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# Post Buckling of Thin Shells

Thu, 2008-10-09 23:56 - Himayat Ullah

It is difficult to conduct post buckling analysis of thin shell under axial compression using Arc Length method in Ansys.

The Minimum & Maximum Arc Length radii are chosen by hit & trial.When imperfections are incorporated in the FE model, some times the solution diverges at a higher critical load that the eigen value buckling, which should be vice versa in actual. Some times , negative eigen values are also shown.

Is there any easy way to solve this nonlinear stability problem?

Himayat

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## Comments

## Here a good example as a reference

It is indeed difficult to solve the convergence problem for post-buckling FEA solution. The following is a good example and wish a good luck for you!

/PREP7

smrt,off

/TITLE, VM17, SNAP-THROUGH BUCKLING OF A HINGED SHELL

:COM CHANG, C.C.,"PERIODICALLY RESTARTED QUASI-NEWTON UPDATES IN

:COM IN CONSTANT ARC-LENGTH METHOD", COMPUTERS AND STRUCTURES,

:COM VOL. 41, NO. 5, PP. 963-972, 1991.

ANTYPE,STATIC ! STATIC ANALYSIS

ET,1,SHELL63,,1

R,1,6.350 ! SHELL THICKNESS

MP,EX,1,3102.75

MP,NUXY,1,0.3

:COM CREATE FINITE ELEMENT MODEL

R1 = 2540 ! SHELL MID-SURFACE RADIUS

L = 254 ! HALF THE LENGTH

PI = 4*ATAN(1) ! VALUE OF PI COMPUTED

THETA = 0.1*180/PI ! 0.1 RADIANS CONVERTED TO DEGREES

CSYS,1 ! CYLINDRICAL CO-ORDINATE SYSTEM

N,1,R1,90 ! NODES 1 AND 2 ARE CREATED AT POINTS

N,2,R1,90,L ! A AND B RESPECTIVELY.

K,1,R1,90

K,2,R1,(90-THETA)

K,3,R1,90,L

K,4,R1,(90-THETA),L

ESIZE,,2 ! TWO DIVISION ALONG THE REGION BOUNDARY

A,1,3,4,2

AMESH,1

NUMMRG,NODE

:COM APPLY BOUNDARY CONDITIONS

NSEL,S,LOC,Z,0

DSYM,SYMM,Z

NSEL,S,LOC,Y,90

DSYM,SYMM,X

NSEL,S,LOC,Y,(90-THETA)

D,ALL,UX,,,,,UY,UZ

NSEL,ALL

FINISH

:COM SOLUTION PHASE

:COM SINCE THE SOLUTION OUTPUT IS SUBSTANTIAL IT IS DIVERTED TO A

:COM SCRATCH FILE

/OUTPUT,SCRATCH

/SOLUTION

NLGEOM,ON ! LARGE DEFLECTION TURNED ON

OUTRES,,1 ! WRITE SOLUTION ON RESULTS FILE FOR EVERY SUBSTEP

F,1,FY,-250 ! 1/4 TH OF THE TOTAL LOAD APPLIED DUE TO SYMMETRY

NSUBST,30 ! BEGIN WITH 30 SUBSTEPS

ARCLEN,ON,4 ! ARC-LENGTH SOLUTION TECHNIQUE TURNED ON WITH

! MAX. ARC-LENGTH KEPT AT 4 TO COMPUTE AND STORE

! SUFFICIENT INTERMEDIATE SOLUTION INFORMATION

SOLVE

FINISH

/OUTPUT

:COM POSTPROCESSING PHASE

/POST26

NSOL,2,1,U,Y ! STORE UY DISPLACEMENT OF NODE 1

NSOL,3,2,U,Y ! STORE UY DISPLACEMENT OF NODE 2

PROD,4,1,,,LOAD,,,4*250 ! TOTAL LOAD IS 4*250 DUE TO QUARTER SYMMETRY

PROD,5,2,,,,,,-1 ! CHANGE SIGNS OF THE DISPLACEMENT VALUES

PROD,6,3,,,,,,-1

*GET,UY1,VARI,2,EXTREM,VMIN

*GET,UY2,VARI,3,EXTREM,VMIN

PRVAR,2,3,4 ! PRINT STORED INFORMATION

/AXLAB,X, DEFLECTION (MM)

/AXLAB,Y, TOTAL LOAD (N)

/GRID,1

/XRANGE,0,35

/YRANGE,-500,1050

XVAR,5

PLVAR,4 ! PLOT LOAD WITH RESPECT TO -UY OF NODE 1

/NOERASE

XVAR,6

PLVAR,4

## Post Buckling of Thin Shells

Pengfei Liu

Thanks a lot for posting a reference example. I am going to run it and will see its convergence behaviour and results.

Himayat

## Dear Himayat and

Dear Himayat and Pengfei,

I think the paper attached in the following link might be useful to your problem

http://imechanica.org/node/4124

## Dear Pengfei Liu

I would like to ask something about your code above. Your model includes a curved geometry so I think it is not necessary to create initial imperfections on your model. My model is a planar model so I must include initial imperfections. I perform postbuckling analysis after an eigenvalue buckling analysis so in APDL code I need to apply inplane loads two times. One for eigenvalue analysis as 1 unit, other for nonlinear analysis as something higher than critical buckling load. I would like to know is this a correct approach? Or could you suggest an alternative approach for initial imperfections?

Thanks....