Dady composite tetrahedral modeling element

• US 20020198693A1
• Filed: 06/21/2002
• Published: 12/26/2002
• Est. Priority Date: 06/22/2001
• Status: Abandoned Application

• Current Assignee: Third Wave Systems, Inc.
• Original Assignee: Third Wave Systems, Inc.
• Inventors: Marusich, Troy
• Application Number:
  US10/177,084
• Publication Number:
  US 20020198693A1
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06T 17/20 Finite element generation, e.g. wire-frame surface description, tesselation

Abstract

A modeling element and method of modeling deformation in a body is shown that reduces volumetric locking. Further, a modeling element and method has been shown that reduces computational complexity. The number of nodes per element is reduced, while still maintaining a reduction in constraints by utilizing a composite element. The modeling element is more amenable to adaptive meshing due to use of first-order elements. The modeling element includes a good aspect ratio in the parent element and sub-elements to improve accuracy and computational efficiency. Incorporating constant pressure on the parent element provides a more ideal constraint ratio.

Claims

1. A computational modeling element, comprising:

a first-order parent tetrahedron having four corner nodes at the corners of the tetrahedron; and

an additional node that defines a number of sub-elements within the first-order tetrahedron.

2. The computational modeling element of claim 1, wherein the additional node forms four first-order edges with each of the four corner nodes of the first-order tetrahedron.

3. The computational modeling element of claim 1, wherein the additional node defines four tetrahedral sub-elements within the first-order tetrahedron.

4. The computational modeling element of claim 1, wherein the first-order tetrahedron includes axial symmetry about at least one axis of rotation.

5. The computational modeling element of claim 4, wherein the first-order tetrahedron includes axial symmetry about four axes of rotation.

6. The computational modeling element of claim 1, wherein the sub-elements each include axial symmetry about at least one axis of rotation.

7. A method of modeling deformation in a body, comprising:

generating a mesh of first-order tetrahedron elements that subdivide a representation of the body;

configuring each first-order tetrahedron element to include an additional node that defines a number of sub-elements within the first-order tetrahedron;

defining a number of element behavior properties; and

calculating deformation data based on the element behavior properties.

8. The method of claim 7, wherein the deformation includes plastic deformation.

9. The method of claim 7, wherein configuring each first-order tetrahedron element to include an additional node includes configuring each first-order tetrahedron element to include an additional node that defines four tetrahedral sub-elements within each first-order tetrahedron element.

10. The method of claim 7, further including transferring the calculated deformation data to a user readable media.

11. The method of claim 7, further including adaptive meshing of selected regions within the body.

12. The method of claim 7, wherein defining a number of element behavior properties includes defining constant pressure for the first-order tetrahedron element with average sub-element pressure.

13. The method of claim 7, wherein defining a number of constraints includes:

utilizing a first pressure formulation for deformation below a critical strain; and

utilizing a second pressure formulation for deformations larger that the critical strain.

14. The method of claim 7, wherein defining a number of element behavior properties includes utilizing average nodal pressure.

15. The method of claim 7, wherein defining a number of element behavior properties includes defining an hourglass mode control.

16. The method of claim 7, wherein the steps are performed in the order presented.

18. The machine-readable medium of claim 17, wherein configuration of each first-order tetrahedron element to include an additional node includes configuration of each first-order tetrahedron element to include an additional node that defines four tetrahedral sub-elements within each first-order tetrahedron element.

19. The machine-readable medium of claim 17, wherein the number of element behavior properties for the first-order tetrahedrons includes constant pressure for each first-order tetrahedron element with average sub-element pressure.

20. The machine-readable medium of claim 17, wherein the number of element behavior properties for the first-order tetrahedrons includes average nodal pressure for each first-order tetrahedron element.

17. A machine-readable medium with instructions stored thereon, the instructions when executed operable to cause:

generation of a mesh of first-order tetrahedron elements that subdivide a representation of a body;

configuration of each first-order tetrahedron element to include an additional node that defines a number of sub-elements within the first-order tetrahedron element;

computation of deformation based on a number of element behavior properties for the first-order tetrahedron elements.