doc RPSReSp
Documentation of the RPSReSp function.
helpFun('RPSReSp')
Rigid Plastic Sliding Response Spectra
[SD,SV,SA]=RPSReSp(DT,XGTT,CF,ALGID,RINF,MAXTOL,JMAX,DAK)
Description
The rigid plastic sliding response spectra for a given time-history
of constant time step and a given Coulomb friction coefficient range
are computed.
Input parameters
DT [double(1 x 1)] is the time step of the input acceleration time
history XGTT.
XGTT [double(1:numsteps x 1)] is the input acceleration time history.
numsteps is the length of the input acceleration time history.
CF [double(1:numSDOFs x 1)] contains the values of the Coulomb
friction coefficient for which the response spectra are
requested. numSDOFs is the number of SDOF oscillators being
analysed to produce the spectra.
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
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).
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
SD [double(1:numSDOFs x 1)] is the Spectral Displacement.
SV [double(1:numSDOFs x 1)] is the Spectral Velocity.
SA [double(1:numSDOFs x 1)] is the Spectral Acceleration.
Example
dt=0.02;
N=1;
a=rand(N,1)-0.5;
b=100*pi*rand(N,1);
c=pi*(rand(N,1)-0.5);
t=(0:dt:(100*dt))';
xgtt=zeros(size(t));
for i=1:N
xgtt=xgtt+a(i)*sin(b(i)*t+c(i));
end
figure()
plot(t,xgtt)
CF=linspace(0.05,0.5,1000)';
AlgID='U0-V0-Opt';
rinf=1;
maxtol=0.01;
jmax=200;
dak=eps;
[Sd,Sv,Sa]=RPSReSp(dt,xgtt,CF,AlgID,rinf,maxtol,jmax,dak);
figure()
plot(CF,Sd)
figure()
plot(CF,Sv)
figure()
plot(CF,Sa)
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Copyright (c) 2018-2023
George Papazafeiropoulos
Major, Infrastructure Engineer, Hellenic Air Force
Civil Engineer, M.Sc., Ph.D.
Email: gpapazafeiropoulos@yahoo.gr
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