doc IDA
Documentation of the IDA function.
helpFun('IDA')
Incremental Dynamic Analysis
[DM,IM]=IDA(DT,XGTT,T,LAMBDAF,IM_DM,M,UY,PYSF,KSI,ALGID,U0,UT0,...
RINF,MAXTOL,JMAX,DAK)
Description
This function performs incremental dynamic analysis of a given
acceleration time history and SDOF oscillator.
Input parameters
DT [double(1 x 1)] is the time step of the input acceleration time
history XGTT.
XGTT [double(:inf x 1)] is the input acceleration time history.
numsteps is the length of the input acceleration time history.
T [double(1 x 1)] contains the eigenperiod of the SDOF system for
which the incremental dynamic analysis response curve is
requested.
LAMBDAF [double(:inf x 1)] contains the values of the scaling factor
(lambda factor) for the incremental dynamic analysis.
IM_DM [char(1 x :inf)] is the Intensity Measure (IM) - Damage Measure
(DM) pair that is to be calculated from the incremental dynamic
analysis. IM_DM can take one of the following values (strings are
case insensitive):
'SA_MU': Spectral acceleration-ductility
'PGD_MU': Peak displacement-ductility
'PGV_MU': Peak velocity-ductility
'PGA_MU': Peak acceleration-ductility
'SA_DISP': Spectral acceleration-displacement
'PGD_DISP': Peak displacement-displacement
'PGV_DISP': Peak velocity-displacement
'PGA_DISP': Peak acceleration-displacement
'SA_VEL': Spectral acceleration-velocity
'PGD_VEL': Peak displacement-velocity
'PGV_VEL': Peak velocity-velocity
'PGA_VEL': Peak acceleration-velocity
'SA_ACC': Spectral acceleration-acceleration
'PGD_ACC': Peak displacement-acceleration
'PGV_ACC': Peak velocity-acceleration
'PGA_ACC': Peak acceleration-acceleration
M [double(1 x 1)] is the mass of the SDOF oscillator.
UY [double(1 x 1)] is the yield displacement of the SDOF oscillator.
PYSF [double(1 x 1)] is the post-yield stiffness factor, i.e. the
ratio of the postyield stiffness to the initial stiffness. PYSF=0
is not recommended for simulation of an elastoplastic system. A
small positive value is always suggested. PYSF is ignored if
MU=1.
KSI [double(1 x 1)] is the fraction of critical viscous damping.
ALGID [char(1 x :inf)] is the algorithm to be used for the time
integration. It can be one of the following strings for superior
optimally designed algorithms:
'generalized a-method': The generalized a-method (Chung &
Hulbert, 1993)
'HHT a-method': The Hilber-Hughes-Taylor method (Hilber,
Hughes & Taylor, 1977)
'WBZ': The Wood–Bossak–Zienkiewicz method (Wood, Bossak &
Zienkiewicz, 1980)
'U0-V0-Opt': Optimal numerical dissipation and dispersion
zero order displacement zero order velocity algorithm
'U0-V0-CA': Continuous acceleration (zero spurious root at
the low frequency limit) zero order displacement zero order
velocity algorithm
'U0-V0-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) zero order displacement zero order
velocity algorithm
'U0-V1-Opt': Optimal numerical dissipation and dispersion
zero order displacement first order velocity algorithm
'U0-V1-CA': Continuous acceleration (zero spurious root at
the low frequency limit) zero order displacement first order
velocity algorithm
'U0-V1-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) zero order displacement first order
velocity algorithm
'U1-V0-Opt': Optimal numerical dissipation and dispersion
first order displacement zero order velocity algorithm
'U1-V0-CA': Continuous acceleration (zero spurious root at
the low frequency limit) first order displacement zero order
velocity algorithm
'U1-V0-DA': Discontinuous acceleration (zero spurious root at
the high frequency limit) first order displacement zero order
velocity algorithm
'Newmark ACA': Newmark Average Constant Acceleration method
'Newmark LA': Newmark Linear Acceleration method
'Newmark BA': Newmark Backward Acceleration method
'Fox-Goodwin': Fox-Goodwin formula
U0 [double(1 x 1)] is the initial displacement of the SDOF
oscillator.
UT0 [double(1 x 1)] is the initial velocity of the SDOF oscillator.
RINF [double(1 x 1)] is the minimum absolute value of the eigenvalues
of the amplification matrix. For the amplification matrix see
eq.(61) in Zhou & Tamma (2004). Default value 0.
MAXTOL [double(1 x 1)] is the maximum tolerance of convergence of the
Full Newton Raphson method for numerical computation of
acceleration.
JMAX [double(1 x 1)] is the maximum number of iterations per
increment. If JMAX=0 then iterations are not performed and the
MAXTOL parameter is not taken into account.
DAK [double(1 x 1)] is the infinitesimal acceleration for the
calculation of the derivetive required for the convergence of the
Newton-Raphson iteration.
Output parameters
DM [double(:inf x 1)] is the Damage Measure.
IM [double(:inf x 1)] is the Intensity Measure.
Example
eqmotions={'elcentro'};
data=load([eqmotions{1},'.dat']);
t=data(:,1);
dt=t(2)-t(1);
xgtt=data(:,2);
sw='ida';
T=1;
lambdaF=logspace(log10(0.001),log10(10),100);
IM_DM='Sa_disp';
m=1;
uy = 0.082*9.81/(2*pi/T)^2;
pysf=0.01;
ksi=0.05;
S5=OpenSeismoMatlab(dt,xgtt,sw,T,lambdaF,IM_DM,m,uy,pysf,ksi);
figure()
plot(S5.DM*1000,S5.IM/9.81,'k','LineWidth',1)
grid on
xlabel('Displacement (mm)')
ylabel('Sa(T1,5%)[g]')
xlim([0,200])
ylim([0,0.7])
__________________________________________________________________________
Copyright (c) 2018-2023
George Papazafeiropoulos
Major, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D.
Email: gpapazafeiropoulos@yahoo.gr
_________________________________________________________________________