3D - Structural Analysis and Optimization

By Suresh Darvath

Problem Statement Variable cross section steel plate

Fixed at the top end

Carries a load of 1500 lb at bottom

Aim: To find the relationship between the fillet radii and deflection/von misses stress

Validation:

Safety factor of 1.5 is chosen

Yield stress of steel is 36 Psi

Therefore the max. stress is 24 Psi

Batch file /UNITS,bin

/filname,3D Structural Analysis and Optimization

/title,3D Structural Analysis and Optimization

R_=0.25 !Radius of the Fillet

T_=0.125 !Thickness of the Model

/prep7

! MATERIAL PROPERTIES

ET,1,Plane82 !2-D 8-Node Structural Solid

ET,2,SOLID45 ! 3-D 8-Node Structural Solid

MP,EX,1,29e6 !define material properties

MP,PRXY,1,0.3

L,1,2

L,2,6

L,6,5

L,5,8

L,8,7

L,7,3

L,3,4

L,4,1

!Fillet Radius (Arbitary Value is 0.125 inch)

LFILLT,3,4,R_ !line 9

LFILLT,4,5,R_ !line 10

AL,1,2,3,9,4,10,5,6,7,8

TYPE,1

MAT,1

LESIZE,1,,,10

LESIZE,2,,,13

LESIZE,3,,,5

LESIZE,9,,,5

LESIZE,4,,,20

LESIZE,10,,,5

LESIZE,5,,,5

LESIZE,6,,,13

LESIZE,7,,,5

LESIZE,8,,,40

AMESH,1

SAVE

! define the keypoint

K,1,0,0,0

K,2,2,0,0

K,3,2,-10,0

K,4,1,-10,0

K,5,1.75,-2.5,0

K,6,2,-2.5,0

K,7,2,-7.5,0

K,8,1.75,-7.5,0

Batch file !Extrude the 2-D model into 3-D model

TYPE,2

MAT,1

EXTOPT,esize,4

EXTOPT,aclear,all

K,20,0,0,T_

L,1,20

EXTOPT,esize,1,1

EXTOPT,aclear,all

VDRAG,all,,,,,,11

SAVE

FINISH

/SOLUTION

ANTYPE,STATIC,NEW

! Applying boundary conditions (displacements)

NSEL,S,LOC,Y,0

D,all,UY,0

NSEL,ALL

!Apply load

NSEL,S,LOC,Y,-10

SF,ALL,PRES,750/T_

NSEL,ALL

SOLVE

FINISH

!GENERAL POSTPROCESSOR

/POST1

ETABLE,AxiStres,LS, 1,4

ETABLE,MaxStres,NMISC, 1,3

ETABLE,MinStres,NMISC,2,4

ETABLE,XForce,SMISC,1,7

ETABLE,YForce,SMISC,2,8

ETABLE,MOMENT, SMISC,6,12

PRETAB,AXISTRES,MAXSTRES,MINSTRES, XFORCE,YFORCE,MOMENT

/EOF

Radii vs Von Mises StressRADIUS RADIUS VON-MISES STRESS RADIUS RADIUS VON-MISES STRESS (IN) (in) NODE VALUE(Ksi) (IN) (in) NODE VALUE(Ksi)

R=1/22 0.0455 64 27.0480 R=1/9 0.111 110 24.778R=1/21 0.0476 110 29.2730 R=1/8 0.125 110 24.550R=1/20 0.0500 66 25.5350 R=1/7.5 0.133 110 24.225R=1/19 0.0526 66 28.0450 R=1/7 0.143 110 21.990R=1/18 0.0556 64 28.2230 R=1/6.5 0.154 110 23.698R=1/17 0.0588 110 27.4310 R=1/6 0.167 110 21.295R=1/16 0.0625 66 20.6940 R=1/5.5 0.182 110 22.932R=1/15 0.0667 110 28.3650 R=1/5 0.200 110 22.956R=1/14 0.0714 110 25.4370 R=1/4.5 0.222 110 21.733R=1/13 0.0769 110 25.9340 R=1/4.4 0.227 110 22.429R=1/12 0.0833 110 26.2340 R=1/4.3 0.233 110 22.334R=1/11 0.0909 110 25.2290 R=1/4.2 0.238 110 22.040R=1/10 0.1000 110 26.5820 R=1/4.1 0.244 110 22.360

Radii vs Von Mises Stress

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

25

30

35

f(x) = 139.134729942805 x² − 66.8715139896775 x + 30.2048138253448R² = 0.620827197224933

Radii vs Von Mises

Radii (in)

Von

Mise

s Str

ess (

ksi)

Radii vs DeflectionRADIUS RADIUS DEFLECTION RADIUS RADIUS DEFLECTION

(IN) (in) Ux Uy Uz Usum (IN) (in) Ux Uy Uz Usum

R=1/22 0.045 0.018 0.004 0.019 0.019 R=1/9 0.111 0.014 0.004 0.003 0.015

R=1/21 0.048 -0.010 0.004 0.011 0.011 R=1/8 0.125 0.017 0.004 -0.024 0.030

R=1/20 0.050 0.016 0.004 0.002 0.017 R=1/7.5 0.133 0.015 0.004 -0.006 0.017

R=1/19 0.053 0.016 0.004 0.001 0.016 R=1/7 0.143 0.013 0.004 0.002 0.014

R=1/18 0.056 0.016 0.004 0.018 0.018 R=1/6.5 0.154 -0.011 0.004 -0.017 0.021

R=1/17 0.059 0.016 0.004 0.001 0.017 R=1/6 0.167 0.016 0.004 -0.003 0.017

R=1/16 0.063 0.012 0.004 0.005 0.014 R=1/5.5 0.182 0.024 0.004 -0.069 0.073

R=1/15 0.067 0.016 0.004 0.002 0.016 R=1/5 0.200 0.016 0.004 -0.001 0.017

R=1/14 0.071 0.009 0.004 0.001 0.010 R=1/4.5 0.222 0.015 0.004 0.003 0.016

R=1/13 0.077 0.016 0.004 0.005 0.017 R=1/4.4 0.227 0.015 0.004 0.003 0.016

R=1/12 0.083 -0.012 0.004 -0.007 0.014 R=1/4.3 0.233 0.015 0.004 -0.010 0.019

R=1/11 0.091 0.017 0.004 0.003 0.017 R=1/4.2 0.238 0.014 0.004 -0.005 0.016

R=1/10 0.100 0.014 0.004 0.036 0.039 R=1/4.1 0.244 0.014 0.004 0.001 0.015

Radii vs Deflection

0 0.05 0.1 0.15 0.2 0.25 0.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

f(x) = 0.0247585081268787 x^0.148059044369599R² = 0.0481522543423294

Radii vs deflection

Radii (in)

Defle

ction

(in)

Mesh Scene

Plan Moving Forward From the above trails, we have come up with

•The R - relevance number of 0.62 is not reasonable

•Adding more number of elements in thickness of the model

•Controlling the minimum number of elements on the radii through smart size

•Improving the mesh by having more number of elements

•Understand the behavior for radii values where the results are not good