Publication

Abstract :

This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 28-node (sextic) triangular element. On using the isoparametric coordinate transformation, the curved triangle in the global (x, y) coordinate system is 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 this triangular element is implicitly replaced by sextic arc. The equation of this arc involves parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in sextic arc 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 triangle will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides.