# Generic Elements

B2000++ elements are always derived from one of the generic elements,
i.e. an element of a specific family, like a triangle, a tetrahedron,
etc. The *generic element type* is not associated to any operator and is
usually known to all processors dealing with elements, like the input
processor, the load processor, or the element processor. Like the
generic element type, the element name must be derived from the *generic
element name*. The element naming convention

`sn.extension`

has been adopted, where `s`

designates the shape, `n`

the number
of nodes defining the element, and `extension`

the actual
description of the element, which also defines the operator. The table
below contains a list of all defined generic element types:

Name |
x |
Description |
---|---|---|

Lx |
2, 3 |
Line or wire element. Generic 1D element, defined in R |

Rx |
2, 3 |
Rod element (solid mechanics) defined in R |

Bx |
2, 3 |
Beam element (solid mechanics) defined in R |

Tx |
3, 6 |
Triangular 2D element, defined in R |

Qx |
4, 8, 9 |
Quadrilateral 2D element, defined in R |

TEx |
4, 10 |
Tetrahedral element, defined in R |

HE |
8, 20, 27 |
Hexahedral element, defined in R |

PRx |
6, 15 |
Prismatic element, defined in R |

Note that if an element is listed in the above table this does not necessarily mean that the corresponding element - for a given operator - is implemented in B2000++.

The field `type`

contains the element class pertaining to the element
geometry, augmented by the number of nodes. The `extension`

field
defines the actual element type, i.e. the operator, and can be chosen
freely. Data set ELEMENT-PARAMETERS contains the element name
translation table.

## Wire, Line (L) and Rod/Cable (R) Elements

*L* (line), *R* (rod and cable) elements define line (wire) elements
without any local y- and z-axis, i.e. the elements have axisymmetric
properties around the local x-axis. *L* elements also constitute the
basis for axisymmetric two-dimensional elements.

The element local x-axis is defined by the vector \(p_{21} = p_2 - p_1\), with \(p_1\) being the coordinate vector of the vertex \(n_1\) and \(p_2\) the coordinate vector of the vertex \(n_2\). The local y- and z-axes are not defined. Note that B2000++ node indices are positive integers (external numbering system) and they must belong to the same branch.

## Beam (B) Elements

Beam elements refer to the beam local orthogonal coordinate system, the local x-axis being tangential to the beam axis, adn the local y-axis and z-axis in a plane normal to the x-axis. The orientation of the local y- and z-axes are defined as follows:

By an orientation vector \(o\) defining the element local x-y plane with respect to the global coordinate system. The orientation vector must be specified by the MDL

`elements`

parameter`beam_orientation`

.By a node \(n_{ref}\) which defines the beam orientation vector \(o = n_{ref} - n_{1}\), where \(n_{1}\) is the coordinate vector of the first node defining the beam element. Note that the node identification is external, see nodes command.

The figures below illustrate the beam element node connectivities. Note that node indices are positive integers and all node indices defining the element must belong to the same branch.

Unless analytical integration is performed the standard Gauss scheme is used, for B2 element a 1 point scheme and for B3 elements a 2 point scheme.

## Triangular (T, TR) Elements

T, TR elements define triangular elements in R^{2} and R^{3}. B2000++ node indices are positive integers and they must
belong to the same branch. The element local x-axis x_{element}
is defined by r_{21} = p_{2} - p_{1}, with p_{2} being the coordinate of the vertex n_{2}, and p_{1} the coordinate of the vertex n_{1}. The element local
z-axis z_{element} is defined by the vector product r_{21} . r_{31}, with r_{31} = p_{3} - p_{1}, and p_{3} being the coordinate of the vertex n_{3}. The element local y-axis y_{element} is then obtained
by the vector product z_{element} . x_{element}.

Edge |
T3 element |
T6 element |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

All triangular elements requiring numerical integration have a built-in
default integration rule. The default integration rule can be changed
with the `ischeme`

MDL element parameter.

Element |
Scheme |
Description |
---|---|---|

T3 |
None |
3 point standard triangle integration scheme. |

T6 |
None |
7 point standard triangle integration scheme. |

## Quadrilateral (Q) Elements

Q elements define quadrilateral elements in R^{2} and R^{3}. B2000++ node indices are positive integers and they must
belong to the same branch. The element local x-axis x_{element}
is defined by r_{21} = p_{2} - p_{1}, with p_{2} being the coordinate of the vertex n_{2}, and p_{1} the coordinate of the vertex n_{1}. The element local
z-axis z_{element} is defined by the vector product r_{21} . r_{31}, with r_{31} = p_{3} - p_{1}, and p_{3} being the coordinate of the vertex n_{3}. The element local y-axis y_{element} is then obtained
by the vector product z_{element} . x:_{element}.

Edge |
Q4 element |
Q8/Q9 element |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

Element |
Scheme |
Description |
---|---|---|

Q4 |
None |
3 point standard 2x2 Gauss integration scheme. |

Q8, Q9 |
None |
9 point standard 3x3 Gauss integration scheme. |

## Tetrahedral (TE) Elements

TE elements define tetrahedral elements in R^{3}. B2000++ node
indices are positive integers and they must belong to the same branch.
The element local x-axis x_{element} is defined by
r_{21} = p:sub:2 - p_{1}, with p_{2} being the
coordinate of the vertex n_{2}, and p_{1} the coordinate of
the vertex n_{1}. The element local z-axis z_{element} is
defined by the vector product r_{21} . r_{31}, with
r_{31} = p_{3} - p_{1}, and p_{3} being the
coordinate of the vertex n_{3}. The element local y-axis
y_{element} is then obtained by the vector product
z_{element} . x x_{element}.

Element face connectivity TE elements The element faces are numbered in
counter-clockwise direction, as seen from outside the element. Thus, the
element face normals (and the element face local z-axis) always point
out from the element. The first 2 nodes of the element face connectivity
list define the element face local x-axis x_{face}. The element
face local y-axis is defined by
y_{face} = r_{21} . r_{31}, with
r_{21} = p_{2} - p_{1} and
r_{31} = p_{3} - p_{1}, p_{1} being the coordinate
of the element face connectivity node 1, p_{2} of node 2, and
p_{3} of node 3. The element face local y-axis y_{face} is
then defined by z_{face} . x_{face}.

Face |
TE4 faces |
TE10 faces |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

Element edge connectivity TE elements The element edge node connectivity
of TE elements are defined as follows: The first 2 nodes of an element
edge connectivity list also define the element edge local x-axis
x_{edge}, the axis running from the first to the second node. The
figure and table below display the element local edge numbering, the
orientation (direction) of the edge local x-axis, as well as the element
nodes defining the edges.

Edge |
TE4 |
TE10 |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

5 |
n |
n |

6 |
n |
n |

Element |
Scheme |
Description |
---|---|---|

TE4 |
None |
3 point standard 2x2 Gauss integration scheme. |

## Hexahedral (HE) Elements

HE elements define hexahedral elements in R^{3}. B2000++ node
indices are positive integers and they must belong to the same branch.
The element local x-axis x_{element} is defined by r_{21} = p_{2} - p_{1}, with p_{2} being the
coordinate of the vertex n_{2}, and p_{1} the coordinate
of the vertex n_{1}. The element local z-axis z_{element}
is defined by the vector product r_{21} . r_{31}, with r_{31} = p_{3} - p_{1}, and p_{3} being the
coordinate of the vertex n_{3}. The element local y-axis y_{element} is then obtained by the vector product z_{element} . x x_{element}.

The element faces are numbered in counter-clockwise direction, as seen
from outside the element. Thus, the element face normals (and the
element face local z-axis) always point out from the element. The
first 2 nodes of the element face connectivity list define the element
face local x-axis x_{face}. The element face local y-axis is
defined by y_{face} = r_{21} . r_{31}, with r_{21} = p_{2} - p_{1} and r_{31} = p_{3} - p_{1}, p_{1} being the coordinate of the
element face connectivity node 1, p_{2} of node 2, and p_{3} of node 3. The element face local y-axis y_{face} is
then defined by z_{face} . x x_{face}.

Face |
HE8 |
HE20 |
HE27 |

1 |
n |
n |
n |

2 |
n |
n |
n |

3 |
n |
n |
n |

4 |
n |
n |
n |

5 |
n |
n |
n |

6 |
n |
n |
n |

Element edge connectivity HE elements The element edge node
connectivity of HE elements are defined as follows: The first 2 nodes
of an element edge connectivity list also define the element edge
local x-axis x_{edge}, the axis running from the first to the
second node. The figure and table below display the element local edge
numbering, the orientation (direction) of the edge local x-axis, as
well as the element nodes defining the edges.

Edge |
HE8 |
HE20/HE27 |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

5 |
n |
n |

6 |
n |
n |

7 |
n |
n |

8 |
n |
n |

9 |
n |
n |

10 |
n |
n |

11 |
n |
n |

12 |
n |
n |

## Prismatic (PR) Elements

PR elements define prismatic elements in R^{3}. B2000++ node
indices are positive integers and they must belong to the same branch.
The element local x-axis x_{element} is defined by r_{21} = p_{2} - p_{1}, with p_{2} being the
coordinate of the vertex n_{2}, and p_{1} the coordinate
of the vertex n_{1}. The element local z-axis z_{element}
is defined by the vector product r_{21} . r_{31}, with r_{31} = p_{3} - p_{1}, and p_{3} being the
coordinate of the vertex n_{3}. The element local y-axis y_{element} is then obtained by the vector product z_{element} . x x_{element}.

Element face connectivity PR elements The element faces are numbered in
counter-clockwise direction, as seen from outside the element. Thus, the
element face normals (and the element face local z-axis) always point
out from the element. The first 2 nodes of the element face connectivity
list define the element face local x-axis x_{face}. The element
face local y-axis is defined by
y_{face} = r_{21} . r_{31}, with
r_{21} = p_{2} - p_{1} and
r_{31} = p_{3} - p_{1}, p_{1} being the coordinate
of the element face connectivity node 1, p_{2} of node 2, and
p_{3} of node 3. The element face local y-axis y_{face} is
then defined by z_{face} . x x_{face}.

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

5 |
n |
n |

Element edge connectivity PR elements The element edge node connectivity
of PR elements are defined as follows: The first 2 nodes of an element
edge connectivity list also define the element edge local x-axis
x_{edge}, the axis running from the first to the second node. The
figure and table below display the element local edge numbering, the
orientation (direction) of the edge local x-axis, as well as the element
nodes defining the edges.

Edge |
PR6 |
PR15 |

1 |
n |
n |

2 |
n |
n |

3 |
n |
n |

4 |
n |
n |

5 |
n |
n |

6 |
n |
n |

7 |
n |
n |

8 |
n |
n |

Edge 9: |
n |
n |

## Point Mass (PMASS) Element

The *PMASS* element adds mass at a given grid point with respect to
the element-local axes. Note that B2000++ node indices are positive
integers and they must belong to the same branch.

## Rigid Body (RBE) Elements

The *RBE* element connects a master node to one or several slave
nodes.