Generalized Plates Generalized Plates

A generalized plate is a structural element defined with a set of nodes along the exterior, and perhaps, a set of points defining a free edge of the generalized plate. An edge of the generalized plate is the line segment between two adajent nodes on the plate, and a "face" is all edges which are on a line.

A generalized plate is defined with the command:

     *NODE(3), *NODE(4), ...    *NODE(n)
     -FSOPT *FP(1), .......

This command defines a generalized plate element of class ~CLASS, connected to nodes named *NODE(1) through *NODE(n). The nodes must be specified so as to go around the element in one direction. Here, ELE_NAME is a name which can be assigned to the element, omitted, MOSES will assign a name. The -OPTIONS have been discussed above. They may be omitted, or valid options may be inserted directly at this location within the command. The class name, ~CLASS, is used to specify the generalized plate's attributes in exactly the same manner as for the beam element.

A generalized plate is composed of subelements (triangular plates) contained within the defined perimeter, and can be any convex shape and some special concave ones. The number of subelements depends on the shape of the perimeter and the number of nodes on each face. For three nodes you get no subelements and with four nodes you get four subelements. If the generalized plate has four faces, the subelements are generated as if it were composed of strips of quadrilateral elements. If not, the subelements are generated along rays (line segments from the average of the coordinates of the specified nodes) to the nodes on the boundary. Subelements will be generated so that the maximum distance of a side is less than or equal to the maximum distance between any two specified nodes. The internal nodes will have names which begin with **IN. Figure 10 shows four typical generalized plates

and Figure 11 shows the corresponding subelements.

The -FSOPT options can be used to define concave generalized plates. Here *FP(i) are points which define a "free edge". The points define the geometry of the edge. The nodes on the other edges will determine where the nodes which will define the subelements will be placed.

If -FSOPT is -HOLE then the free edge defines a hole contained within the generalized plate and *FP(i) are points defining the geometry of the hole. Here *FP(1) should be closest to NODE(1) and the order of the *FP(i) should be the same order as NODE(i). The actual nodes on the free edge are at the intersection of the ray from the center of the generalized plate with the free edge. Each of these defining rays passing through an exterior node. Thus, the more nodes on the exterior, the better representation one gets of the hole. The nodes created around the free edge will be named beginning with **CN. A word of caution here. The weight and centroid of this generalized plate are computed properly, but any other load is computed ignoring the hole.

If -FSOPT is -FREE_EDGE then the free edge defines a concave portion of the exterior of the element exterior. Here, the points *FP(2) and *FP(2) are actually NODES defining a face "opposite" the free surface; i.e. here we actually have a shape which can be mapped into a lattice with the face between the nodes *FP(1) and *FP(2) opposite the free edge. Also, the NODES(i) and FP(3), ... FP(n) should be in order around the element. Another word of caution since the generalized plate may not be convex, it also may not be star shaped with respect to its centroid. If it is not any load other than weight will be in error. Figure 12 shows a generalized plate with a free edge defined with 17 points beginning with the characters *CP,

and Figure 13 shows the corresponding nodes and subelements.

Finally, and Figure 14 shows what happens if the number of nodes opposite the free edge is increased.

The only non-intrinsic load attribute one can specify for a generalized plate is a temperature specified with the -T_PRESSURE option on the &ENV command and a T_PRESSURE command.

One can refine the edges of generalized plate elements with the command:

     REFINE, MAX_DIST, WHAT, SEL(1), SEL(2), .......

This command causes the edges of all generalized plates selected by the selectors specified to be refined so that the maximum length of an edge is MAX_DIST (feet or meters). Here WHAT can be either: EDGE, ELEMENT, or BOX. If one specifies EDGE, the following SEL(i) should be in pairs of selectors; e.g. a pair *Q@ *R@ will select any edge that has two nodes which match the two selectors. If one specified ELEMENT, the following selectors select elements based on element name; e.g. QP@ refines all edges of elements whose name matches QP@. Finally, a WHAT of BOX refines edges which are totally with a box. Here, the values of SEL(i) should be X_MIN, X_MAX, Y_MIN, Y_MAX, Z_MIN, and ZMAX. These are distances (feet or meters) specified in the part system. Notice, all of these things can be used together. For example, one can have a BOX inside of a BOX with the interior one having a smaller MAX_DIST. Then the interior one will have the interior MAX_DIST and the exterior one the larger distance. The nodes added as a result of a refinement have names which begin with **RN. The REFINE command can be issued both when performing an INMODEL and in the MEDIT Menu. Figures 15 through 18 show a square generalized plate with none, one, two, and four edges refined.