MPC184-Spherical

Multipoint Constraint Element: Spherical Joint

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## 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:

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 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.

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.

### 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

None

None

None

None

Special Features
 Large deflection Linear perturbation
KEYOPT(1)

Element behavior:

15  --

Spherical joint element

## MPC184 Spherical Joint Output Data

The solution output associated with the element is in two forms:

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

NameDefinitionOR
ELElement number-Y
NODESElement node numbers (I, J)-Y
FXConstraint force in X direction-Y
FYConstraint force in Y direction-Y
FZConstraint force in Z direction-Y
JRP4Joint relative position of DOF 4-Y
JRP5Joint relative position of DOF 5-Y
JRP6Joint relative position of DOF 6-Y
JRU4Joint relative rotation of DOF 4-Y
JRU5Joint relative rotation of DOF 5-Y
JRU6Joint relative rotation of DOF 6-Y
JRV4Joint relative rotational velocity of DOF 4-Y
JRV5Joint relative rotational velocity of DOF 5-Y
JRV6Joint relative rotational velocity of DOF 6-Y
JRA4Joint relative rotational acceleration of DOF 4-Y
JRA5Joint relative rotational acceleration of DOF 5-Y
JRA6Joint 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

NameDefinitionOR
E1X-I, E1Y-I, E1Z-IX, Y, Z components of the evolved e1 axis at node I-Y
E2X-I, E2Y-I, E2Z-IX, Y, Z components of the evolved e2 axis at node I-Y
E3X-I, E3Y-I, E3Z-IX, Y, Z components of the evolved e3 axis at node I-Y
E1X-J, E1Y-J, E1Z-JX, Y, Z components of the evolved e1 axis at node J-Y
E2X-J, E2Y-J, E2Z-JX, Y, Z components of the evolved e2 axis at node J-Y
E3X-J, E3Y-J, E3Z-JX, Y, Z components of the evolved e3 axis at node J-Y
JFX, JFY, JFZConstraint forces expressed in the evolved coordinate system specified at node I-Y
JMX, JMY, JMZConstraint 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
ItemE
FXSMISC1
FYSMISC2
FZSMISC3
JRP4-6SMISC34-36
JRU4-6SMISC64-66
JRV4-6SMISC70-72
JRA4-6SMISC76-78

Table 184sphe.4:  MPC184 Spherical Joint Item and Sequence Numbers - NMISC Items

Output Quantity Name ETABLE and ESOL Command Input
ItemE
E1X-INMISC1
E1Y-INMISC2
E1Z-INMISC3
E2X-INMISC4
E2Y-INMISC5
E2Z-INMISC6
E3X-INMISC7
E3Y-INMISC8
E3Z-INMISC9
E1X-JNMISC10
E1Y-JNMISC11
E1Z-JNMISC12
E2X-JNMISC13
E2Y-JNMISC14
E2Z-JNMISC15
E3X-JNMISC16
E3Y-JNMISC17
E3Z-JNMISC18
JFXNMISC19
JFYNMISC20
JFZNMISC21
JMXNMISC22
JMYNMISC23
JMZNMISC24

## 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.

• 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.

## MPC184 Spherical Joint Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

ANSYS Mechanical Pro

• Linear perturbation is not available.