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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| Format: | Article |
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Research Publication
2020
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| 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. |
| collection | ePrints |
| 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. |
| first_indexed | 2024-03-05T20:59:12Z |
| format | Article |
| id | utm.eprints-93241 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T20:59:12Z |
| publishDate | 2020 |
| publisher | Research Publication |
| record_format | dspace |
| spelling | utm.eprints-932412021-11-19T03:23:33Z http://eprints.utm.my/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 |
| spellingShingle | QA Mathematics Akeremale, O. C. Olaiju, O. A. Yeak, S. H. Generation of shape functions by optimization |
| title | 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_short | Generation of shape functions by optimization |
| title_sort | generation of shape functions by optimization |
| topic | QA Mathematics |
| work_keys_str_mv | AT akeremaleoc generationofshapefunctionsbyoptimization AT olaijuoa generationofshapefunctionsbyoptimization AT yeaksh generationofshapefunctionsbyoptimization |