PressureDependMultiYield-Example 5

<center>Plastic Pressure Dependent Dry Level Pushover</center>

Input File

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  1. Created by Zhaohui Yang (zhyang@ucsd.edu)
  2. plastic pressure dependent material
  3. plane strain, single element, monotonic pushover.
  4. SI units (m, s, KN, ton)
  5. 4 3
  6. ——- –> F (loads applied to node 3)
  7. |
  8. |
  9. |
  10. 1——-2 (nodes 1 and 2 fixed)
  11. ^ ^

wipe

  1. some user defined variables

set massDen 2. ;# mass density set massProportionalDamping 0.0 ; set InitStiffnessProportionalDamping 0.001 ; set fangle 31.40 ;#friction angle set ptangle 26.50 ;#phase transformation angle set E 90000.0 ;#Young’s 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 500 ;# Number of analysis steps set gamma 0.500 ;# Newmark integration parameter set period 1 ;# Period of applied sinusoidal load set pi 3.1415926535 ; set inclination 0 ; set unitWeightX [expr \(massDen*9.81*sin(\)inclination/180.0\(pi)] ;# unit weight in X direction set unitWeightY [expr -\)massDen9.81*cos(\(inclination/180.0*\)pi)] ;# unit weight in Y direction set loadIncr 1 ;# Static shear load bias

  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 00 0.015 1.0

  1. 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

  1. 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

  1. fix the base in vertical direction

fix 1 1 1 fix 2 1 1 equalDOF 3 4 1 2 ;#tie nodes 3 and 4

  1. GRAVITY APPLICATION (elastic behavior)
  2. 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

  1. create the Analysis

analysis Static

  1. analyze

analyze 2

  1. switch the material to plastic

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 0.0

wipeAnalysis

  1. create a LoadPattern with a Linear time series

pattern Plain 1 Linear { load 3 $loadIncr 0.0 ;#load applied in x direction }

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

  1. create the Analysis

constraints Transformation; # Penalty 1.0e18 1.0e18 ;# test NormDispIncr 1.e-12 25 0 algorithm Newton numberer RCM system ProfileSPD rayleigh $massProportionalDamping 0.0 $InitStiffnessProportionalDamping 0. integrator Newmark \(gamma [expr pow(\)gamma+0.5, 2)/4] analysis VariableTransient

  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

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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’);

fs=[0.5, 0.2, 4, 6];

%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),‘r’); title (‘Lateral displacement at element top’); xLabel(‘Time (s)’); yLabel(‘Displacement (m)’); set(gcf,‘paperposition’,fs); saveas(gcf,‘D’,‘jpg’);

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Displacement Output File

PD_Ex12Disp.png

Stress-Strain Output File

PD_Ex12SS_PQ13.png

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