The contact element may be used to impose inequality constraints between nodes. Either perfect friction (i.e. "stick") or frictionless (i.e. "slip") conditions may be achieved. A contact element is defined by two nodes a spring constant, or "penalty parameter," k; and a fixed direction vector, N. The present location of node A (A = 1, 2) is given by X(A) + D(A) where X(A) is the initial position vector and D(A) is the displacement vector. The contact plane passes through the point X(A) + D(A) and is perpendicular to N (see Fig. 9.5.1).
Figure 9.5.1 Contact Surface
The contact/release condition is defined as follows
d
> 0 release d 
0 contact
where
d = L . N
L= (X(B) + D(B)) - (X(A) + D(A))
The quantity d is a measure of the distance between X(B) + D(B) and the contact plane. When contact is noted, a contact element stiffness and out-of-balance force are added to the global equations. These arrays are defined as follows:
Stiffness Matrices
(two-dimensional case)
(three-dimensional case)
Out-of-Balance Force
If k > 0 is sufficiently large, the point X(B) + D(B) will be forced to lie (approximately) on the contact plane. In subsequent steps, only the contact stiffness is assembled and the decision to remain in contact, or release, is made on the basis of the sign of d, as above.
For purposes of interpreting output, the contact element "displacement" is defined to be d, and the "force" is given by
k.d if d < 0
0 if
d 
0
CONTACT_SURFACE
Element_name = CONTACT_SURFACE stick = on, etc...
m, stiff(m), ( an(i, m), i = 1, nsd ) < m = 1, numat >
< connectivity data >
< field output data >
< terminate with a blank record >.
9.5.1 Element Group Control
Information
Must follow the element name (same data record), and define the control parameters as follows:
Note Variable Name Type Default Description
(1) stick list [on] Contact condition
on / off
formulation list [penalty] Formulation
penalty
augmented_lagrangian
Notes/
(1) The contact condition may be either perfect friction (i.e. "stick") or frictionless (i.e. "slip"). In the stick case, no relative motion is allowed between nodes when in contact. In the slip case, frictionless sliding is allowed in the contact plane.
9.5.2 Geometric / Material Properties Data (Numat sets)
Note Variable Default Description
M [0] Geometric/material set number
STIFF(M) [0.0] Spring constant k (i.e. "penalty parameter")
AN(1,M) [0.0] Component 1 of direction vector N
AN(2,M) [0.0] Component 2 of direction vector N
AN(3,M) [0.0] Component 3 of direction vector N
9.5.3 Element Nodal Connectivity Data
Consult Chapter 11 for details; for this element NEN = 2.
9.5.4 Element Output History Requests
"On-line" and Calcomp plots of various element response components may be obtained. Each component required is plotted versus time. Plots of this type are useful in providing quick information concerning the time history behavior of important data. The total number of components to be plotted must equal NOUT, which is defined on the element group control record (see Section 9.1.1).
Note Variable Default Description
(1) N [0] Element
number 1 and Numel
(2) NG [0] Generation
increment 0
(3) NTEMP(1) [0] Component
number 1 and 2
NTEMP(2) [0] Component number 1 and 2
Notes/
(1) Element components history output data
must be input for elements at which the time history of one or more components
is to be plotted. Records need not be
read in order. Terminate with a blank record.
(2) Element components history output data can be generated by employing a two record sequence as follows:
Record 1: L,LG,LTEMP(1),LTEMP(2)
Record 2: N,NG,NTEMP(1),NTEMP(2)
The output time history requests of all elements
L+LG, L+2*LG,...,N-MOD(N-L,LG)
(i.e., less than N) are set equal to those of node L. If LG is blank or zero, no generation takes place between L and N.
(3) Output history information is stored in the array IHS in element group data. The dimension of IHS is 2 x NOUT. The first row of IHS contains element numbers and the second row contains output history component numbers. Two different component numbers may be plotted as described above. The corresponding component numbers and output labels are:
Component Number Description Output Label
1 Displacement DELT
2 Contact force FORC
Notes . .