MPC184-Spherical
Multipoint Constraint Element: Spherical Joint
MPC184 Spherical Joint Element Description
The MPC184 spherical joint element is a two-node element with the relative displacement degrees of freedom constrained. The relative rotational degrees of freedom are left unconstrained. These rotations cannot be controlled. The kinematic constraints are imposed using the Lagrange multiplier method.
MPC184 Spherical Joint Input Data
Set KEYOPT(1) = 15 to define a two-node spherical joint element.
Figure 184sphe.1: MPC184 Spherical Joint Geometry shows the geometry and node locations for this element. Two nodes define the element. The two nodes (I and J) are expected to have identical spatial locations initially. If the two nodes are not coincident, the relative positions of the two nodes are maintained.
A local Cartesian coordinate system should be specified at the first node, I, of the element. The specification of the second local coordinate system at node J is optional. If the local coordinate system is not specified at node J, the local coordinate system at node J is assumed to be the same as that at node I. Use the SECJOINT command to specify the identifiers of the local coordinate systems.
The constraints imposed in a spherical joint element are described below. Referring to Figure 184sphe.1: MPC184 Spherical Joint Geometry, the constraints imposed at any given time are as follows:
The relative rotations between nodes I and J are characterized by the Cardan (or Bryant) angles as follows:
The following definitions are for relative rotations:
where:
 ,  , and  = reference angle specifications, angle1, angle2, and angle3 on the
SECDATA command |
Since the output of relative rotations is characterized by the Cardan (or Bryant) angles, the rotation around the local e2 axis is limited to between -PI/2 to +PI/2 (see the expression for Φ above). When this rotation value reaches |PI/2|, the other two angles become indeterminate. Therefore, if the accumulated angles around an axis of rotation is greater than |PI/2|, the axis of rotation should typically be specified as the local e1 or e3 axis.
Other input data that are common to all joint elements (material behavior, stops and limits, locks, etc.) are described in "Joint Input Data" in the MPC184 element description.
MPC184 Spherical Joint Input Summary
This input summary applies to the spherical joint element option of MPC184: KEYOPT(1) = 15.
- Nodes
I, J,
Note: For a grounded spherical joint element, specify either node I or node J in the element definition and leave the other node (the grounded node) blank.
- Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ
- Real Constants
None
- Material Properties
Use the JOIN label on the TB command to define stiffness, damping, and Coulomb friction behavior. (See MPC184 Joint in the Material Reference for detailed information on defining joint materials.)
- Surface Loads
None
- Body Loads
- Temperatures --
T(I), T(J)
- Element Loads
- Rotations --
ROTX, ROTY, ROTZ
- Forces/Moments --
MX, MY, MZ
- Special Features
- KEYOPT(1)
Element behavior:
- 15 --
Spherical joint element
- KEYOPT(2)
Element constraint imposition method:
- 0 --
Lagrange multiplier method (default)
- 1 --
Penalty-based method
MPC184 Spherical Joint Output Data
The solution output associated with the element is in two forms:
Nodal displacements included in the overall nodal solution
Additional element output as shown in Table 184sphe.1: MPC184 Spherical Joint Element Output Definitions and Table 184sphe.2: MPC184 Spherical Joint Element - NMISC Output.
These tables use the following notation:
A colon (:) in the Name column indicates the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.out. The R column indicates the availability of the items in the results file.
In either the O or R columns, Y indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and a - indicates that the item is not available.
Table 184sphe.1: MPC184 Spherical Joint Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element number | - | Y |
| NODES | Element node numbers (I, J) | - | Y |
| FX | Constraint force in X direction | - | Y |
| FY | Constraint force in Y direction | - | Y |
| FZ | Constraint force in Z direction | - | Y |
| CSTOP4-6 | Constraint force if stop is specified on DOFs 4-6 | - | Y |
| CLOCK4-6 | Constraint force if lock is specified on DOFs 4-6 | - | Y |
| CSST4-6 | Constraint stop status on relative DOFs 4-6 [1] | - | Y |
| CLST4-6 | Constraint lock status on relative DOFs 4-6 [2] | - | Y |
| JRP4-6 | Joint relative position of DOFs 4-6 | - | Y |
| JCD4-6 | Joint constitutive displacement/rotation of DOFs 4-6 | - | Y |
| JEF4-6 | Joint elastic force/moment 4-6 | - | Y |
| JDF4-6 | Joint damping force/moment 4-6 | - | Y |
| JFF4-6 | Components of joint friction moment | - | Y |
| JRU4-6 | Joint relative rotation of DOFs 4-6 | - | Y |
| JRV4-6 | Joint relative rotational velocity of DOFs 4-6 | - | Y |
| JRA4-6 | Joint relative rotational acceleration of DOFs 4-6 | - | Y |
| JTEMP | Average temperature in the element [3] | - | Y |
| JFST6 | Stick/slip status when friction is specified [4] | - | Y |
| JFNF6 | Normal moment in friction calculations | - | Y |
| JFEQ | Equivalent friction moment around spherical axis | - | Y |
0 = stop not active, or deactivated 1 = stopped at minimum value 2 = stopped at maximum value 0 = lock not active 1 = locked at minimum value 2 = locked at maximum value Average temperature in the element when temperatures are applied on the nodes of the element using the BF command, or when temperature are applied on the element using the BFE command.
Stick/slip status when friction is active:
0 = friction is not activated 1 = sticking 2 = slipping or sliding
The following table shows additional non-summable miscellaneous (NMISC) output available for the spherical joint element.
Note: This output is intended for use in the Ansys Workbench program to track the evolution of local coordinate systems specified at the nodes of joint elements.
Table 184sphe.2: MPC184 Spherical Joint Element - NMISC Output
| Name | Definition | O | R |
|---|---|---|---|
| E1X-I, E1Y-I, E1Z-I | X, Y, Z components of the evolved e1 axis at node I | - | Y |
| E2X-I, E2Y-I, E2Z-I | X, Y, Z components of the evolved e2 axis at node I | - | Y |
| E3X-I, E3Y-I, E3Z-I | X, Y, Z components of the evolved e3 axis at node I | - | Y |
| E1X-J, E1Y-J, E1Z-J | X, Y, Z components of the evolved e1 axis at node J | - | Y |
| E2X-J, E2Y-J, E2Z-J | X, Y, Z components of the evolved e2 axis at node J | - | Y |
| E3X-J, E3Y-J, E3Z-J | X, Y, Z components of the evolved e3 axis at node J | - | Y |
| JFX, JFY, JFZ | Constraint forces expressed in the evolved coordinate system specified at node I | - | Y |
| JMX, JMY, JMZ | Constraint moments expressed in the evolved coordinate system specified at node I | - | Y |
Table 184sphe.3: MPC184 Spherical Joint Item and Sequence Numbers -SMISC Items and Table 184sphe.4: MPC184 Spherical Joint Item and Sequence Numbers - NMISC Items list output available via the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table for further information. The table uses the following notation:
- Name
output quantity as defined in the Element Output Definitions table.
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
Table 184sphe.3: MPC184 Spherical Joint Item and Sequence Numbers -SMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| FX | SMISC | 1 |
| FY | SMISC | 2 |
| FZ | SMISC | 3 |
| CSTOP4-6 | SMISC | 10-12 |
| CLOCK4-6 | SMISC | 16-18 |
| CSST4-6 | SMISC | 22-24 |
| CLST4-6 | SMISC | 28-30 |
| JRP4-6 | SMISC | 34-36 |
| JCD4-6 | SMISC | 40-42 |
| JEF4-6 | SMISC | 46-48 |
| JDF4-6 | SMISC | 52-54 |
| JFF4-6 | SMISC | 58-60 |
| JRU4-6 | SMISC | 64-66 |
| JRV4-6 | SMISC | 70-72 |
| JRA4-6 | SMISC | 76-78 |
| JTEMP | SMISC | 79 |
| JFST6 | SMISC | 82 |
| JFNF6 | SMISC | 86 |
| JFEQ | SMISC | 87 |
Table 184sphe.4: MPC184 Spherical Joint Item and Sequence Numbers - NMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| E1X-I | NMISC | 1 |
| E1Y-I | NMISC | 2 |
| E1Z-I | NMISC | 3 |
| E2X-I | NMISC | 4 |
| E2Y-I | NMISC | 5 |
| E2Z-I | NMISC | 6 |
| E3X-I | NMISC | 7 |
| E3Y-I | NMISC | 8 |
| E3Z-I | NMISC | 9 |
| E1X-J | NMISC | 10 |
| E1Y-J | NMISC | 11 |
| E1Z-J | NMISC | 12 |
| E2X-J | NMISC | 13 |
| E2Y-J | NMISC | 14 |
| E2Z-J | NMISC | 15 |
| E3X-J | NMISC | 16 |
| E3Y-J | NMISC | 17 |
| E3Z-J | NMISC | 18 |
| JFX | NMISC | 19 |
| JFY | NMISC | 20 |
| JFZ | NMISC | 21 |
| JMX | NMISC | 22 |
| JMY | NMISC | 23 |
| JMZ | NMISC | 24 |
MPC184 Spherical Joint Assumptions and Restrictions
The nodes I and J should be coincident. If the nodes are not coincident, the relative positions between the two nodes are maintained.
Boundary conditions cannot be applied on the nodes forming the spherical element.
Rotational degrees of freedom are activated at the nodes forming the element. When these elements are used in conjunction with solid elements, the rotational degrees of freedom must be suitably constrained. Since boundary conditions cannot be applied to the nodes of the spherical joint, a beam or shell element with very weak stiffness may be used with the underlying solid elements at the nodes forming the joint element to avoid any rigid body modes.
In a nonlinear analysis, the components of relative motion are accumulated over all the substeps. For the values to be accumulated correctly, it is essential that the substep size be restricted such that the rotation in a given substep is less than π.
The element currently does not support birth or death options.
Frictional calculations may be indicated as active even when the relative motion is zero due to stops or locks. The frictional calculations are carried out on the axis of rotation of the spherical joint, whereas the stops and locks are imposed on the relative rotation degrees of freedom of the joint.
For the Lagrange multiplier element formulation (KEYOPT(2) = 0) and the penalty-based element formulation (KEYOPT(2) = 1), the equation solver (EQSLV) must be the sparse or the PCG solver.
Lagrange multiplier-based joint elements (KEYOPT(2) = 0) and penalty-based joint elements (KEYOPT(2) = 1) cannot be connected to each other.
The element coordinate system (/PSYMB,ESYS) is not relevant.