Authors : Silvia Ortiz Santamaria Angel Martinez Aja

Validation of post-buckling behaviour of unstable Validation of post-buckling behaviour of unstable cross-section structures under compression loadscross-section structures under compression loads

2002 3RD Worldwide Aerospace Conference and Technology Showcase

Validation of post-buckling behaviour of unstable cross-

section structures under compression loads

Authors : Silvia Ortiz Santamaria

Angel Martinez Aja



ITP CAPACITIESDESIGN ,MANUFACTURE and PRODUCT SUPPORT

Rotating components

GAS TURBINE

Casing

NOZZLE

RADIAL STRUCTURES

Static components



WHY POST-BUCKLING?Aeronautical structures weight improvement

More reliable structures

Great competitiveness

APPLICATIONSEngine radial structures

Casings for aircraft engines



ADVANTAGES

Traditional methodology of post-buckling analysis

particular geometries and load types

Post-buckling analysis using FEM

general methodology for any geometry and load type

Is FEM post-buckling analysis reliable?



Crippling = Post-buckling

Residual strength analysis after local buckling

CRIPPLING ANALYSIS PROBLEM DEFINITION FOR FEM POST-BUCKLING

VALIDATION

Local buckling

Stable behaviour PP

P

Crippling load

Local buckling load



TWO CORNER FORMED CROSS-SECTIONS

X785-C SECTION

LS-160 SECTION

MULTI CORNER FORMED CROSS-SECTION

B2-SHAPE SECTION

Tested specimens from NACA 3784

Material: AlClad2024-T3

CRIPPLING ANALYSIS PROBLEM EXAMPLES ANALYSED



CRIPPLING ANALYSIS FEM SIMULATION USING MSC.Nastran

Analysis Steps

1.- FEM using QUAD4 elements

2.- Linear buckling analysis to obtain the column length

representative of the behaviour of an infinite long column.

3.- FEM perturbation of initial geometry with MSC.Patran.

4.- Non-linear static analysis (elasto-plastic material behaviour +

large displacement) to obtain the collapse load/stress.



First buckling Mode 9526 psi

X3/16 R

3/16 R

1 1/4

7/8

1/2

Y

t= 0.04

Central Point

X785-C section



Test Crippling Stress: 30489 psi [Ref. NACA 3784]FEM Crippling Stress: 29700 psi Error = 2,65%

X785-C section

Displacements at crippling point Displacement-Load Curve

0

500

1000

1500

2000

2500

3000

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.012

Displacement [in]

Lo

ad [

lbf]

0

5000

10000

15000

20000

25000

30000

Ave

rag

e st

ress

[p

si]

Theoretical Collapse avg. stress = 30489

FEM Collapse avg.stress = 29700 psiError = 2.65 %



5/8

1

R 1/8

R 3/16 t = 0.04

X

Y

Central Point

LS-160 sectionFirst buckling Mode 33830 psi



Test Crippling Stress: 32400 psi [Ref. NACA 3784] FEM Crippling Stress: 33710 psi Error= 4.0 %

LS-160 section


0

500

1000

1500

2000

2500

3000

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Displacement [in]

Lo

ad

[lb

f]

0

5000

10000

15000

20000

25000

30000

35000

Av

era

ge

str

es

s [

ps

i]



Crippling of two corner formed sectionsAl Clad 2024-T3; Ref. NACA 3784

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

5 10 15 20 25

AlClad2024-T3 Test dataRecommended Curve (beta=4)LS160 - NASTRANX785-C NASTRAN

31

cy

2 Et

A÷÷ø

öççè

æhs

cy

f

ss

MSC.Nastran results available crippling test data



First buckling Mode 13390 psi

B2-Shape section

0.082

1.198

1.001

0.445

t=0.032

R=3t



Test Crippling Stress 27100 psi [Ref. NACA 3784]FEM Crippling Stress 27893 psi Error= 2,9 %

B2-Shape section


0

1000

2000

3000

4000

5000

6000

7000

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

disp (in)

loa

d (

lbf)

0

5000

10000

15000

20000

25000

30000

str

es

s (

ps

i)



MSC.Nastran results available Crippling test data

Crippling of multi corner formed sectionsAl Clad 2024-T3;Ref.NACA 3784

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

5 7 9 11 13 15 17 19 21 23 25

Recommended curve ( beta=4) AlClad 2024-T3 test data

B2-SHAPE NASTRAN

cy

f

ss

2

1

2 ÷÷ø

öççè

æ

Et

A cy

hs



CONCLUSIONPost-buckling analysis using finite element method offers a general methodology for

any geometry and load type

Documents

Authors : Silvia Ortiz Santamaria Angel Martinez Aja