Mesh generation with quasi-equilateral triangulation for finite element analyses

Claim 2

In combination with a computer having means to read, interpret and execute a program and a program therein having means to accept data input and means to perform an initial meshing triangulation for finite element analysis of polygonal two-dimensional objects, meshing means having embedded therein at least one operator selected from a group of operators node-on-edge, node-in-interior, edge-swapping and node-relocation, said meshing means always including the operator node-in-interior, where: node-on-edge finds a boundary node location and triangulates an element adjacent the boundary, node-in-interior finds an interior node location within a quadrilateral and triangulates the quadrilateral, edge-swapping improves a mesh quality by swapping an interior edge of a quadrilateral for the other interior edge of the quadrilateral, and node-relocation finds a new interior node location within a quadrilateral when node-in-interior fails to meet a lower bound criterion.

Claim 3

The computer and program of claim 1 including means to find a longest edge in the mesh prior to application of any of the operators to the mesh.

Claim 4

The computer and program of claim 2 including means to cease the meshing operation on an object when the longest edge in the mesh is less than a user-defined element length.

Claim 5

The computer and program of claim 2 including means to cease the meshing operation on an object when all angles of triangles in the mesh equal or exceed the lower bound criterion for the angles.

Claim 6

The computer and program of claim 1 wherein the initial meshing triangulation comprises a Constrained Delaunay Triangulation.

Claim 7

A computer implemented method to generate two-dimensional meshes for finite element analysis of polygonal objects comprising the steps of: inputting a configuration of the polygonal object to the computer, performing an initial meshing triangulation of the object, iteratively applying meshing operators to the meshed object, the meshing operators comprising four operators: node-on-edge, node-in-interior, edge-swapping and node relocation, said node-in-interior being applied at least once, until all triangles of the mesh meet a user specified criterion, where a node-on-edge operator finds a boundary node location and triangulates an element adjacent the boundary, a node-in-interior operator finds an interior node location within a quadrilateral and triangulates the quadrilateral, an edge-swapping operator improves a mesh quality by swapping an interior edge of a quadrilateral, and a node-relocation operator finds a new interior node location within a quadrilateral when node-in-interior fails to meet a lower bound criterion.

Claim 8

A computer implemented method to generate two-dimensional meshes for finite element analysis of polygonal objects comprising the steps of: inputting a configuration of the polygonal object to the computer, performing an initial meshing triangulation of the object, iteratively applying meshing operators to the meshed object, the meshing operators comprising four operators: node-on-edge, node-in-interior, edge-swapping and node relocation, said node-in-interior being applied at least once, until all triangles of the mesh meet a user specified criterion, where a node-on-edge operator finds a boundary node location and triangulates an element adjacent the boundary, a node-in-interior operator finds an interior node location within a quadrilateral and triangulates the quadrilateral, an edge-swapping operator improves a mesh quality by swapping an interior edge of a quadrilateral, and a node-relocation operator finds a new interior node location within a quadrilateral when node-in-interior fails to meet a lower bound criterion.

Claim 9

The computer implemented method of claim 6 wherein the meshing operators comprising the four operators is a uniform meshing algorithm and the user specified criterion is a maximum length for the edges of all triangles in the object mesh.

Claim 10

The computer implemented method of claim 6 wherein the meshing operators comprising the four operators is a graded meshing algorithm and the user specified criterion is a minimum angle for all angles of all triangles in the meshed object.

Claim 11

The computer implemented method of claim 6 wherein the meshing operators first find a longest edge in the mesh before applying any of the four operators in each iteration.

Claim 12

The computer implemented method of claim 6 wherein the initial meshing triangulation comprises a Constrained Delaunay Triangulation.

Claim 13

The computer implemented method of claim 6 including the step of identifying one or two triangles which share the edge whenever an edge is invoked, the edge being identified by its end point vertices.