Isoparametric elements
Isoparametric elements can be used for all problem types.
Each element is described in the name.i1 file using one EL batch:
EL T ITE E IE N IN$_1$ IN$_2$ $\dots$ IN$_\mathtt{NNE}$ G NG H $h_1$ $h_2$ $\dots$ $h_\mathtt{NNE}$
The T group can be omitted if $\mathtt{ITE}={}$$\mathtt{ITED}$.
| $\mathtt{ITE}$ | The element type identification number. | |
|---|---|---|
| $=4$ | 2D triangle, see the Reference Manual | |
| $=5$ | axisymmetric triangle, see the Reference Manual | |
| $=6$ | 2D quadrilateral, see the Reference Manual | |
| $=7$ | axisymmetric quadrilateral, see the Reference Manual | |
| $=54$ | tetrahedron, see the Reference Manual | |
| $=55$ | pentahedron, see the Reference Manual | |
| $=56$ | hexahedron, see the Reference Manual | |
| $=57$ | pyramid, see the Reference Manual | |
| $\mathtt{IE}$ | The element number. | |
| $\mathtt{IN}_j$ | The node numbers of the element in the prescribed order, see the Reference Manual. Midside nodes may be omitted by writing 0 in the corresponding positions. In that case, the quadratic shape function along the element edge is reduced to linear, and the accuracy of the computation deteriorates. This reduction is used only in exceptional cases. | |
| $j$ | The local number of the element node, $1\le j\le\mathtt{NNE}$. | |
| $\mathtt{NNE}$ | The total number of nodes in the element, including any omitted midside nodes. | |
| $\mathtt{NG}$ | The order of numerical integration for the element, $2\le\mathtt{NG}\le4$. If the G group is missing, the value $\mathtt{NGD}$ applies. Usually $\mathtt{NG}=\mathtt{NGD}=3$. | |
| $h_j$ | The nodal thicknesses of a plane element $\mathtt{ITE}\in\{4,6\}$. If only one value is specified, it applies to all nodes of the element. If the H group is missing, the value $\mathtt{THDEF}$ applies to all nodes of the element. The thicknesses are automatically multiplied by the $\mathtt{SCALE}$ scale factor; for example, the value $\mathtt{SCALE}=0.001$ means that all thicknesses are given in millimeters. | |
Note
The EL batch can have any number of continuation lines. Data are written from column 3 to column 72 (the first two columns are generally reserved for two-letter batch names), see the Reference Manual.
Example
Let us consider an isoparametric triangle. The global node numbers follow from the specific numbering of the mesh.
According to the Reference Manual, the node numbers can be written in three ways:
22 24 77 23 44 43 24 77 22 44 43 23 77 22 24 43 23 44
depending on which node the numbering starts from.
The numbering of the element also determines the local numbers of the faces and edges. In the case of the sequence 24 77 22 44 43 23, the curve 24–44–77 is the first face, the curve 77–43–22 the second face, and the curve 22–23–24 the third face (for plane elements, the edges have a nonzero thickness, which is why we define them as faces).
If we decided to omit node 44, the list would take the form:
24 77 22 0 43 23
Omitting node 44 results in the straightening of face 24–(44)–77 and a deterioration in the quality of the solution approximation along this face. Omitting a midside node has no effect on the local face numbers. The line segment 24–77 thus remains the first face even after node 44 is omitted.
A typical form of the EL batch will be:
EL T 4 E 211 N 24 77 22 44 43 23
The order of numerical integration and the thickness of the element will be given by the default values $\mathtt{NGD}$ and $\mathtt{THDEF}$. If only triangular elements occurred in the mesh, the notation could be simplified by specifying $\mathtt{ITED}=4$, and the T 4 group would be omitted.