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BEM2D
2D boundary element
Description
Boundary element using the “BEM” method in linear mechanical analysis.
A group of BEM boundary elements defines a region considered as an equivalent finite element.
Type: 60
Implemented by: X.C. Wang, 1987 - Last revision: A-M. Habraken, 1991
Files
Prepro: BEM2DA.F
Lagamine: BEM2DB.F
Input file
| Title (A4) | |
|---|---|
| TITLE | “BEM2D” in the first 5 columns |
| Control data (I5) | |
| NEFEQ | Number of equivalent finite elements |
Definition of an equivalent finite element
This section must be repeated NEFEQ times.
| Control data (8I5) | |
|---|---|
| LMATE | Material law - only the elastic material is accessible |
| NSUBE | Number of boundary BEM elements |
| NSUBD | Total number of nodes taken into account in the boundary elements (in case of a closed contour, do not count the first and last node twice) |
| NSIGP | Number of interior points where stresses should be computed |
| IFTRA | Index for the calculation of nodal traction at each step: = 1 Yes ≠ 1 No |
| INSOL | Index for the choice of fundamental solution (see explanation below): = 0 Kelvin (finite domain) = 1 Kelvin (infinite domain) = 2 Melan (semi-infinite) |
| NRI | = 0 0 → No rotation = -1 -1 → Rotation during deformation; the code computes the two most distant points = I J → Rotation during deformation: I is the first node to define the angle of rotation; J is the second node to define the angle of rotation |
| NRJ | |
| Definition of the points of stress computation (2G10.0) - repeated NSIGP times | |
| XP | Coordinates of the point where the stress must be computed |
| YP | |
| Definition of the BEM elements (2I5/3I5) | |
| NNO | Number of nodes (2 or 3 in plane state, 3 in axisymmetric) |
| NINTE | Number of Gauss integration points (2, 4, or 6 in plane state; 0 in axisymmetric because the program computes it automatically) |
| NODE(I) I=1,NNO | List of nodes of the BEM element (Beware: the elements must be in order - the the first node of element i = the last node of element j) |
Fundamental solution
Two fundamental solutions are available: the Kelvin solution and the Melan solution.
The Kelvin solution is used for a border defining a closed contour. The considered domain is either the interior (finite domain) or the exterior (infinite domain). The order of numbering for the nodes is indicated in the figure below.
The problem can be in plane strain state or in axisymmetric state. No volumetric force is taken into account (no specific weight, thermal dilatation, or effective stresses).
The Melan solution is used for a semi-inifinite domain with a straight border. Only the deviations from this line must be discretized. The problem is in plane strain state. No volumetric force is taken into account.
