MPC184-Spherical
## MPC184 Spherical Joint Element Description

## MPC184 Spherical Joint Input Data

### MPC184 Spherical Joint Input Summary

## MPC184 Spherical Joint Output Data

## MPC184 Spherical Joint Assumptions and Restrictions

**Multipoint Constraint Element: Spherical Joint**

Compatible Products: – | Pro | Premium | Enterprise | Ent PP | Ent Solver | –

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.

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:

For output purposes, the relative rotations between nodes I and J are characterized by the Cardan (or Bryant) angles as follows:

Since the output of relative rotations is characterized by the
Cardan (or Bryant) angles, the rotation around the local e_{2} 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 e_{1} or e_{3} axis.

Since the relative rotational degrees of freedom cannot be controlled, the spherical joint element does not allow stops and locks or material behavior specifications. Other input data that are common to all joint elements are described in "Joint Input Data" in the MPC184 element description.

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**None

**Surface Loads**None

**Body Loads**None

**Element Loads**None

**Special Features**Large deflection Linear perturbation **KEYOPT(1)**Element behavior:

**15 --**Spherical joint element

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 |

JRP4 | Joint relative position of DOF 4 | - | Y |

JRP5 | Joint relative position of DOF 5 | - | Y |

JRP6 | Joint relative position of DOF 6 | - | Y |

JRU4 | Joint relative rotation of DOF 4 | - | Y |

JRU5 | Joint relative rotation of DOF 5 | - | Y |

JRU6 | Joint relative rotation of DOF 6 | - | Y |

JRV4 | Joint relative rotational velocity of DOF 4 | - | Y |

JRV5 | Joint relative rotational velocity of DOF 5 | - | Y |

JRV6 | Joint relative rotational velocity of DOF 6 | - | Y |

JRA4 | Joint relative rotational acceleration of DOF 4 | - | Y |

JRA5 | Joint relative rotational acceleration of DOF 5 | - | Y |

JRA6 | Joint relative rotational acceleration of DOF 6 | - | Y |

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 e_{1} axis at node I | - | Y |

E2X-I, E2Y-I, E2Z-I | X, Y, Z components of the evolved e_{2} axis at node I | - | Y |

E3X-I, E3Y-I, E3Z-I | X, Y, Z components of the
evolved e_{3} axis at node I | - | Y |

E1X-J, E1Y-J, E1Z-J | X, Y, Z components of the evolved e_{1} axis
at node J | - | Y |

E2X-J, E2Y-J, E2Z-J | X, Y, Z components of the evolved
e_{2} axis at node J | - | Y |

E3X-J, E3Y-J, E3Z-J | X, Y,
Z components of the evolved e_{3} 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.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 |

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.

Stops (

**SECSTOP**) and locks (**SECLOCK**) are not applicable to this element.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.

The equation solver (

**EQSLV**) must be the sparse solver or the PCG solver. The command**PCGOPT**,,,,,,,ON is also required in order to use the PCG solver.The element coordinate system (

**/PSYMB**,ESYS) is not relevant.