PressureIndependentMultiYield-Example 1
| Elastic Pressure Independent Wet Level Dynamic |
Input File
#Created by Zhaohui Yang (zhyang@ucsd.edu)
#elastic pressure independent material
#plane strain, single element, dynamic analysis (input motion: sinusoidal acceleration at base)
#SI units (m, s, KN, ton)
#
# 4 3
# -------
# | |
# | |
# | |
# 1-------2 (nodes 1 and 2 fixed)
# ^ ^
# <--> input motion: sinusoidal acceleration at base
wipe
#
#some user defined variables
#
set accMul 9.81 ;
set massDen 2.000 ;# solid mass density
set fluidDen 1.0 ;# fluid mass density
set massProportionalDamping 0.0 ;
set stiffnessProportionalDamping 0.001 ;
set cohesion 30 ;
set peakShearStrain 0.1 ;
set E1 90000.0 ;#Young's modulus
set poisson1 0.40 ;
set G [expr $E1/(2*(1+$poisson1))] ;
set B [expr $E1/(3*(1-2*$poisson1))] ;
set press 0 ;# isotropic consolidation pressure on quad element(s)
set period 1 ;# Period of applied sinusoidal load
set deltaT 0.01 ;# time step for analysis
set numSteps 2000 ;# Number of analysis steps
set gamma 0.5 ;# Newmark integration parameter
set pi 3.1415926535 ;
set inclination 0 ;
set unitWeightX [expr ($massDen-$fluidDen)*9.81*sin($inclination/180.0*$pi)] ;# buoyant unit weight in X direction
set unitWeightY [expr -($massDen-$fluidDen)*9.81*cos($inclination/180.0*$pi)] ;# buoyant unit weight in Y direction
#############################################################
#create the ModelBuilder
model basic -ndm 2 -ndf 2
# define material and properties
nDMaterial PressureIndependMultiYield 2 2 $massDen $G $B $cohesion $peakShearStrain
nDMaterial FluidSolidPorous 1 2 2 2.2e6
# define the nodes
node 1 0.0 0.0
node 2 1.0 0.0
node 3 1.0 1.0
node 4 0.0 1.0
# define the element thick material maTag press density gravity
element quad 1 1 2 3 4 1.0 "PlaneStrain" 2 $press 0.0 $unitWeightX $unitWeightY
updateMaterialStage -material 2 -stage 0
# fix the base in vertical direction
fix 1 1 1
fix 2 1 1
#############################################################
# GRAVITY APPLICATION (elastic behavior)
# create the SOE, ConstraintHandler, Integrator, Algorithm and Numberer
system ProfileSPD
test NormDispIncr 1.e-12 25 0
constraints Transformation
integrator LoadControl 1 1 1 1
algorithm Newton
numberer RCM
# create the Analysis
analysis Static
#analyze
analyze 2
#############################################################
# NOW APPLY LOADING SEQUENCE AND ANALYZE (plastic)
# rezero time
setTime 0.0
wipeAnalysis
equalDOF 3 4 1 2 ;#tie nodes 3 and 4
# create a LoadPattern
pattern UniformExcitation 1 1 -accel "Sine 0 10 $period -factor $accMul"
# create the Analysis
constraints Penalty 1.0e18 1.0e18 ;# Transformation; #
test NormDispIncr 1.e-12 25 0
algorithm Newton
numberer RCM
system ProfileSPD
rayleigh $massProportionalDamping 0.0 $stiffnessProportionalDamping 0.
integrator Newmark $gamma [expr pow($gamma+0.5, 2)/4]
analysis VariableTransient
#create the recorder
recorder Node -file disp.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 disp
recorder Node -file acce.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 accel
recorder Element -ele 1 -time -file stress1.out -dT 0.01 material 1 stress
recorder Element -ele 1 -time -file strain1.out -dT 0.01 material 1 strain
recorder Element -ele 1 -time -file stress3.out -dT 0.01 material 3 stress
recorder Element -ele 1 -time -file strain3.out -dT 0.01 material 3 strain
#analyze
set startT [clock seconds]
analyze $numSteps $deltaT [expr $deltaT/100] $deltaT 10
set endT [clock seconds]
puts "Execution time: [expr $endT-$startT] seconds."
wipe #flush ouput stream
MATLAB Plotting File
clear all;
a1=load('acce.out');
d1=load('disp.out');
s1=load('stress1.out');
e1=load('strain1.out');
s5=load('stress3.out');
e5=load('strain3.out');
fs=[0.5, 0.2, 4, 6];
accMul = 9.81;
%integration point 1 p-q
po=(s1(:,2)+s1(:,3)+s1(:,4))/3;
for i=1:size(s1,1)
qo(i)=(s1(i,2)-s1(i,3))^2 + (s1(i,3)-s1(i,4))^2 +(s1(i,2)-s1(i,4))^2 + 6.0* s1(i,5)^2;
qo(i)=sign(s1(i,5))*1/3.0*qo(i)^0.5;
end
figure(1); clf;
%integration point 1 stress-strain
subplot(2,1,1), plot(e1(:,4),s1(:,5),'r');
title ('Integration point 1 shear stress \tau_x_y VS. shear strain \epsilon_x_y');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('Integration point 1 confinement p VS. deviatoric q relation');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ1','jpg');
%integration point 3 p-q
po=(s5(:,2)+s5(:,3)+s5(:,4))/3;
for i=1:size(s5,1)
qo(i)=(s5(i,2)-s5(i,3))^2 + (s5(i,3)-s5(i,4))^2 +(s5(i,2)-s5(i,4))^2 + 6.0* s5(i,5)^2;
qo(i)=sign(s5(i,5))*1/3.0*qo(i)^0.5;
end
figure(4); clf;
%integration point 3 stress-strain
subplot(2,1,1), plot(e5(:,4),s5(:,5),'r');
title ('Integration point 3 shear stress \tau_x_y VS. shear strain \epsilon_x_y');
xLabel('Shear strain \epsilon_x_y');
yLabel('Shear stress \tau_x_y (kPa)');
subplot(2,1,2), plot(-po,qo,'r');
title ('Integration point 3 confinement p VS. deviatoric q relation');
xLabel('confinement p (kPa)');
yLabel('q (kPa)');
set(gcf,'paperposition',fs);
saveas(gcf,'SS_PQ5','jpg');
figure(2); clf;
%node 3 displacement relative to node 1
subplot(2,1,1),plot(d1(:,1),d1(:,6),'r');
title ('Lateral displacement at element top');
xLabel('Time (s)');
yLabel('Displacement (m)');
set(gcf,'paperposition',fs);
saveas(gcf,'D','jpg');
s=accMul*sin(0:pi/50:20*pi);
s=[s';zeros(1000,1)];
s1=interp1(0:0.01:20,s,a1(:,1));
figure(3); clf;
%node 3 relative acceleration
subplot(2,1,1),plot(a1(:,1),s1+a1(:,5),'r');
title ('Lateral acceleration at element top');
xLabel('Time (s)');
yLabel('Acceleration (m/s^2)');
set(gcf,'paperposition',fs);
saveas(gcf,'A','jpg');
Displacement Output File
Stress-Strain Output File (Integration Point 1)
Stress-Strain Output File (Integration Point 3)
Acceleration Output File
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