A New Approach to Automesh Generation of all β graded triangular and quadrilateral Finite Elements over Analytical Surfaces by using the Parabolic Arcs passing through four points on the Boundary Curve

Abstract

This paper presents a new mesh generation method for a simply connected curved domain of a planar region which has curved boundary described by one or more analytical equations. We first decompose this curved domain into simple sub regions in the shape of curved triangles. These simple regions are then triangulated to generate a fine mesh of linear triangles in the interior and curved triangles near to the boundary of curved domain. These simple regions are then triangulated to create 6-node triangles by inserting midside nodes to these triangles. Each isolated 6-node triangle is then split into four triangles according to the usual scheme, that is, by using straight lines to join the midside nodes. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex curved or cracked convex curved domains into all triangles, thus propagating refinements and .The quadrangulation of graded 3-node linear triangles is done by inserting three midside nodes and a centroidal node.Then each graded triangle is split into three quadrilaterals by using straight lines to join the centroid to the midside nodes. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. We have approximated the curved boundary arcs by equivalent parabolic arcs.To preserve the mesh conformity, a similar procedure is also applied to every triangle of the domain to fully discretize the given curved domain into all triangles and quadrilaterals, thus propagating a uniform refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples of a circular disk and a cracked circular disk are presented to illustrate the simplicity and efficiency of the new mesh generation method. We have appended the MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable output on the nodal coordinates ,element connectivity and graphic display of the all triangular and quadrilateral mesh for application to finite element analysis.