A 3D contact smoothing method using Gregory patches

In this work, a method is developed for smoothing three‐dimensional contact surfaces. The method can be applied to both regular and irregular meshes. The algorithm employs Gregory patches to interpolate finite element nodes and provide tangent plane continuity between adjacent patches. The resulting surface interpolation is used to calculate gaps and contact forces, in a variationally consistent way, such that contact forces due to normal and frictional contact vary smoothly as slave nodes transition from one patch to the next. This eliminates the ‘chatter’ which typically occurs in a standard contact algorithm when a slave node is situated near a master facet edge. The elimination of this chatter provides a significant improvement in convergence behaviour, which is illustrated by a number of numerical examples. Furthermore, smoothed surfaces also provide a more accurate representation of the actual surface, such that resulting stresses and forces can be more accurately computed with coarse meshes in many problems. This fact is also demonstrated by the numerical examples. Published in 2002 by John Wiley & Sons, Ltd.

[1]  B. M. Fraeijs de Veubeke,et al.  A conforming finite element for plate bending , 1968 .

[2]  J. A. Gregory.  Smooth interpolation without twist constraints , 1974 .

[3]  Hiroaki Chiyokura,et al.  Design of solids with free-form surfaces , 1983, SIGGRAPH.

[4]  David J. Benson,et al.  Sliding interfaces with contact-impact in large-scale Lagrangian computations , 1985 .

[5]  H Chiyokura,et al.  Localized surface interpolation method for irregular meshes , 1986 .

[6]  Ramon F. Sarraga,et al.  G1 interpolation of generally unrestricted cubic Bézier curves , 1987, Comput. Aided Geom. Des..

[7]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[8]  Jörg Peters,et al.  Local cubic and bicubic C1 surface interpolation with linearly varying boundary normal , 1990, Comput. Aided Geom. Des..

[9]  P. Wriggers,et al.  FINITE ELEMENT FORMULATION OF LARGE DEFORMATION IMPACT-CONTACT PROBLEMS WITH FRICTION , 1990 .

[10]  Tony DeRose,et al.  Necessary and sufficient conditions for tangent plane continuity of Bézier surfaces , 1990, Comput. Aided Geom. Des..

[11]  John E. Howland,et al.  Computer graphics , 1990, IEEE Potentials.

[12]  J. C. Simo,et al.  A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems , 1993 .

[13]  F. Armero,et al.  A new dissipative time-stepping algorithm for frictional contact problems: formulation and analysis , 1999 .

[14]  P. Wriggers,et al.  On Smooth Finite Element Discretizations for Frictional Contact Problems , 2000 .

[15]  T. Laursen,et al.  A framework for development of surface smoothing procedures in large deformation frictional contact analysis , 2001 .