Generation of quadrilateral mesh over analytical curved surfaces

Abstract An automatic adaptive quadrilateral mesh conversion scheme for the generation of adaptive refinement meshes over analytical curved surfaces is proposed. The starting point of the quadrilateral mesh generator is a background triangular mesh of the curved surface. By a carefully controlled process to merge two triangles at a time the triangular mesh can be completely converted to quadrilaterals. A rapidly graded quadrilateral mesh with node spacing compatible with the desired element size distribution can be obtained from a well-graded triangular mesh. The quality of the quadrilateral mesh can be subsequently enhanced by a series of mesh modifications and element shape improvement procedures. The present scheme can be used in conjunction with an adaptive surface triangular mesh generator to generate quadrilaterial meshes suitable for adaptive shell refinement analysis.

[1]  S. H. Lo,et al.  Generating quadrilateral elements on plane and over curved surfaces , 1989 .

[2]  L. Carter Wellford,et al.  A finite element transitional mesh generation procedure using sweeping functions , 1988 .

[3]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[4]  O. C. Zienkiewicz,et al.  Plate bending elements with discrete constraints: New triangular elements , 1990 .

[5]  David C. Anderson,et al.  Composite mappings for planar mesh generation , 1987 .

[6]  J. Z. Zhu,et al.  The finite element method , 1977 .

[7]  C. Lee,et al.  A new scheme for the generation of a graded quadrilateral mesh , 1994 .

[8]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[9]  O. C. Zienkiewicz,et al.  An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co‐ordinates , 1971 .

[10]  John M. Sullivan,et al.  Automatic conversion of triangular finite element meshes to quadrilateral elements , 1991 .

[11]  Jeffrey A. Talbert,et al.  Development of an automatic, two‐dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition , 1990 .

[12]  S. H. Lo,et al.  Finite element mesh generation over analytical curved surfaces , 1996 .

[13]  Bernard Amadei,et al.  A new method for finite element transitional mesh generation , 1991 .

[14]  D. Lavender,et al.  An assessment of higher-order isoparametric elements for solving an elastic problem , 1986 .

[15]  O. Zienkiewicz,et al.  A new approach to the development of automatic quadrilateral mesh generation , 1991 .

[16]  E. Hinton,et al.  A new nine node degenerated shell element with enhanced membrane and shear interpolation , 1986 .

[17]  O. C. Zienkiewicz,et al.  Adaptive finite element analysis with quadrilaterals , 1991 .

[18]  H. A. ElMaraghy,et al.  An expert system for forming quadrilateral finite elements , 1990 .