Aqwa allows structures to be connected by articulated joints. These do not permit relative translation of the two structures but allow relative rotational movement in a number of ways that can be defined by the user.
The reactions at the articulations can be output in global, structure or local articulation axes; see LSAR and LAAR options (Administration and Calculation Options for the Aqwa Suite).
A maximum of 99 articulations is allowed.
2 5 7 11 16 21 26 31 36 41 46 51
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X| | |DCON| | | | |XXXXX| | | |XXXXX|
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| | | | | | | |_(7)-(9)Node Numbers(2I5)
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| | | | | | |_(6)Second Structure Number(I5)
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| | | | | |_(3)-(5)Node Numbers(2I5)
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| | | | |_(2)First Structure Number(I5)
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| | | |_(1)Number of Locked Rotational Freedoms at the Constraint(I5)
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| | |_Compulsory Data Record Keyword(A4)
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| |_Optional User Identifier(A2)
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|_Compulsory END on last data record in data category(A3)
Constraint Definition
(1) Four types of constraint are valid in the program which are coded as 0, 1, 2 and 3, representing the number of rotational freedoms which are locked at the constraint. Therefore, rotational reactions or moments transmitted through the joint at the constraint, from the first structure to the second structure, and vice versa, also correspond to these numbers. The four types of joint are as follows:
| 0 | Ball and Socket | Free to rotate in all freedoms |
| 1 | Universal | Free to rotate in two freedoms transmitting a moment in the third freedom at right angles to the first two |
| 2 | Hinged | Transmitting a moment in two freedoms and free to rotate in the third freedom at right angles the first two |
| 3 | Locked | Transmitting a moment in all three freedoms and not free to rotate at all. This type of constraint enables the user to find the reactions between two or more parts of the same structure. This type of joint rigidly connects the parts together so that the solution of the equations of motion are the same as if one structure was defined. These parts must be defined as separate structures in Data Category 2 (see also (2)) |
(2) This is the number of the first structure on which the constraint is defined. If '1' is input then this will correspond to the structure defined in Data Category ELM1. If '2' is input then this will correspond to the structure defined in Data Category ELM2, and so on.
If '0' is input the program will recognize that the constraint is connected to a fixed position in the Fixed Reference Axis System corresponding to the position of the nodes in columns 21-35 as defined in Data Category 1.
See rules concerning how structures may and may not be connected at the end of this section.
(3)-(5) The first node (3) defines the position and the second (4) node defines the orientation of the constraint with respect to the structure specified in (2). Different numbers of nodes must be input to uniquely define each type of constraint, and are tabulated below.
| Type | Joint | Mandatory Input | |
| For Structure 1 | For Structure 2 | ||
| 0 | B/Socket | (3) | (7) |
| 1 | Universal | (3) (4) | (7) (8) |
| 2 | Hinged | (3) (4) | (7) (8) |
| 3 | Locked | (3) | (7) |
(6) This is the number of the second structure on which the constraint is defined otherwise as in (2) except that '0' structure number is illegal. See rules at the end of this section.
(7)-(9) As for the first node. See (3)-(5).
Function of the Nodal Input on Each Structure
First node: Position of the constraint with respect to the first structure.
Second node: The axis about which the two structures are free to rotate relative to one another is given by the line going from the first node to this node.
Function of the Nodal Input for Each Constraint
| 0 | Ball and Socket Joint | The first node is the position of the joint. |
| 1 | Universal Joint | The axis defined on each structure by the second node will give two axes which will always be at right angles to each other. The joint will only allow relative motion about these two axes. |
| 2 | Hinged Joint | The axis defined on each structure by the second node will give two axes which will always be coincident. The joint will only allow relative motion about this coincident axis. |
| 3 | Locked Joint | The first node is the position of the joint. |
Local Axis Systems for the Constraint Reactions Output
FRA = Fixed Reference Axis. X, Y, Z axis are local axes.
| 0 | Ball and Socket Joint |
X – Parallel to the FRA Y – Parallel to the FRA Z – Parallel to the FRA |
| 1 | Universal Joint |
X – Axis defined by the second node on the first structure Y – Axis defined by the second node on the second structure Z – At right angles to X and Y |
| 2 | Hinged Joint |
X – Axis defined by the second node on the first/second structure Y – At right angles to X and parallel to the XY plane in the FRA Z – At right angles to X and Y with +ve Local Z on the +ve side of the XY plane of the FRA In the special case where the local Z axis lies in the XY plane of the FRA the local Y axis is coincident with the Y axis of the FRA. |
| 3 | Locked Joint |
X – Parallel to the FRA Y – Parallel to the FRA Z – Parallel to the FRA |
Defining the Initial Position with Constraints
When constraints are defined on a structure, the usual specification of initial or starting positions for the analysis (input in Data Category 15) is not treated in the same manner as when there are no constraints. This is because the specification of the 6 degrees of freedom for each center of gravity may not be geometrically compatible with the position of constraints defined within this data category, e.g. it is possible to input the positions of two structures where the position of the common constraint is not coincident.
It is realized that it is tedious for the user to have to calculate the exact positions of the structures so that common constraint positions are coincident. Indeed if a fixed constraint is specified, the position of the structures can be uniquely defined by the rotational Degrees of Freedom only.
The program will take the position of the first structure within any articulated group of structures, and connect the remaining structures to the first structure using only the orientation of these remaining structures (Note that this includes structure '0', a fixed constraint, as the first structure).
If the program is unable to achieve this due to the manner in which the user has modeled a group of structures, the model is invalid.
Rules for Joining Structures with Constraints
Note: In order to achieve a valid model of a group of structures joined together by constraints (outlined above) the rules below must be followed.
'Closed loops' are now permitted, (e.g. Structure 1, to Structure 2, connected to Structure 3 which is connected back to Structure 1, is now legal).
If a fixed constraint, i.e. Structure '0', is present within a group of articulated structures, then '0' must be the first structure number on a DCON data record.
Only one fixed constraint, i.e. Structure '0', may be present within any one group of articulated structures.
Redundant systems of constraints may cause a statically indetermined solution of the reaction force/moments on the joints. A simple example of a redundant system is two structures connected by two locked articulations. As the structures are also rigid, it is impossible to determine how the reactions should be divided between the two joints. A single locked articulation will suffice to fix two structures together.