Triangulation in SPRING


Having completed the node generation in the entire model area or parts thereof, you can start generating triangular elements. The element generation algorithm uses the advancing front technique.

The global mesh generator starts at the outer contour boundary. It generates triangles until each of the nodes is linked to the mesh. Each element is optimized following the criteria for the angles of an element.

The local mesh generation does not require any contour boundary. The generation area is defined by selecting the outer boundary manually where finally the mesh generation starts. Furthermore, the local mesh generation uses the same algorithm as the global generation.

The triangulation algorithm automatically takes the contour data into account: An element is not allowed to intersect with an existing contour line!

 

The triangulation algorithm can only be used on condition that

each contour point, each start, end and division point of a contour line is a node of the mesh,

there are no mesh nodes on contour lines which are no division points of the contour line,

the contours are optimized,

no double nodes ( two or more nodes with the same coordinates) exist.

 

SPRING includes a mesh-optimization code, with several algorithms for the boundary and the grid nodes. You should run the optimization after the contours have been completed. It will indicate the errors, a short description and the corresponding node number. Errors incurred during the triangulation can be caused by:

manually selected nodes (double nodes, nodes on contours without contour points ...),

additionally inserted nodes (contour points without nodes, contours without optimization, ...)

nodes which have been moved (double nodes, contour points without the nodes) or similar operations.

 

You can find the errors and remove them with the help of one of the following algorithms:

optimizing the contours

starting the boundary node generator with 0 steps (generates mesh nodes at contour nodes)

controlling the distances between the nodes (Mesh Checks)

 

The mesh generation with triangles and quadrangles always starts with a triangulation algorithm which produces only triangles. Subsequently, neighbouring triangles are combined into quadrangles. This is necessary to reduce the number of elements and thus the required computing time and memory space.

 

Unbending the mesh