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Proportional isoparametric transformations for quadratic Lagrangian finite elements
Abstract A modification to the method of isoparametric co-ordinate transformations in finite element analysis greatly improves the accuracy of the method. It is shown that allowing the side and interior nodes of a quadratic Lagrangian element to remain at the same relative positions with respect to the corner nodes in local and global space provides significant computational advantages compared to the standard isoparametric transformation which centers these nodes in local space. The method for positioning these nodes in local space is developed and tested for cases using two-dimensional, quadrilateral elements, but is also applicable to other shapes and higher dimension elements. The computational tests presented demonstrate that use of the new transformation generally gives a solution of better accuracy than the classical transformation. The new technique also adds to the overall stability of the isoparametric transformation by enabling solutions to be computed when nodes are positioned almost anywhere in the element space.
Proportional isoparametric transformations for quadratic Lagrangian finite elements
Abstract A modification to the method of isoparametric co-ordinate transformations in finite element analysis greatly improves the accuracy of the method. It is shown that allowing the side and interior nodes of a quadratic Lagrangian element to remain at the same relative positions with respect to the corner nodes in local and global space provides significant computational advantages compared to the standard isoparametric transformation which centers these nodes in local space. The method for positioning these nodes in local space is developed and tested for cases using two-dimensional, quadrilateral elements, but is also applicable to other shapes and higher dimension elements. The computational tests presented demonstrate that use of the new transformation generally gives a solution of better accuracy than the classical transformation. The new technique also adds to the overall stability of the isoparametric transformation by enabling solutions to be computed when nodes are positioned almost anywhere in the element space.
Proportional isoparametric transformations for quadratic Lagrangian finite elements
Soll, Wendy E. (author) / Gray, William G. (author)
Engineering Analysis ; 2 ; 61-66
1985-01-01
6 pages
Article (Journal)
Electronic Resource
English
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