Initial conditions define the state of the system at the start of the analysis. In structural finite element analyses, initial conditions are defined in terms of initial displacements, velocities, and accelerations at all independent degrees of freedom (DOFs).
Because all time-integration schemes (such as the Newmark method and the HHT method) rely on the history of displacements, velocities and accelerations, it is important to define consistent initial conditions. By default, a zero value is assumed for initial displacements, velocities, and accelerations at DOFs that are not otherwise specified (via the IC command).
Inconsistencies in initial conditions introduce errors into the time-integration scheme and lead to excitation of undesired (spurious) modes. Accumulation of these errors over several time increments adversely affects the solution and very often causes the time-integration scheme to fail. Applying numerical damping or other forms of damping can suppress the growth of these errors. However, such additions also affect the solution, especially, when long term transient behavior is being studied in the analysis.
It is not always possible, however, to have complete information about the initial state of a system being modeled for transient analysis. In such situations, it is helpful to run a dummy load step before the actual transient analysis of interest to bring the system into a consistent initial state. The purpose of such a load step is to eliminate the error introduced by inconsistent initial conditions.
Following are two ways to run a dummy load step:
This technique is useful in cases where initial accelerations are non-zero, are known, and are uniform over the entire model. Applying acceleration loading (via the ACEL command) introduces non-zero accelerations into the system. After the analysis has run through one substep, the actual transient analysis can be carried out without the acceleration loading.
Example
Consider a rigid beam of length l rotating in the x-y plane about a pinned end at a constant angular velocity ω. The free end of the beam has a tangential velocity of ωl and a centripetal acceleration of ω2l. The beam is assumed to have all of its mass concentrated at the free end. To perform the analysis, model the rigid beam using the MPC184 element with Lagrange multipliers to enforce the rigid beam constraints. With one end of the rigid beam pinned, apply initial velocity normal to the beam axis at the free end. To introduce centripetal acceleration, use acceleration loading as illustrated in the following input file:
Transient Analysis of a Rigid 3D Beam Rotating About a Fixed Node
/title,Transient analysis of a rigid 3D beam rotating about a fixed node /prep7 et,1,mass21 keyopt,1,3,2 !3d mass without rotary inertia et,2,mpc184 keyopt,2,1,1 !rigid beam keyopt,2,2,1 !lagrange multiplier n,1,0.0,0.0 !pinned end (node 1) n,2,1.0,0.0 !free end (node 2) type,1 real,1 m = 1.0 r,1,m en,1,2 !3d mass at free end (node 2) type,2 real,2 en,2,1,2 !rigid beam finish /solu vel = 6.2831853072 !tangential velocity ic,2,uy,0.0,vel !initial condition for velocity antype,trans time,1.e-9 acel,0.0,-vel*vel,0.0 !apply centripetal acceleration kbc,1 !step loading nlgeom,on nsub,1,1,1 !use 1 substep for analysis trnopt,full, , , , ,HHT !use HHT time integration tintp,0.0 !no numerical damping outres,all,all solve d,1,all ddel,1,rotz d,2,uz d,2,rotx d,2,roty time,6.0 acel,0.0,0.0,0.0 !remove centripetal acceleration kbc,1 midtol,on,1e2 !automatic time stepping with MIDTOL nsub,600,1e7,400 trnopt,full, , , , ,HHT tintp,0.05 !small numerical damping for HHT outres,all,all solve finish /post26 /xrange,0.,6.0 nsol,2,2,u,x,ux !x displacement for node 2 nsol,3,2,u,y,uy !y displacement for node 2 nsol,4,2,v,x,vx !x velocity for node 2 nsol,5,2,v,y,vy !y velocity for node 2 nsol,6,2,a,x,ax !x acceleration for node 2 nsol,7,2,a,y,ay !y acceleration for node 2 /axlab,x,Time T /axlab,y,D/V/A /gropt,divx,10 /gropt,divy,10 /gthk,curve,2 /title,Transient analysis of a rigid 3D beam rotating about a fixed node plvar,ux,uy,vx,vy,ax,ay finish
This technique is of a more general nature and uses numerical damping to eliminate errors or numerical noise due to inconsistent initial conditions. After the noise has been damped out over several substeps, you can perform the actual transient analysis with smaller numerical damping.
Some potential drawbacks exist in cases where high frequency content of flexible multibody systems is important for analysis. Applying high numerical damping in the dummy analysis can affect the desired high-frequency response. Ansys, Inc. recommends using the HHT method for this technique because the integration scheme shows good dissipation properties with numerical damping.
Example
Consider a rigid-flexible double pendulum made up of a rigid and a flexible beam. One end of the rigid beam is pinned and the other end is hinged to the flexible beam. The other end of the flexible beam is free. The rigid beam is assumed to have all of its mass concentrated at the end that is hinged to the flexible beam. The system is given an initial velocity tangential to the flexible beam axis at its free end, as shown in the following input file:
Transient Analysis of a Rigid-Flexible Double Pendulum
/title,Transient analysis of a rigid-flexible double pendulum /prep7 et,1,mass21 keyopt,1,3,2 !3d mass without rotary inertia et,2,mpc184 keyopt,2,1,1 !rigid beam keyopt,2,2,1 !lagrange multiplier et,3,mpc184 keyopt,3,1,6 !revolute joint between rigid and flexible beam et,4,beam188 !flexible beam n,1,0.0,0.0 !pinned (supported) end of rigid beam n,2,1.0,0.0 !hinged end of rigid beam (node 2) n,3,1.0,0.0 !hinged end of flexible beam n,4,1.25,0.0 n,5,1.5,0.0 n,6,1.75,0.0 n,7,2.0,0.0 !free end of flexible beam (node 7) type,1 real,1 m = 390 r,1,m en,1,2 !3d mass at the end of rigid beam type,2 real,2 en,2,1,2 !rigid beam local, 11, 0, 0.0, 0.0, 0.0, , , 90 sectype, 3, JOIN, REVO, TESTREVO secjoin, , 11, 11 type,3 real,3 secnum,3 en,3,3,2 !revolute joint mp,ex,1,2e11 !material properties for flexible beam mp,nuxy,1,0.3 mp,density,1,7.8e3 sectype,4,beam,csolid secdata,1,0.1784124116 !c-s area is 0.1 type,4 real,4 secnum,4 mat,1 en,4,3,4 !flexible beam elements en,5,4,5 en,6,5,6 en,7,6,7 d,1,all ddel,1,rotz finish /solu vel = 6.2831853072 !tangential velocity ic,7,uy,0.0,vel !initial condition for velocity antype,trans time,0.1 kbc,1 nlgeom,on nsub,50,50,50 !use multiple substeps trnopt,full, , , , ,HHT !use HHT time integration tintp,0.2 !use high numerical damping outres,all,all solve time,6.0 midtol,on,10 !automatic time stepping with MIDTOL nsub,100,1e6,100 trnopt,full, , , , ,HHT tintp,0.05 !small numerical damping for HHT outres,all,all solve finish /post26 nsol,2,7,u,x,ux !x displacement for node 7 nsol,3,7,u,y,uy !y displacement for node 7 nsol,4,2,u,x,ux1 !x displacement for node 2 nsol,5,2,u,y,uy1 !y displacement for node 2 nsol,4,3,v,x,vx !x velocity for node 7 nsol,5,3,v,y,vy !y velocity for node 7 nsol,6,7,a,x,ax !x acceleration for node 7 nsol,7,7,a,y,ay !y acceleration for node 7 /axlab,x,Time T /axlab,y,D/V/A /gropt,divx,10 /gropt,divy,10 /gthk,curve,2 /title,Transient analysis of a rigid-flexible double pendulum plvar,ux,uy,ux1,uy1,vx,vy,ax,ay finish