A STUDY OF THE EQUATION OF THE IMPLIED CURVE FOR ISOPARAMETRIC QUADRATIC TRIANGULAR FINITE ELEMENT

Document Type : Original Article

Authors

1 DR., Lecturer, Mathematic Dept., Faculty of Science, Zagazig University.

2 Post—graduate student.

Abstract

Many practical problems solved by the finite element method have curved boundaries which are mainly approximated by use of isoparametric elements. These curved elements have a wide applications in mechanical engineering, e.g. design of gearing, dynamics of shell structure, ... etc. The use of isoparametric quadratic triangular elements of Lagrange and
Hermite type is well established in the finite element method. In this paper the derivation of the equation of the implied curve when a curved edge is approximated using isoparametric quadratic triangles. The implied curve depends only on the parameters of the nodes associated with the curved side and does not depend on the basis function used. The .general six point isoparametric transformation is analysed with respect to a triangle with two sides and one curve side. Special case of the trans-formation is considered which lead to implied curve of the form of symmetric parabola, thus enabling isoparametric transformations to match a :variety of boundary shapes. The above study of the isoparametric quadratic curve is applied on the circle which is divided into equal angle sectors. The continuity of this curve between elements was studied for different angle sectors.

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