US 5,497,451 A · Computerized method for decomposing a geometric model of surface or volume into finite elements

Abstract

A computerized process for defining finite elements in a surface or volume for ultimately predicting a physical characteristic of the surface or volume. For the surface, for example, the process includes a first step of inputting surface boundary point coordinates of a geometric model of the surface to a computer system, the computer system including an image display screen displaying the geometric model. The process further includes preparing the boundary edges of surface by generating piecewise geometrically smooth bezier curves between boundary points and converting the bezier curves to cubic interpolation polynomials and defining evenly spaced points on each cubic interpolation polynomial and decomposing the surface with divider curves, if the surface is not already 3, 4, or 5 sided, into 3, 4, and 5 sided primitives. Thereafter, a determination is made of the largest acceptable element size and the number of elements disposed along each edge of each primitive. The next steps are readjusting one of the divider curves to match a closest even element vertices and mapping in 3 and 5 sided clusters and then preparing remaining 4 sided primitives for decomposition into 4 sided elements and mapping in elements and element patches. Thereafter, method includes the steps of optimising the elements in the mesh and writing the resulting mesh to a storage file.

Claims22

Dependent claims

A method for defining finite elements in a surface for ultimately predicting a physical characteristic of the surface, which method comprises:

providing a computer system having a computer connected to an input device, to an image display screen and to a storage file, the storage file including instructions and data for at least steps (iii) through (xi) of said method;
(i) inputting, through the input device, surface boundary point coordinates of a geometric model of a surface;
(ii) displaying a surface object on the image display screen, the surface object consisting of the geometric model of the surface;
(iii) preparing boundary edges of the surface object by generating piecewise geometrically smooth bezier curves between boundary points and converting the bezier curves to cubic interpolation polynomials and defining evenly spaced points on each cubic interpolation polynomial;
(iv) decomposing the surface object with divider curves, if the surface object is not already 3, 4, or 5 sided, into 3, 4, and 5 sided primitives;
(v) determining a largest acceptable element size;
(vi) determining a number of elements disposed along each edge of each primitive;
and
(vii) readjusting one of the divider curves to match closest even element vertices;
(viii) mapping in 3 and 5 sided clusters;
(ix) preparing remaining 4 sided primitives for decomposition into 4 sided elements;
(x) mapping in elements and element patches to develop a mesh from the surface object;
(xi) optimizing the elements in the mesh;
and
(xii) writing the mesh having the optimized elements to the storage file.

12 more elements

A method for defining finite elements in a volume for ultimately predicting a physical characteristic of said volume, which method comprises:

(i) providing a computer system having a computer connected to an input device, to an image display screen and to a storage file, the storage file including instructions and data for at least steps (iv) through (xviii) of said method;
(ii) inputting, through the input device, surface boundary point coordinates of a geometric model of each surface of a volume;
(iii) displaying on the image display screen a surface object for each surface of the volume, each surface object consisting of the geometric model of the surface;
(iv) inputting points defining boundaries of each surface of the volume to produce an outward pointing normal away from an interior of the volume;
(v) setting up an initial surface adjacency description for the volume;
(vi) initializing a volume adjacency array;
(vii) excising non-linear extrusions from the volume;
(viii) decomposing remaining sub-volumes not having 3, 4, or 5 sides into volumes with 3, 4, or 5 sides;
(ix) decomposing any composite sub-volumes;
(xi) decomposing any symmetric sub-volumes;
(xii) generating real divider surfaces for each volume adjacency array axis;
(xii) converting sub-volume data to an extrusion volume data format;
(xiii) optimizing all three sided extrusions;
(xiv) optimizing all five sided extrusions;
(xv) determining a number of elements per extrusion edge;
(xvi) generating extrusion surface;
(xvii) mapping in elements and element patches into the extrusion surfaces to develop a mesh from each surface object of the volume;
(xviii) converting the volume to hexahedron elements;
and
(ixx) writing the mesh to a file in the storage file.

17 more elements

Dependencies are inferred from the claim text.

Computerized method for decomposing a geometric model of surface or volume into finite elements

Life of this patent

Computerized method for decomposing a geometric model of surface or volume into finite elements

Life of this patent

Abstract

Claims22