial chosen to interpolate the field vari-ables over the element are called shape functions. The shape functions establish the relationship between the displacement at any point in the element with the nodal displacement of the element. However, the polynomial cannot guarantee the shape function of all the transition elements as the inverse of the matrix generated from some of the transition elements are not feasible. This paper of-fers an insight into the derivation of shape function using minimization theory. In the case of irregular elements, such as transition elements, improvements are made regarding the derivation so as to capture the peculiarities of the so-called transition elements. All the shape functions derived using minimization approach are validated according to interpolation properties.
format Article
author Akeremale, O. C.
Olaiju, O. A.
Yeak, S. H.
author_facet Akeremale, O. C.
Olaiju, O. A.
Yeak, S. H.
author_sort Akeremale, O. C.
title Generation of shape functions by optimization
title_short Generation of shape functions by optimization
title_full Generation of shape functions by optimization
title_fullStr Generation of shape functions by optimization
title_full_unstemmed Generation of shape functions by optimization
title_sort generation of shape functions by optimization
publisher Research Publication
publishDate 2020
url http://eprints.utm.my/id/eprint/93241/
http://dx.doi.org/10.37418/amsj.9.11.47
_version_ 1717093440636846080
score 13.211869

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