Direct determination of shape functions for isoparametric elements with arbitrary node configuration
Shape functions have been derived to describe different forms of elements, notably triangles and rectangles in 2-D, and tetrahedrons, cuboids, and triangular prisms in 3-D. There are generalised solutions for some regular node configurations, and hierarchical correction algorithms help with more dif...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2015-11-01
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| Series: | Open Engineering |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0049/eng-2015-0049.xml?format=INT |
| _version_ | 1818843777982267392 |
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| author | Hoth Julian Kowalczyk Wojciech |
| author_facet | Hoth Julian Kowalczyk Wojciech |
| author_sort | Hoth Julian |
| collection | DOAJ |
| description | Shape functions have been derived to describe
different forms of elements, notably triangles and rectangles
in 2-D, and tetrahedrons, cuboids, and triangular
prisms in 3-D. There are generalised solutions for some regular
node configurations, and hierarchical correction algorithms
help with more difficult node distributions. But to
this point there is no single formula or set of formulae that
allows the direct determination of shape functions for any
node configuration without restrictions. This paper shows
how a general set of formulae can be derived which is applicable
to any isoparametric element type with arbitrary
node configuration. This formulation is in such a form that
it is clear and concise. The approach is based on the Lagrange
polynomial considering up to three Cartesian and
four volume coordinates. Additionally, the correction procedure
that is inherent in the formulation to guarantee an
appropriate evaluation of the generalised shape functions
and to fulfil all four isoparametric shape function criteria
is discussed. The proof of validity illustrates the correctness
of the method. |
| first_indexed | 2024-12-19T05:03:16Z |
| format | Article |
| id | doaj.art-c6acbd04b2294adda9f11f855c798e5f |
| institution | Directory Open Access Journal |
| issn | 2391-5439 |
| language | English |
| last_indexed | 2024-12-19T05:03:16Z |
| publishDate | 2015-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Engineering |
| spelling | doaj.art-c6acbd04b2294adda9f11f855c798e5f2022-12-21T20:35:01ZengDe GruyterOpen Engineering2391-54392015-11-015110.1515/eng-2015-0049eng-2015-0049Direct determination of shape functions for isoparametric elements with arbitrary node configurationHoth Julian0Kowalczyk Wojciech1University of Duisburg- Essen, Faculty of Engineering, Chair of Mechanics and Robotics, Lotharstr. 1, 47057 Duisburg, GermanyUniversity of Duisburg- Essen, Faculty of Engineering, Chair of Mechanics and Robotics, Lotharstr. 1, 47057 Duisburg, GermanyShape functions have been derived to describe different forms of elements, notably triangles and rectangles in 2-D, and tetrahedrons, cuboids, and triangular prisms in 3-D. There are generalised solutions for some regular node configurations, and hierarchical correction algorithms help with more difficult node distributions. But to this point there is no single formula or set of formulae that allows the direct determination of shape functions for any node configuration without restrictions. This paper shows how a general set of formulae can be derived which is applicable to any isoparametric element type with arbitrary node configuration. This formulation is in such a form that it is clear and concise. The approach is based on the Lagrange polynomial considering up to three Cartesian and four volume coordinates. Additionally, the correction procedure that is inherent in the formulation to guarantee an appropriate evaluation of the generalised shape functions and to fulfil all four isoparametric shape function criteria is discussed. The proof of validity illustrates the correctness of the method.http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0049/eng-2015-0049.xml?format=INTFinite elements Isoparametric elements Shape functions |
| spellingShingle | Hoth Julian Kowalczyk Wojciech Direct determination of shape functions for isoparametric elements with arbitrary node configuration Open Engineering Finite elements Isoparametric elements Shape functions |
| title | Direct determination of shape functions for
isoparametric elements with arbitrary node
configuration |
| title_full | Direct determination of shape functions for
isoparametric elements with arbitrary node
configuration |
| title_fullStr | Direct determination of shape functions for
isoparametric elements with arbitrary node
configuration |
| title_full_unstemmed | Direct determination of shape functions for
isoparametric elements with arbitrary node
configuration |
| title_short | Direct determination of shape functions for
isoparametric elements with arbitrary node
configuration |
| title_sort | direct determination of shape functions for isoparametric elements with arbitrary node configuration |
| topic | Finite elements Isoparametric elements Shape functions |
| url | http://www.degruyter.com/view/j/eng.2015.5.issue-1/eng-2015-0049/eng-2015-0049.xml?format=INT |
| work_keys_str_mv | AT hothjulian directdeterminationofshapefunctionsforisoparametricelementswitharbitrarynodeconfiguration AT kowalczykwojciech directdeterminationofshapefunctionsforisoparametricelementswitharbitrarynodeconfiguration |