13.184. MPC184 - Multipoint Constraint

MPC184 represents a general class of multipoint constraint elements that implement kinematic constraints using Lagrange multipliers. The elements are loosely classified here as "constraint elements" and "joint elements". All of these elements are used in situations that require you to impose some kind of constraint to meet certain requirements. Since these elements are implemented using Lagrange multipliers, the constraint forces and moments are available for output purposes. The different constraint elements and joint elements are identified by KEYOPT(1).

 

13.184.1. Slider Element

The slider element (KEYOPT(1) = 3) is a 3-node element that allows a dependent node to slide on a line joining two independent nodes.

Figure 13.33: 184.2 Slider Constraint Geometry

184.2 Slider Constraint Geometry

The constraints required to maintain the dependent node on the line joining the two independent nodes are as follows:

Define a unit vector n as:

(13–307)

where:

x I , x J = position vectors of nodes I and J in the current configuration

Identify unit vectors l and m such that l, m, and n form an orthonormal set.

The constraints are then defined as:

(13–308)

(13–309)

where:

xk = position vector of the node K in the current configuration

Let i, j, and k be the global base vectors. Then we can define the unit vector l as:

(13–310)

If n = l, then:

(13–311)

Finally, the unit vector m is defined as:

(13–312)

The virtual work contributions are obtained from taking the variations of the above equations.

 

13.184.2. Joint Elements

The equations for the constraints imposed in joint elements are described in the individual element descriptions: