MAKROS differentiates between macro and finite elements. Macro elements serve the purpose of defining a rough geometry of the solid to be calculated. The macro model is in most cases generated within AutoCAD. After the definition of how the macro elements should be divided, a finite element model will be generated out of the macro model. Finite elements will be used as input to a finite element calculation.
Table 2.1 shows all available geometric element types.
The geometrical form of the elements is defined by a geometrical type ID consisting of 2 (3) digits. The first digit (except for digit 7) defines the number of corner nodes for the element:
1 = node element
2 = line element
3 = triangular element
4 = quadrilateral element
6 = pentahedron
7 = tetrahedron
8 = hexahedron
10 = plane surface with up to 10 straight or curved edges
40 = plane surface element with up to 40 straight or circular edges.
The second digit distinguishes the number of nodes on edges between the corner nodes and in the inner of the element surface:
0 = straight edge with no nodes between the element corners (exception type 400)
2 = curved edge with 1 node between the element corners
3 = curved edge with 2 nodes between the element corners
5 = curved edge with a variable number of nodes between the element corners
6 = curved edge with 1 node between the element corners and 1 node in the interior
7 = 2 nodes between the element corners and 2*2 nodes in the interior of the element surface (triangle elements only have 1 node in the interior).
As macro elements only the types x0, x2, x5 can be used, where x = 2,3,4,6,8,10,40. Finite elements can be used with all types except for x5 and 400. Using the command Type2Type (Chapter “Commands to generate new nodes and elements”) a conversion between some different types can be done where additional nodes between the element corners and in the interior can be generated automatically.
For each element following data will be stored:
external element ID
geometrical type ID
mechanical type ID
external ID’s of element nodes in the order shown in Table 2.1a – 2.1h
With mechanical type ID’s elements of identical geometrical shape (and type) can be distinguished due to their different mechanical behavior (for example plates and shells). The real meaning of different mechanical types depends on the used FE calculation program, (see e.g. NASTRAN interface).
With group IDs several elements can be grouped together, e.g. for displaying parts of the structure with different colors or to assign materials and loads.
The element types usually are automatically generated from AutoCAD entities or by subdividing macro elements. Should individual elements be defined numerically (command “Element definition”), following rules are to be followed:
For element types 10 – 85 first corner nodes of the elements have to be given, then intermediate nodes on element edges and in the end nodes in the inner of the elements.
Hint: Intermediate nodes on straight element edges may be given as 0 with macro elements, with finite elements only if the used FE program does this allow (transition elements).
In case of element type x5 the number of intermediate nodes on edges is variable. To mark the last intermediate node for an edge, this node gets a minus sign ( except for type 105 ). 0 for an edge indicates that there are no intermediate nodes for this edge.
In case of element type 105 the number of corner nodes and intermediate nodes on edges is variable. For this type all nodes are given in continuous order as a polyline and all intermediate nodes on curved edges are marked by a minus sign. First and last node of the polyline must be identical. Between corner nodes several intermediate nodes can be given. In case of a single intermediate node a circular arc and in case of multiple intermediate nodes a spline curve will be generated for the corresponding edge. Elements of type 105 can have an object height, which is given by an additional node. The connection between this node and the first element node will be used as the first perpendicular edge for this element (see Table 2.1g). All other perpendicular edges are assumed to be parallel to this edge.
Elements of type 105 can be meshed freely or using a regular pattern for 4 node elements (see chapter “Subdivision of macro elements into finite elements“). For regular pattern these nodes, which serve as element corners must be known. The external IDs of these nodes can explicitly be specified during the definition of these elements. They will be saved after the node specifying the element’s height. The first node of such an element will always be used as the first corner; only the following 3 corner nodes must explicitly be specified. In case no corner nodes are specified, MAKROS uses for a subdivision with a regular pattern those 3 vertices with the smallest angles in addition to the first node.
Elements of type 400 are plane elements with up to 40 corners, all nodes are given in continuous order as a polyline and intermediate nodes on circular edges are marked by a minus sign (same as with element type 105). First and last node of the polyline must be identical. Only straight edges with 0 intermediate node and circular edges with 1 intermediate node are allowed.
Elements of type 105 and 400 may contain holes in the inner of the element. To define holes, one node of the border of the hole is connected with a node on the border of the element, so that a closed polyline can be defined containing al borders of the element (see example below).
With Command „Element definition“ it is possible to specify individual elements by giving the IDs of the element nodes. For example the elements shown in Table 2.1a – 2.1h are defined as follows:
Type 45: 1, 2, 3, 4, 5, 6, -7, -8, 9, 10, -11, -12
Type 85: 1, 2, 3, 4, 5, 6, 7, 8, 9, -10, 11, -12, 13, -14, 15, -16, 17,-18,19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32
Type 105: 1, 2, 3, -4, 5, 6, -7, 8, 9, 1,
With object height ( node 11 ) and explicit definition of corner nodes ( nodes 1, 2, 5, 9 ), for the subdivision of the element with a regular pattern, the shown type 105 has to be defined as follows:
1, 2, 3, -4, 5, 6, -7, 8, 9, 1, 11, 2, 5, 9
Type 400 (with holes and circular edges):
1, -2, 3, 4, -5, 6, 7, -8, 9, -10, 7, 6, -13, 14, 15, -16, 17, 18, -19, 20, -21, 18, 17, -24, 15, 14, -27, 28, 29, -30, 31, -32, 29, 28, -35, 4, 3, -38, 1
Table 2.1a Types of macro and finite elements