For an example of the GENEL element, consider the robotic arm shown inFigure 6-1. The arm consists of three simple bar members with a complex joint connecting members 1 and 2. For the problem at hand, suppose that the goal is not to perform a stress analysis of the joint but rather to compute the deflection of the end where the force is acting. You can make a detailed model of the joint, but it will take a fair amount of time and the results will still be questionable.
The ideal choice is to take the joint to the test lab and perform a static load test and use those results directly.
Figure 6-1. Robotic Arm with Joint
The GENEL element is the ideal tool for this job. The joint is tested in the test lab by constraining one end of the joint and applying six separate loads to the other end as shown inFigure 6-2.
Figure 6-2. The Test Arrangement to Obtain the Flexibility Matrix Table 6-1summarizes the displacements measured for each of the applied loads.
Table 6-1. Test Results for the Joint
Deflection (10—7) Due to Unit Loads
F1 F2 F3 M1 M2 M3
Table 6-1. Test Results for the Joint
Table 6-1also represents the flexibility matrix of the joint with the rigid body properties removed.
By specifying all of the degrees of freedom at grid point 2 as being in the dependent set {ud} and the [S ] degrees of freedom at grid point 3 as being in the independent set {ui}, the matrix is not required. The input file showing the model with the GENEL is shown inListing 6-1.
$
0.0 0.0 0.0 2.38E-7 1.58E-7 0.0 -2.38E-70.0 6.18E-7 0.0 0.0 4.75E-7 0.0 4.75E-7
$
PBAR 1 1 .2179 .02346 .02346 .04692
$
MAT1 1 1.+7 .3
Listing 6-1. GENEL Element Input File
The flexibility matrix generated from the test data was properly aligned with the model geometry with the use of a local coordinate (note the CD field of grid points 2 and 3). Using this local coordinate system, the output displacement X-axis corresponds to the F1 direction, etc.
As an alternative approach, you can use direct matrix input (DMIG entries) to input structure matrices.
See Also
• “Direct Matrix Input” in the NX Nastran User’s Guide
6.2 Bushing (CBUSH) Elements
The bushing (generalized spring and damper) elements consist of the following:
• CBUSH
• CBUSH1D
The generalized spring-damper element CBUSH is a structural scalar element connecting two noncoincident grid points, or two coincident grid points, or one grid point with an associated PBUSH entry. This combination is valid for any structural solution sequence. To make frequency dependent the PBUSH need only have an associated PBUSHT Bulk Data entry. The PBUSHT entry for frequency dependency is only used in SOL 108 and SOL 111. You can also use the PBUSHT entry to define load-displacement dependency in SOL 106.
Figure 6-3shows some of the advantages of using the CBUSH element over CELASi elements.
For example, if you use CELASi elements and the geometry isn’t aligned properly, internal constraints may be induced. The CBUSH element contains all the features of the CELASi elements plus it avoids the internal constraint problem. The following example demonstrates the use of the CBUSH element as a replacement for scalar element for static analysis. The analysis joins any two grid points by user-specified spring rates, in a convenient manner without regard to the location or the displacement coordinate systems of the connected grid points. This method eliminates the need to avoid internal constraints when modeling.
The model shown inFigure 6-3has two sheets of metal modeled with CQUAD4 elements. The sheets are placed next to each other. There are grid points at the common boundary of each sheet of metal, which are joined by spot welds. The edge opposite the joined edge of one of the sheets is constrained to ground. The grid points at the boundary are slightly misaligned between the two sheets due to manufacturing tolerances. There is a nominal mesh size of 2 units between the grid points, with 10 elements on each edge. The adjacent pairs of grid points are displaced from each other in three directions inside a radius of 0.1 units in a pattern that maximizes the offset at one end, approaches zero at the midpoint, and continues to vary linearly to a maximum in the opposite direction at the opposite end.
CELASi elements are used in the first model, and CBUSH elements are used in a second, unconnected model. PLOTEL elements are placed in parallel with the CELAS2 elements to show their connectivity. The second model is identical to the first model with respect to geometry, constraints, and loading.
A static loading consisting of a point load with equal components in all three directions on the center point opposite the constrained edge is applied. The first loading condition loads only the first model and the second loading condition loads only the second model, allowing comparison of the response for both models in one combined analysis. The input file bushweld.dat is in the test problem library.
In modal frequency response, the basis vectors (system modes) [f] will be computed only once in the analysis and will be based on nominal values of the scalar frequency dependent springs.
In general, any change in their stiffness due to frequency will have little impact on the overall contribution to the structural modes.
The stiffness matrix for the CBUSH element takes the diagonal form in the element system:
For the B matrix replace the k terms with b.
When transformed into the basic system, there is coupling between translations and rotations, thus ensuring rigid body requirements.
The element axes are defined by one of the following procedures:
• If a CID is specified then the element x-axis is along T1, the element y-axis is along T2, and the element z-axis is along T3 of the CID coordinate system. The options GO or (X1,X2,X3) have no meaning and will be ignored. Then [Tab] is computed directly from CID.
• For noncoincident grids (GA ≠ GB), if neither options GO or (X1,X2,X3) is specified and no CID is specified, then the line AB is the element x-axis. No y-axis or z-axis need be specified.
This option is only valid when K1 (or B1) or K4 (or B4) or both on the PBUSH entry are specified but K2, K3, K5, K6 (or B2, B3, B5, B6) are not specified. If K2, K3, K5, K6 (or B2, B3, B5, B6) are specified, a fatal message will be issued. Then [Tab] is computed from the given vectors like the beam element.