GAPCON

User subroutine to define conductance between contact surfaces or nodes in a fully coupled temperature-displacement analysis, coupled thermal-electrical-structural analysis, or pure heat transfer analysis.

User subroutine GAPCON:

assumes that the heat transfer between surfaces is modeled as $q = k (θ_{A} - θ_{B})$ , where q is the heat flux per unit area flowing between corresponding points A and B on the surfaces, k is the gap conductance, and $θ_{A}$ and $θ_{B}$ are the surface temperatures;
is used to define k, providing greater flexibility than direct gap conductance definition in specifying the dependencies of k (for example, it is not necessary to define the gap conductance as a function of the average of the two surfaces' temperatures, mass flow rates, or field variables);
will be called at the slave nodes of a contact pair and at the integration points in a contact or a gap element for which the heat conductance definition contains a user-subroutine-defined gap conductance; and
ignores any dependencies or data specified for the gap conductance outside the user subroutine.

The following topics are discussed:

Usage with contact pairs and gap elements
User subroutine interface
Variables to be defined
Variables passed in for information

Usage with contact pairs and gap elements

When this subroutine is used with a contact pair, point A is on the slave surface and point B is on the master surface.

When GAPCON is used with gap elements of type DGAP or GAPUNIT, point A is on the first node of the element and point B is the second node of the element.

User subroutine interface

      SUBROUTINE GAPCON(AK,D,FLOWM,TEMP,PREDEF,TIME,CINAME,SLNAME,
     1 MSNAME,COORDS,NOEL,NODE,NPRED,KSTEP,KINC)
C
      INCLUDE 'ABA_PARAM.INC'
C
      CHARACTER*80 CINAME,SLNAME,MSNAME
C
      DIMENSION AK(5),D(2), FLOWM(2), TEMP(2), PREDEF(2,*),
     1 TIME(2), COORDS(3)
      user coding to define AK(1) -- AK(5)
      RETURN
      END

Variables to be defined

AK(1): Gap conductance, k. The units of k are energy per time (flux) per area per temperature (JT⁻¹L⁻² $θ$ ⁻¹).
AK(2): $\partial k / \partial d$ , derivative of the gap conductance with respect to the clearance between the bodies. If the gap conductance is not a function of gap clearance, AK(2)=0.0. This variable needs to be defined only for fully coupled temperature-displacement and coupled thermal-electrical-structural analyses.
AK(3): $\partial k / \partial p$ , derivative of the gap conductance with respect to the pressure between the bodies. If the gap conductance is not a function of the pressure, AK(3)=0.0. This variable needs to be defined only for fully coupled temperature-displacement and coupled thermal-electrical-structural analyses.
AK(4): $\partial k / \partial θ_{A}$ , derivative of the gap conductance with respect to the temperature of point A on the first surface of the interface.
AK(5): $\partial k / \partial θ_{B}$ , derivative of the gap conductance with respect to the temperature of point B on the second surface of the interface.

Variables passed in for information

D(1): Separation between the surfaces, d.
D(2): Pressure transmitted across the surfaces, p. This pressure is zero in pure heat transfer analysis.
FLOWM(2): ${| \dot{m} |}_{A}$ , ${| \dot{m} |}_{B}$ , magnitudes of the mass flow rate per unit area at points A and B.
TEMP(2): Current temperature at points A and B.
PREDEF(2,NPRED): An array containing pairs of values of all of the user-specified field variables at the end of the current increment at points A and B (initial values at the beginning of the analysis and current values during the analysis).
TIME(1): Value of step time at the end of the increment.
TIME(2): Value of total time at the end of the increment.
CINAME: User-specified surface interaction name associated with the heat conductance definition, left justified. For contact elements it is the element set name given for the interface definition associated with the heat conductance definition; if an optional name is assigned to the interface definition, CINAME is passed in as this name, left justified. For gap elements it is the element set name for the element definition associated with the heat conductance definition.
SLNAME: Slave surface name. Passed in as blank if contact or gap elements are used.
MSNAME: Master surface name. Passed in as blank if contact or gap elements are used.
COORDS: An array containing the coordinates of point A. These are the current coordinates if geometric nonlinearity is accounted for during the step (see Defining an analysis); otherwise, the array contains the original coordinates of the point.
NOEL: Element label for contact or gap elements. Passed in as zero if contact surfaces are defined.
NODE: Slave node number (point A) if GAPCON is called for a contact pair.
NPRED: Number of predefined field variables.
KSTEP: Step number.
KINC: Increment number.