Publication Type : Journal Article
Publisher : Finite Elements in Analysis and Design
Source : Finite Elements in Analysis and Design, Volume 44, Number 15, p.920-932 (2008)
Url : https://www.sciencedirect.com/science/article/pii/S0168874X08000930
Keywords : Finite element method, Numerical integration, Point transformations, Triangular elements
Campus : Bengaluru
School : School of Engineering
Department : Mathematics
Year : 2008
Abstract : 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.
Cite this Research Publication : H. T. Rathod, Nagaraja, K. V., Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “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.