Publication Type:

Journal Article


Finite Elements in Analysis and Design, Volume 44, Number 15, p.920-932 (2008)



Computational mechanics, Coordinate measuring machines, Drug products plants, Finite element method, Numerical integration, Point transformations, Quadratic programming, Triangular elements, Triangulation


<p>This paper is concerned with curved boundary triangular elements having one curved side and two straight sides. The curved elements considered here are the 6-node (quadratic), 10-node (cubic), 15-node (quartic) and 21-node (quintic) triangular elements. On using the isoparametric coordinate transformation, these curved triangles in the global (x, y) coordinate system are mapped into a standard triangle: { (ξ, η) / 0 ≤ ξ, η ≤ 1, ξ + η ≤ 1 } in the local coordinate system (ξ, η). Under this transformation curved boundary of these triangular elements is implicitly replaced by quadratic, cubic, quartic and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are 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 with one curved side and two straight sides. © 2008 Elsevier B.V. All rights reserved.</p>


cited By (since 1996)3

Cite this Research Publication

H. Ta Rathod, .V.Nagaraja, K., Naidu, VaKesavulu, and Venkatesh, B., “The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements”, Finite Elements in Analysis and Design, vol. 44, pp. 920-932, 2008.