VDISP

User subroutine to specify prescribed boundary conditions.

User subroutine VDISP:

can be used to prescribe translational and rotational boundary conditions;
is called for all degrees of freedom listed in the associated boundary condition;
allows user to specify values for either the degree of freedom or its time derivatives such as velocity and acceleration;
releases the boundary condition by default if the user does not specify a value for the boundary condition;
can be used to apply a concentrated load, instead, by adjusting the default motion of the node;
can be called for blocks of nodes for which the boundary conditions are defined in the subroutine.

The following topics are discussed:

Initial velocity
Acceleration
User subroutine interface
Variables to be defined
Variables passed in for information
Example: Imposition of acceleration on a rigid body with nonzero initial velocity

Initial velocity

At the beginning of each step user subroutine VDISP is called once to establish the initial velocity; and then, it is called once on each configuration, including the initial configuration, to establish the nodal acceleration.

The first call to user subroutine VDISP is made to establish the initial velocity, which is indicated by the passing of a step time value of $- d t$ into the subroutine, where $d t$ is the current time increment. If displacement is prescribed, the returned variable, rval, corresponds to $u_{o} - v_{o} d t$ , where $u_{o}$ and $v_{o}$ are the initial displacement and velocity respectively. If velocity is prescribed, the returned variable corresponds to the initial velocity $v_{o}$ . If acceleration is prescribed, the returned variable corresponds to $\frac{v_{o}}{d t}$ , where $v_{o}$ is the initial velocity.

The default value of rval is consistent with the velocity at the end of previous step or that specified as an initial condition in case of the first step. You only need to reset the rval if a different initial velocity is desired. The arrays u and v stand for the default initial displacement and velocity, respectively. The array a contains a zero value.

Acceleration

During time incrementation user subroutine VDISP is called once for each configuration, including the initial configuration, to establish the nodal acceleration.

If displacement is prescribed, the returned variable should be set equal to the displacement at stepTime+dtNext, where stepTime is the step time and dtNext is the next time increment. If velocity is prescribed, the returned variable should be set equal to the mean velocity at stepTime+dtNext/2. If acceleration is prescribed, the returned variable should be set equal to the acceleration at stepTime. Note that stepTime is zero for the initial configuration.

The variable rval has a default value that is computed with the constraints not yet applied. You can leave rval at this value, if desired. The variable u contains values at stepTime. Whereas, the variable v contains initial velocity when stepTime is zero and, otherwise, velocity at stepTime—dt/2. The variable a contains values at stepTime computed with the constraints not yet applied.

Tip: If the node does not participate in any other conflicting constraints or connector elements, leaving rval at the incoming value would amount to leaving the node unconstrained. Alternatively, if you want to apply a concentrated load at such a node (instead of the boundary condition), you can compute the change in acceleration due to this load and modify the rval value to account for that change. The nodal mass and the rotary inertia are available in VDISP for computing the change in acceleration. In addition, the default value of rval at the node already reflects the forces from any contact, user-defined load, and elements (except for connectors) at that node.

User subroutine interface

      subroutine vdisp(
c Read only variables -
     1   nblock, nDof, nCoord, kstep, kinc,
     2   stepTime, totalTime, dtNext, dt,
     3   cbname, jBCType, jDof, jNodeUid, amp,
     4   coordNp, u, v, a, rf, rmass, rotaryI,
c Write only variable -
     5   rval )
c
      include 'vaba_param.inc'
c
      character*80 cbname
      dimension jDof(nDof), jNodeUid(nblock), 
     1          amp(nblock), coordNp(nCoord,nblock),
     2          u(nDof,nblock), v(nDof,nblock), a(nDof,nblock),
     3          rf(nDof,nblock), rmass(nblock), rotaryI(3,3,nblock),
     4          rval(nDof,nblock)
c
      do 100 k = 1, nblock
      do 100 j = 1, nDof
         if( jDof(j) .gt. 0 ) then
            user coding to define rval(j, k)
         end if
  100 continue
c
      return
      end

Variables to be defined

rval(nDof, nblock): Values of the prescribed variable for degrees of freedom 1–6 (translation and rotation) at the nodes. The variable can be displacement, velocity, or acceleration, depending on the type specified in the associated boundary condition. The variable type is indicated by jBCType. The variable rval has a default value that is computed without taking the constraints into account. You may reset the rval.

Variables passed in for information

nblock: Number of nodal points to be processed in this call to VDISP.
nDof: Number of degrees of freedom (equals 6).
nCoord: Number of coordinate components (equals 3).
kstep: Step number.
kinc: Increment number.
stepTime: Value of time since the step began.
totalTime: Value of total time. The time at the beginning of the step is given by totalTime-stepTime.
dtNext: Next time increment size.
dt: Current time increment size.
cbname: User-specified name corresponding to the associated boundary condition.
jBCType: Indicator for type of prescribed variable: 0 for displacement, 1 for velocity, and 2 for acceleration.
jDof(nDof): Indicator for prescribed degrees of freedom. The values given by rval(j,k) are prescribed only if jDof(j) equals 1.
jNodeUid(nblock): Node numbers.
amp(nblock): Amplitude values corresponding to the associated amplitude functions. These values are passed in for information only and will not contribute to the values of the prescribed variable automatically.
coordNp(nCoord, nblock): Nodal point coordinates.
u(nDof, nblock): Initial displacements when stepTime is negative, and, otherwise, displacement at stepTime. All translations are included if one or more translational degrees of freedom are prescribed. All rotations are included if one or more rotational degrees of freedom are prescribed.
v(nDof, nblock): Initial nodal velocities when stepTime is non-positive and, otherwise, mean velocities at stepTime-dt/2 during time incrementation. All translational velocities are included if one or more translational degrees of freedom are prescribed. All angular velocities are included if one or more rotational degrees of freedom are prescribed.
a(nDof, nblock): Contains a zero value when stepTime is negative and, otherwise, the accelerations, computed without accounting for the boundary condition, at stepTime. All translational accelerations are included if one or more translational degrees of freedom are prescribed. All angular accelerations are included if one or more rotational degrees of freedom are prescribed.
rf(nDof, nblock): Nodal point reaction at stepTime-dt. All reaction forces are included if one or more translational degrees of freedom are prescribed. All reaction moments are included if one or more rotational degrees of freedom are prescribed.
rmass(nblock): Nodal point masses.
rotaryI(3, 3, nblock): Nodal point rotary inertia.

Example: Imposition of acceleration on a rigid body with nonzero initial velocity

In this example a sinusoidal acceleration is imposed on the reference node of a rigid body. Nonzero initial velocity is also specified for the rigid body. User subroutine VDISP given below illustrates how the return value array is to be computed for different phases of the solution. The analysis results show that both the initial velocity and acceleration are correctly specified.

Input file

HEADING
 Test VDISP with S4R element
NODE, NSET=NALL
 1,
 2, 2., 0.
 3, 0., 2.
 4, 2., 2.
 9, 1., 1., 0.
ELEMENT, TYPE=S4R, ELSET=SHELL
 10, 1,2,4,3
SHELL SECTION, ELSET=SHELL, MATERIAL=ELSHELL
  2.0000000e-02,     3 
MATERIAL, NAME=ELSHELL
DENSITY
7850.0, 
ELASTIC
  2.5000000e+11,   3.0000000e-01
RIGID BODY, REF NODE=9, ELSET=SHELL
INITIAL CONDITIONS, Type=VELOCITY
 9, 1, 0.4
STEP
DYNAMIC, EXPLICIT, DIRECT USER CONTROL
 0.01, 0.8
BOUNDARY, USER, TYPE=ACCELERATION
 9, 1
OUTPUT, HISTORY, TIME INTERVAL=0.01, OP=NEW
NODE OUTPUT, NSET=NALL
 U, V, A
END STEP

User subroutine

      subroutine vdisp(
c Read only variables -
     *   nblock, nDof, nCoord, kstep, kinc, 
     *   stepTime, totalTime, dtNext, dt, 
     *   cbname, jBCType, jDof, jNodeUid, amp,
     *   coordNp, u, v, a, rf, rmass, rotaryI, 
c Write only variable -
     *   rval )
c
      include 'vaba_param.inc'
      parameter( zero = 0.d0, half = 0.5d0, one = 1.d0 )
c
      character*80 cbname
      dimension jDof(nDof), jNodeUid(nblock), 
     *   amp(nblock), coordNp(nCoord,nblock), 
     *   u(nDof,nblock), v(nDof,nblock), a(nDof,nblock), 
     *   rf(nDof,nblock), rmass(nblock), 
     *   rotaryI(3,3,nblock), rval(nDof,nblock)
c      
c     Impose acceleration
c
      if( jBCType .eq. 2 ) then
c
         if( stepTime .lt. zero ) then
c
c           Initialization 1
c
            do 310 k=1, nblock
            do 310 j=1, nDof
               if ( jDof(j) .gt. 0 ) then
                  v0 = v(j,k)
                  rval(j,k)  = v0/dt 
               end if
310         continue
c
         else
c
c           Time incrementation
c
            amplitude = 2.0
            period = 0.8
            twopi = 6.2831853d0
c
            do 350 k=1, nblock
            do 350 j=1, nDof
               if ( jDof(j) .gt. 0 ) then
                  rval(j,k) = amplitude*
*                           sin( twopi*stepTime / period )
               end if
350         continue      
         end if
      end if
c
      return
     
end