SDT-nlsim         Contents     Functions              PDF Index

2.3  Time domain test cases

• Single mass test of various non-linearities
• Single mass stepped sine
• CBush with orientation
• Beam with non-linear rotation spring
• Lap joint with non-linear springs
• Parametric experiments in time

• sdtweb('_eval','d_fetime.m#BumpStop') simple mass on spring with bumpstop non-linearity.

2.3.1  Single mass test of various non-linearities

Single mass test of various non-linearities t_nlspring ModalNewmark. Supported examples are

• Maxwell viscoelastic spring,
• tabular stiffness,
• Dahl model with constant normal force.

 % Sample example with tabular stiffness and output spectrogram
  li={'MeshCfg{"d_fetime(1DOF):MaxwellA{q0}"}';';'
     'SimuCfg{ModalNewmark{.1m,.3,fc,chandle1}}'};
  RT=sdtm.range(struct,li);mdl=RT.nmap('CurModel');
 mdl=stack_set(mdl,'info','DefaultZeta',@(f)zeros(size(f)));
 
  x=[-100 -1e-4 1e-4 100]';Fu=struct('X',{{x}},'Y',x.*[10 0 0 10]');
  NLdata=struct('type','nl_inout','lab','TabK','keepLin',0,...
   'isens',3,'MatTyp',{{[3]}},'Fu',{{Fu}});
  mdl=feutil('setpro 1000',mdl,'NLdata',NLdata);
  mo2=nl_solve('ReducFree 2 10 0 -float2 -SE',mdl);% With internal DOF
 opt=d_fetime('TimeOpt dt=1e-4 tend=100 ModalNewmark');
 RB=struct('spec','BufTime 20 Overlap .75 fmin0 fmax60 -window hanning','ci',3);
 opt=stack_set(opt,'ExitFcn','Tip', ...
   struct('FinalCleanup',{{'nl_solve','PostCdof'}},'DOF',2.03,'DoFreq',RB));
 opt=stack_set(opt,'info','RangeTime',fe_range('grid',struct('A',logspace(-3,0,5))));
 d2=fe_time(opt,mo2);d2=fe_def('subdef',d2,d2.data>d2.data(2));

2.3.2  Single mass stepped sine

The d_hbm TestSteppedSine example illustrates the stepped sine procedure implemented with the ModalNewmark solver.

See also d_tdoexxx.

In such computations, it is assumed that the excitation frequency is fixed during the transient, so that the following parameters can be used the the run options

• .Nper number of periods for each computation
• .NperPer number of points per period. Alternatively time step .dt=1/freq/NperPer can be defined and used to set the initial value of .NperPer).
• .freq vector of frequencies for a series of stepped sine simulations.
• .A vector of amplitudes applied globally on the load case.

After the time computation of the target number of periods the ExitFcn entries in RT.Stack are processed by order. Typical entries would be

• PostFirstStab performs .ite time simulations without trying to check for stabilization to allow the transient to stabilize before any
• PostConstit extract non-linear stress/strains and possibly performs harmonic extraction with doFreq callback.

2.3.3  CBush with orientation

The example is detailed in

d_fetime('tutoCbushOrient')

2.3.4  Beam with non-linear rotation spring

First do a sweep

sdtweb('_eval','d_fetime.m#TestBeamNLRed')

2.3.5  Lap joint with non-linear springs

This test case is discussed with Marco Rosatello. See t_bjoint('TestTime').

The axial behavior of the C2 connector is given by a non-linear law in tabular F_z(e₃) form. This force is output as the generalized stress during time computations, while for equations actually solved one uses

(2.1)

For two directions x and y, the tangential behavior is incremented using a Dahl integration scheme

(2.2)

Since this integration does not guarantee | F_x(t)| <= | µ F_z(t)| , the condition is enforced at each time step. Again there is the need to distinguish F_x(t) and the tangential load which needs to account for adherence stiffness in the nominal model used to generate the modal basis serving to define DOFs for time integration. Thus

(2.3)

Iwan model with Dahl cells. Data is sigma slope at no load, α shape parameter, µ F_z normal load.

(2.4)

2.3.6  Parametric experiments in time

nl_solve handles experiments associated with a series of time computations defined using the fe_range format. Typical applications are frequency and amplitude stepping experiments associated with HBM testing. For examples see

The principle of the experiment is that at each design point parameters are first changed before starting a time computation followed by postprocessing steps. The expression for changing the parameter can be given manually as in the first d_fetime doTimeRange example where

R1.param.Zener_c1.SetFcn='NL.opt(10:11)=[1 -1]*10/500*val(j1);'; 

changes the constants in NL.opt(10:11).

Other predefined set functions are

• fin_coef do a stepped scaling coefficient on the time step. The Jacobian is updated but the loading profile is kept constant. This is typical of harmonic testing.
• A,A0 can be used to
• m_coef adjust density for quasi-static testing.

xxx