A new method for finite element transitional mesh generation

Abstract

SUMMARYIn the preparation of finite element meshes, inclusion of transitional blocks is important in order to construct optimal meshes. In this paper, a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes. These meshes are well graded and do not require any mesh smoothening algorithm. The inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones. This new algorithm is described in detail and its efficiency is illustrated with appropriate examples.Different methods available for inverse isoparametric mapping are discussed with their merits and limitations. Many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type. These techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements. In this paper, a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping. The computations in this approach are already part of every finite element program based on the isoparametric formulation. Hence implementation of the new algorithm is very simple and straightforward.

Impact fracture analysis enhanced by contact of peridynamic and finite element formulations

“…Murti and Valliappan [49] presented a numerical technique by bisecting a line passing a point and a node of known natural coordinates, and this method was extended to three-dimensional space by Murti et al [50]. However, the bisection method has its limitations [51]. A more generalized approach for inverse isoparametric mapping was presented by Chinnaswamy et al [51].…”

“…However, the bisection method has its limitations [51]. A more generalized approach for inverse isoparametric mapping was presented by Chinnaswamy et al [51]. For the inverse mapping of a point ðb x; b y; b zÞ, the equation to be solved is written as…”

“…By expanding the vector f in Taylor's series and omitting the second and higher order terms, it can be shown that [51]. …”

Element free formulation used for connecting domain boundaries

“…However, intended quadrilateral element meshes will largely increase the difficulty of mesh generation. (Zienkiewicz and Phillips, 1971;Gordon and Hall, 1973;Wordenweber, 1984;Kikuchi, 1985;Talbert and Parkinson, 1990;Chinnaswamy et al, 1991;Blacker and Stephenson, 1991;Zhu et al, 1991;Rank et al, 1993;Lee and Lo, 1994;Cheng and Li, 1996;Sarrate and Huerta, 2000;Kwak et al, 2002). Therefore, many scholars have put their efforts into research on mesh generation.…”

“…General software packages for commercial use which have automatic mesh generation are largely based on the mapping method (Cohen, 1980;Haber et al, 1981;Brown, 1981;Ho-Le, 1988;Zienkiewicz and Phillips, 1971;Gordon and Hall, 1973;Kikuchi, 1985;Chinnaswamy et al, 1991;Cheng and Li, 1996). This method is fast, simple and easily controls geometry and mesh density as well as being applicable to highly changeable geometric boundaries and mesh shapes.…”