PressureDependMultiYield-Example 10

<center>Plastic Pressure Dependent Wet Inclined Dynamic</center>

Input File

<syntaxhighlight lang=“tcl”>

  1. Created by Zhaohui Yang (zhyang@ucsd.edu)
  2. plastic pressure dependent material
  3. plane strain, single element, dynamic analysis (input motion: sinusoidal acceleration at base)
  4. SI units (m, s, KN, ton)
  5. 4 3

  6. |
  7. |
  8. |
  9. 1——-2 (nodes 1 and 2 fixed)
  10. ^ ^
  11. <–> input motion: sinusoidal acceleration at base

wipe

  1. some user defined variables

set accMul 2 ;# acceleration multiplier set massDen 2.00 ;# solid mass density set fluidDen 1.0 ;# fluid mass density set massProportionalDamping 0.0 ; set stiffnessProportionalDamping 0.001 ; set fangle 31.40 ;#friction angle set ptangle 26.50 ;#phase transformation angle set E 90000.0 ;#shear modulus set poisson 0.40 ; set G [expr \(E/(2*(1+\)poisson))] ; set B [expr \(E/(3*(1-2*\)poisson))] ; set press 0.0 ;# isotropic consolidation pressure on quad element(s) set deltaT 0.010 ;# time step for analysis set numSteps 2000 ;# Number of analysis steps set gamma 0.600 ;# Newmark integration parameter set period 1 ;# Period of applied sinusoidal load set pi 3.1415926535 ; set inclination 4 ; set unitWeightX [expr (\(massDen-\)fluidDen)9.81sin(\(inclination/180.0*\)pi)] ;# unit weight in X direction set unitWeightY [expr -(\(massDen-\)fluidDen)9.81cos(\(inclination/180.0*\)pi)] ;# unit weight in Y direction

  1. create the ModelBuilder

model basic -ndm 2 -ndf 2

  1. define material and properties

nDMaterial PressureDependMultiYield 2 2 $massDen $G $B \(fangle .1 80 0.5 \ \)ptangle 0.17 0.4 10 10 0.015 1.0 nDMaterial FluidSolidPorous 1 2 2 2.2D+6

  1. define the nodes

node 1 0.0D0 0.0D0 node 2 1.0D0 0.0D0 node 3 1.0D0 1.0D0 node 4 0.0D0 1.0D0

  1. define the element thick material maTag press density gravity

element quad 1 1 2 3 4 1.0 “PlaneStrain” 1 $press 0.0 $unitWeightX $unitWeightY

updateMaterialStage -material 1 -stage 0 updateMaterialStage -material 2 -stage 0

  1. fix the base

fix 1 1 1 fix 2 1 1

  1. tie nodes 3 and 4

equalDOF 3 4 1 2

  1. GRAVITY APPLICATION (elastic behavior)
  2. create the SOE, ConstraintHandler, Integrator, Algorithm and Numberer

system ProfileSPD test NormDispIncr 1.D-12 25 0 constraints Transformation integrator LoadControl 1 1 1 1 algorithm Newton numberer RCM

  1. create the Analysis

analysis Static

  1. analyze

analyze 2

  1. switch the material to plastic

updateMaterialStage -material 1 -stage 1 updateMaterialStage -material 2 -stage 1 updateMaterials -material 2 bulkModulus [expr $G*2/3.];

  1. analyze

analyze 1

  1. NOW APPLY LOADING SEQUENCE AND ANALYZE (plastic)
  1. rezero time

setTime 0.0

  1. loadConst -time 0.0D0

wipeAnalysis

pattern UniformExcitation 1 1 -accel “Sine 0 1000 $period -factor $accMul”

  1. create the Analysis

constraints Transformation; test NormDispIncr 1.D-6 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

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 recorder Element -ele 1 -time -file press1.out -dT 0.01 material 1 pressure recorder Element -ele 1 -time -file press3.out -dT 0.01 material 3 pressure

  1. 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 </syntaxhighlight>

MATLAB Plotting File

<syntaxhighlight lang=“matlab”> 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’); p1=load(‘press1.out’); p3=load(‘press3.out’);

fs=[0., 0.2, 4, 6]; accMul = 2;

%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))1/3.0qo(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 _x_y VS. shear strain _x_y’); xLabel(’Shear strain _x_y’); yLabel(’Shear stress _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))1/3.0qo(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 _x_y VS. shear strain _x_y’); xLabel(’Shear strain _x_y’); yLabel(’Shear stress _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)*100,‘r’); title (‘Lateral displacement at element top’); xLabel(‘Time (s)’); yLabel(‘Displacement (cm)’); set(gcf,‘paperposition’,fs); saveas(gcf,‘D’,‘jpg’);

s=accMulsin(0:pi/50:40pi); s1=interp1(0:0.01:20,s,a1(:,1));

figure(1); 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’);

figure(5); clf; %integration point 1 excess pore water pressure subplot(2,1,1),plot(p1(:,1),-p1(:,2),‘r’); title (‘Integration point 1 excess pore pressure’); xLabel(‘Time (s)’); yLabel(‘Excess pore pressure (kPa)’);

subplot(2,1,2),plot(p1(:,1),p1(:,3),‘r’); title (‘Integration point 1 excess pore pressure ratio’); xLabel(‘Time (s)’); yLabel(‘Excess pore pressure ratio’); set(gcf,‘paperposition’,fs); saveas(gcf,‘EPWP’,‘jpg’); </syntaxhighlight>

Displacement Output File

PD_Ex17Disp.png

Stress-Strain Output File (Integration Point 1 & Integration Point 3)

PD_EEx17SS_PQ13.png

Excess Pore Pressure Output File

PD_EEx17EPP.png

Acceleration Output File

PD_EEx17Accel.png

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