Connectivity-based, all-hexahedral mesh generation method and apparatus

• US 5,768,156 A
• Filed: 10/25/1995
• Issued: 06/16/1998
• Est. Priority Date: 10/25/1995
• Status: Expired due to Fees

• Current Assignee: Sandia Corporation (Martin Marietta Corporation)
• Original Assignee: Sandia Corporation (Martin Marietta Corporation)
• Inventors: Mitchell, Scott A., Murdoch, Peter, Blacker, Ted D., Tautges, Timothy James
• Primary Examiner(s): Trans, Vincent N.
• Application Number:
  US08/548,286
• Time in Patent Office: 965 Days
• Field of Search: 364/578, 364/488, 495/119, 495/123, 495/141
• US Class Current: 703/2
• CPC Class Codes: G06T 17/20 Finite element generation, e.g. wire-frame surface description, tesselation

Abstract

The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as "whisker chords." This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method.

Claims

1. An automated system for hexahedral volume discretization of a geometric object having interior and exterior boundaries,

means for representing a three-dimensional arrangement of surfaces and converting the arrangement to a two-dimensional hexahedral mesh;

means for constructing a plurality of initial loops, sheets, chords, and sheetchords; and

processing means for iteratively locating at least three pair-wise adjacent chords;

for iteratively constructing a whisker hex by crossing the at least three pair-wise adjacent chords; and

for iteratively checking for invalid connectivity on all sheets involved in the whisker hex to form a mesh of hexahedral elements defining the geometric object.

2. The automated system of claim 1, wherein said mesh of the hexahedral elements is boundary sensitive.

3. The automated system of claim 1, wherein said mesh of the hexahedral elements is orientation insensitive.

4. In a finite element analysis comprising generating a mesh of quadrilateral elements defining a geometric object to be analyzed, introducing a stimulus responsive to an input by an operator to which the response of the geometric object is to be modeled, performing finite element analysis on the geometric region in response to the stimulus to produce analysis data, and using the resulting analysis data, a method of automatically generating a mesh of hexahedral elements comprising the steps of:

grouping the dual of a quadrilateral surface mesh into a plurality of logical loops, wherein said grouping results in an arrangement of a plurality of sheets, the arrangement of sheets defining chords formed by the intersection of said plurality of logical sheets;

representing said plurality of sheets in two dimensional topological structure;

locating at least two pair-wise adjacent chords on said plurality of logical sheets;

crossing the at least two pair-wise adjacent chords to construct a logical hexahedron; and

checking for invalid connectivity on all of said plurality of logical sheets involved in the logical hexahedron after iteratively crossing the at least two pair-wise adjacent chords until an all-hexahedral mesh is completed.

5. The method of claim 4, wherein a complete mesh is indicated by all the plurality of chords intersecting the quadrilateral surface mesh.

6. The method of claim 4, wherein a complete mesh is indicated by forming a closed curve within the geometric object.

7. The method of claim 4, further comprising the steps of iteratively locating at least two pair-wise adjacent chords on said plurality of logical sheets;

iteratively crossing the at least two pair-wise adjacent chords to construct a logical hexahedron; and

iteratively checking for invalid connectivity on all of said plurality of logical sheets involved in the logical hexahedron after iteratively crossing the at least two pair-wise adjacent chords.