## Advantages of cubic arcs for approximating curved boundaries by subparametric transformations for some higher order triangular elements

Publication Type : Journal Article

Publisher : Applied Mathematics and Computation

Source : Applied Mathematics and Computation, Volume 219, Number 12, p.6893-6910 (2013)

Keywords : Choice of parameters, Co-ordinate transformation, Computational mechanics, Curved boundary, Finite element method, Four-point, Global coordinate systems, Iso-parametric, Local coordinate system, Numerical example, Numerical integrations, Point transformations, Quintic, Triangular elements

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Verified : Yes

Year : 2013

Abstract : In the finite element method, the most popular technique for dealing with curved boundaries is that of isoparametric coordinate transformations. In this paper, the 10-node (cubic), 15-node (quartic) and 21-node (quintic) curved boundary triangular elements having one curved side and two straight sides are analyzed using the isoparametric coordinate transformations. By this method, these curved triangles in the global coordinate system are mapped into a isosceles right angled unit triangle in the local coordinate system and the curved boundary of these triangular elements are implicitly replaced by cubic, quartic, and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. Relations are deduced for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a cubic arc which passes through four points of the original curve, thus ensuring a good approximation. The point transformations thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements. Numerical examples are given to demonstrate the accuracy and efficiency of the method. © 2013 Elsevier Inc. All rights reserved.

Cite this Research Publication : Dr. V. Kesavulu Naidu and Dr. K.V. Nagaraja, “Advantages of cubic arcs for approximating curved boundaries by subparametric transformations for some higher order triangular elements”, Applied Mathematics and Computation, vol. 219, pp. 6893-6910, 2013.