## 10.3. Surface-Based Constraints

A surface-based constraint can be used to couple the motion of nodes on the contact surface to a single pilot node on the target surface. The multipoint constraint (MPC) capability of the contact elements (KEYOPT(2) = 2) allows you to define three types of surface-based constraints:

• Rigid surface constraint - In this type of constraint, the contact nodes are constrained to the rigid body motion defined by the pilot node (see Figure 10.7: Rigid Surface Constraint), similar to a constraint defined by the CERIG command.

• Force-distributed constraint - In this type of constraint, forces or displacements applied on the pilot node are distributed to contact nodes (in an average sense) through shape functions (see Figure 10.8: Force-Distributed Constraint), similar to a constraint defined by the RBE3 command.

• Coupling constraint - In this type of constraint, the degrees of freedom of contact nodes are constrained to have the same solution as the degrees of freedom of the pilot node (see Figure 10.9: Coupling Constraint), similar to a constraint defined by the CP command.

In Figure 10.9: Coupling Constraint, the pilot node's x-direction has been rotated by 45 degrees. Only UX is included in the coupling constraint, so UY on the contact nodes are left free. The resulting deformation shows that UX (rotated 45 degrees from global x) is constant on the contact nodes, but UY is nonuniform.

These surface-based constraints can be used in the following applications:

• To apply loads and boundary conditions to the pilot node (such as torque load or drill rotation). Example: a bolt head submitted to a torque force using a force-distributed constraint.

• To model rigid bodies. Example: rigid body definition in multi-body dynamics.

• To model rigid end conditions. Example: using a rigid surface constraint to model a rigid end plate or rigid plane section of 3-D solid elements.

• To model interactions with other joints. Example: two flexible parts linked by a hinge. This can be modeled by two force-distributed constraint definitions whose pilot nodes are connected by a revolute joint element.

• To define transitions between solid and structure elements. Example: a beam element connected to a solid element face.

### 10.3.1. Defining Surface-Based Constraints

The contact surface can be generated via the ESURF command. The contact nodes on the contact surface are the slave nodes of the MPC equations. The pilot node is the only target segment on the target surface side. It is the master node of the MPC equations. Forces and displacements can be applied on the pilot node and the contact nodes. You can define a follower element (FOLLW201) on the pilot node so that the element-specified external forces and moments on the follower element will follow the motion of the pilot node.

For a force-distributed constraint, use the following contact element key options:

 Force-distributed Constraint KEYOPT Settings KEYOPT(2) = 2 MPC based approach KEYOPT(12) = 5 or 6 Bonded always or bonded initial KEYOPT(4) = 1 Indicates a force-distributed constraint for CONTA171, CONTA172, CONTA173, CONTA174, CONTA175, CONTA176, and CONTA177

For a rigid surface constraint, use the following contact element key options:

 Rigid Surface Constraint KEYOPT Settings KEYOPT(2) = 2 MPC based approach KEYOPT(12) = 5 or 6 Bonded always or bonded initial KEYOPT(4) = 2 Indicates a rigid surface constraint for CONTA171, CONTA172, CONTA173, and CONTA174 KEYOPT(4) = 0 Indicates a rigid surface constraint for CONTA175 , CONTA176, and CONTA177

For a coupling constraint, use the following contact element key options:

 Coupling Constraint KEYOPT Settings KEYOPT(2) = 2 MPC based approach KEYOPT(12) = 5 or 6 Bonded always or bonded initial KEYOPT(4) = 3 Indicates a coupling constraint for CONTA171, CONTA172, CONTA173, CONTA174, CONTA175, CONTA176, and CONTA177

The following key options are ignored for surface-based constraints: KEYOPT(8), KEYOPT(5), KEYOPT(7), KEYOPT(10).

With the exception of PINB, none of the standard contact real constants are used for surface-based constraints using internal MPC.

### 10.3.2. Defining Influence Range (PINB)

By default, all the contact nodes are included in the surface-based constraints. You can select a subset of nodes from these contact nodes by defining a radius of influence range, PINB. The nodes that lie within the spherical range (radius = PINB) centered about the pilot node are selected for the definition of the surface-based constraints.

### 10.3.3. Degrees of Freedom of Surface-Based Constraints

Use KEYOPT(1) of the contact elements to specify the degrees of freedom to be used in the constraint set. You may include other field degrees of freedom in addition to the structural DOFs.

The pilot node has both translational and rotational degrees of freedom. The active degrees of freedom at the pilot node depend on the defined type of target elements. Use TARGE169 for 2-D surface-based constraints that contain UX, UY, and ROTZ degrees of freedom. Use TARGE170 for 3-D surface-based constraints that contain UX, UY, UZ, and ROTX, ROTY, ROTZ degrees of freedom. Generally, you should always set KEYOPT(2)=1 for the target element to indicate that boundary conditions for rigid target nodes will be user-specified; otherwise, the program may apply internal constraints on the pilot node.

The degrees of freedom of the surface-based constraints can also be controlled by using KEYOPT(4) of the target element (TARGE169 or TARGE170). For example, for the 3-D case (TARGE170), you might specify that only UX, UY, and ROTZ be used in the constraint. You can do this by entering a six digit value for KEYOPT(4). The first to sixth digits represent ROTZ, ROTY, ROTX, UZ, UY, UX, respectively. The number 1 (one) indicates the DOF is active, and the number 0 (zero) indicates the DOF is not active. Therefore, to specify that UX, UY, and ROTZ be used in the constraint, you would enter 100011 as the KEYOPT(4) value.

The basic formulation for the rigid surface constraint is similar to the MPC184 rigid beam and rigid link elements. However, this constraint type offers additional flexibility when you fully or partially constrain the degrees of freedom. For examples, the following are possible configurations:

### 10.3.4. Specifying a Local Coordinate System

You can specify the surface-based constraint in a local coordinate system. For the rigid surface constraint, rotate the contact nodes into a local coordinate system. For the force-distributed constraint and the coupling constraint, rotate the pilot node into a local coordinate system.

When KEYOPT(12) = 5 is set on the contact elements, the coordinate system does not rotate and it keeps its initial configuration. When the rotation is finite and KEYOPT(12) = 6 is set on the contact elements, the coordinate system in which the constrained degrees of freedom are specified will be co-rotated according to the rotation of the pilot node. The degrees of freedom of the surface-based constraints will be assigned with the co-rotated system. This is true even for the constrained degrees of freedom specified in the global coordinate system.

Note:  If all degrees of freedom are included in the constraint equations, there will be no difference between the KEYOPT(12) = 5 and KEYOPT(12) = 6 settings.

Figure 10.10: Slider Link shows an example of a slider link modeled with contact. A local cylindrical coordinate system is defined at a contact node such that the x-direction is coincident with the line connecting the contact node and pilot node. KEYOPT(4) = 10 is set for the target element type to specify that only the y degree of freedom is constrained and other degrees of freedom are free. The coordinate system at the contact node will be co-rotated according to the rotation of the pilot node.

In another example, a cylindrical ring is clamped at one end and loaded by a torque at the other end (Figure 10.11: Free Radial Expansion Under Torque Load). A rigid surface constraint is used with all the contact nodes rotated into a cylindrical coordinate system. If the x-direction constraint is free (KEYOPT(4) = 110), the ring is allowed to expand in the radial direction.

### 10.3.5. Additional Guidelines for a Force-Distributed Constraint

• The pilot node is a dependent node (meaning the degrees of freedom for this node are removed). The contact nodes are independent nodes (the degrees of freedom are retained). If the pilot node has constraints applied to it, internally-generated MPC equations are rewritten so that the degrees of freedom of the pilot node are no longer dependent DOF.

• KEYOPT(4) of TARGE169 and TARGE170 controls the number of degrees of freedom of the pilot node.

• The number of internally-generated MPCs is equal to the number of degrees of freedom defined by KEYOPT(4) of TARGE169 and TARGE170.

• When the constrained surface is built on a symmetric geometry model instead of the “full” geometry model, you must define the symmetry conditions using KEYOPT(6) of the target element (TARGE169 or TARGE170). Otherwise, you might get unexpected results (as shown by (c) in the figure below). When defining symmetric conditions, the pilot node must be located on the symmetry plane/edge.

### 10.3.6. Additional Guidelines for a Rigid Surface Constraint

• The pilot node is an independent (retained) node in the constraint equation. The contact nodes are the dependent (removed) nodes. Use great caution when you apply any displacement constraints, coupling (CP command), or constraint equations (CE command) on the contact nodes since redundant constraints are likely to occur.

• KEYOPT(4) of TARGE169 and TARGE170 controls the DOF set (the number of DOF) of the contact (dependent) nodes used in the internally-generated MPCs.

• The number of internally-generated MPCs is equal to the number of contact nodes times the number of DOF.

• The contact surface does not require underlying elements.

### 10.3.7. Additional Guidelines for a Coupling Constraint

• The pilot node is an independent (retained) node in the constraint equation. The contact nodes are the dependent (removed) nodes. It is strongly recommended that you do not apply any displacement constraints, coupling (CP command), or constraint equations (CE command) on the contact nodes in the same DOF direction as the coupling constraint since redundant constraints are likely to occur.

• KEYOPT(4) of TARGE169 and TARGE170 controls the DOF set (the number of DOF) of the pilot node (the independent DOF) used in the internally-generated MPCs.

• The DOF set defined by KEYOPT(4) follows the nodal coordinate system of the pilot node. Each contact node can have its own nodal coordinate system, which does not affect the solution.

• The number of internally-generated MPCs is equal to the number of contact nodes times the number of DOF.

### 10.3.8. Modeling a Beam-Solid Assembly

The surface-based constraint technique can be used to apply transitions between solid and structure elements; for example, a beam element connected to the solid or shell element face. One beam end node must be the pilot node and the solid/shell nodes must be the contact nodes. The rigid surface constraint is generally well-suited for the solid beam to solid surface case (see Figure 10.13: Beam-Solid Assembly Defined by Rigid Surface Constraint), and the force-distributed constraint is well-suited for the flexible beam (such as a thin wall beam) to solid/shell surface case (see Figure 10.14: Beam-Solid Assembly Defined by Force-distributed Constraint).