# Linear Gap

Linear gap is the simplest contact form used in Nastran simulations.

Linear gap can solve a large class of problems, such as hole bearing, heel-toe interaction and fitting contacts. Linear does not include friction, large displacements and material non-linearity. CGAP contact elements (node-to-node defined in the FEM environment) run in both linear static (SOL101) and non-linear analysis (SOL106).

The linear gaps provide for simple contact (compressive) forces only. MPC’s are used to define the gaps. The displacements and MPC-forces are used to determine if each gap is "welded" or "free".
• Displacement criteria: no penetration (MPC displacement > =0)
• MPCFORCE criteria: compressive force only (MPC force < =0)
The solution converges when there is no penetration of MPC's (gap deflection > = 0.0) and there are no tensile forces. An iterative procedure (CDITER-constrained displacement iterative technique) is used to solve the model based on displacements/MPC forces. The image below is an example where the CGAP is modeled.

The equation for the gap displacement can be written as:

Uygap = Uyopening – Uyclosing + Uyinitial

Rearranging in MPC format and setting Uyclosing as the dependent (first) term:

Uyclosing – Uyopening + Uygap – Uyinitial = 0

The Nastran commands to use for linear gaps are the following:

SPOINT (scalar point definition) is used to define the Ugap and Uinit :

SPOINT 55 155

The SUPORT entry specifies reference degrees-of-freedom for rigid body motion, and it puts SPOINT 55 (Ugap) in the R-set for iteration:

SUPORT 55 0

SPC selects a single-point constraint set to be applied and defines the initial gap opening = .05 (Uinit):

SPC 101106 155 0 .05

MPC entry: (equations of motion: Uy3 – Uy2 + Ugap – Uinit = 0)

$SID G1 C1 A1 G2 C2 A2 MPC 101106 3 2 1.0 2 2 -1.0$ G3 C3 A3 G4 C4 A4

55 0 1.0 155 0 -1.0

Related MSC/Nastran Bulk Data Entries are:
• PARAM, CDITER (integer) maximum number of iterations to determine open/closed
• PARAM, CDPRT (yes/no) print iteration history of constraint violations
• PARAM, CDPCH (yes/no) punches DMIG, CDSHUT entries for final solutions
• DMIG, CDSHUT: input vector of initial open/closed state of gaps (default = all closed)