Technical reports

Automatic mesh generation of 2 & 3 dimensional curvilinear manifolds

Burkard Wördenweber

November 1981, 128 pages

This technical report is based on a dissertation submitted November 1981 by the author for the degree of Doctor of Philosophy to the University of Cambridge, St John’s College.

Abstract

The research reported in this dissertation was undertaken to investigate methods for automatic generation of finite element meshes from shapes defined using the techniques of computer-aided design.

A theory of decomposition of shapes into triangles or tetrahedra has been developed using topological properties of manifolds. It has been applied to 2 and 3-dimensional, planar and curvilinear manifolds, where it results in a close to minimal mesh of elements.

Techniques for mesh refinement have been derived from existing work on shape grammars, and have been used in local regions of a mesh. In this way a coarse mesh of the initial decomposition can be converted gradually into a mesh suitable for finite-element analysis.

Existing knowledge in finite-element analysis suggests a method of controlled refinement where refinement of the mesh proceeds according to the difference between actual and desired mesh properties. It is shown that the properties may be specified either directly or using empirical rules and inference. Provision is also made to allow refinement to take place according to error estimates of preliminary analysis runs. The result of controlled refinement is the finite-element mesh for a specific shape and loadcase, suitable for subsequent analysis.

Based upon these theoretical studies a program was implemented in conjunction with the BUILD-3 geometric modeller and used to produce finite-element meshes.

Full text

Only available on paper (could be scanned on request).

BibTeX record

@TechReport{UCAM-CL-TR-18,
  author =	 {W{\"o}rdenweber, Burkard},
  title = 	 {{Automatic mesh generation of 2 \& 3 dimensional
         	   curvilinear manifolds}},
  year = 	 1981,
  month = 	 nov,
  institution =  {University of Cambridge, Computer Laboratory},
  address =	 {15 JJ Thomson Avenue, Cambridge CB3 0FD, United Kingdom,
          	  phone +44 1223 763500},
  doi = 	 {10.48456/tr-18},
  number = 	 {UCAM-CL-TR-18}
}