#106: Nonlinear Buckling in MSC Nastran (SOL106)

Sep 25, 2020 | buckling, nastran

#106: Nonlinear Buckling (SOL106)

1) Linear buckling of Euler column. For clamped-free boundary conditions the critical load is:

Pcrit = (pi**2)*E*I/(4*(L**2)),
where,
E = 10.5E6, I = 8.333-5, L=10 means Pcrit = 21.59

2) Nonlinear buckling with PARAM,BUCKLE,2
In f06 result file search for following message (right after eigenvalue table).

*** USER INFORMATION MESSAGE 9040 (SUBDMAP NLSTATIC)
CRITICAL BUCKLING FACTOR (ALPHA)= 3.510785E+00

In following example Subcase 102 gives ALPHA = 3.510785E+00
This is how one can calculate buckling Load.

General Formula : Pn + Alpha * (Delta P)

where
Pn = Total Load at Subcase Id where Param,buckle,2 is applied
Delta P = is the (Delta Load or (P(n) – P(n-1)) / No_of_increment.

Let us consider Subcase 102 (Alpha = 3.510785)
Total Load Pn = 20.00 (subcase 102)

Delta Load = (20.00 – 19.00) = (Load @ (Subcase 2 – Subcase 1) = 1.00

Pcr = Pn + (Delat_Load)/No_of_incr) * Alpha = 20.0 + (1.0/2) * 3.510785E+00 = 21.755

Or just print out OLOAD that will give buckling load: Oload = 10.8777 * 2 (at two nodes) = 21.755

b106-buck.dat

TIME 100
SOL 106 $ Nonlinear Statics
CEND
$
TITLE = CANTILEVERED BEAM MADE OF PLATES
$
oload = all
SUBCASE 101
LABEL = Total Load = 19.0 Lbs (0 to 19 lbs)
LOAD = 91
NLPARM = 1
SUBCASE 102
LABEL = Total Load = 20.0 Lbs (19 to 20 lbs)
LOAD = 92
NLPARM = 2
param, buckle,2
method = 10
force = all
spcforce = all
disp = all
oload = all
BEGIN BULK
$
$ Cantilevered Beam Made of Plates Model
$
$ \201 202 203 204 205 206 207 208 209 210 211
$ Y \*----*----*----*----*----*----*----*----*----*----*
$ ^ \| | | | | | | | | | |
$ | \| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
$ | \| | | | | | | | | | |
$ +--->X \*----*----*----*----*----*----*----*----*----*----*
$ \101 102 103 104 105 106 107 108 109 110 111
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
PARAM LGDISP 1
param,post,-1
$
$
$
NLPARM 1 5 ITER 1
NLPARM 2 2 ITER 1
$1234567$1234567$1234567$1234567$1234567$1234567$1234567$1234567$1234567
EIGRL 10 3 MASS
GRID 101 0. 0. 0. 123456
GRID 102 1. 0. 0.
GRID 201 0. 1. 0. 123456
GRID 202 1. 1. 0.
$
CQUAD4 1 1 101 102 202 201
MAT1 1 10.5E6 .3 2.588-4 1.E-6 0.
PSHELL 1 1 .1 1
$
FORCE 91 111 9.500 -1.0 0. 0.
FORCE 91 211 9.500 -1.0 0. 0.
$
FORCE 92 111 10.00 -1.0 0. 0.
FORCE 92 211 10.00 -1.0 0. 0.
$
FORCE 93 111 10.50 -1.0 0. 0.
FORCE 93 211 10.50 -1.0 0. 0.
$
FORCE 94 111 11.00 -1.0 0. 0.
FORCE 94 211 11.00 -1.0 0. 0.
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
ENDDATA

b106-buck.f06

R E A L E I G E N V A L U E S
MODE EXTRACTION EIGENVALUE RADIANS CYCLES GENERALIZED GENERALIZED
NO. ORDER MASS STIFFNESS
1 1 3.510785E+00 1.873709E+00 2.982100E-01 6.169645E-02 2.166030E-01
2 2 3.593726E+02 1.895713E+01 3.017120E+00 1.379434E-01 4.957308E+01
3 3 1.113806E+03 3.337373E+01 5.311595E+00 3.651141E-01 4.066663E+02
*** USER INFORMATION MESSAGE 9040 (SUBDMAP NLSTATIC)
CRITICAL BUCKLING FACTOR (ALPHA)= 3.510785E+00

Command line to run Nastran. Note option IFPSTAR=NO (select the MSC Nastran IFP for bulk data processing)

nastran.exe old=no scr=yes news=no IFPSTAR=NO mem=estimate b106-buck.dat

Run 1: Applied load is 19.
To decide the approximate value of buckling load in the 1st run we will try to find range of the critical load.
LOAD FACTOR 0.4000000
LOAD FACTOR 0.6000000
This means the critical load is between 0.4*P and 0.6*P, i.e., from 16 to 24. For example, we can take 20.


SOL 106 $ Nonlinear Statics
CEND
$
TITLE = CANTILEVERED BEAM MADE OF PLATES MODEL / Linear PCRIT = 21.59
$
$
oload = all
SUBCASE 101
LABEL = Total Load = 19.0 Lbs (0 to 19 lbs)
LOAD = 91
NLPARM = 1
$SUBCASE 102
$ LABEL = Total Load = 20.0 Lbs (19 to 20 lbs)
$ LOAD = 92
$ NLPARM = 2
param, buckle,2
method = 10
force = all
spcforce = all
disp = all
oload = all
BEGIN BULK
$
$ Cantilevered Beam Made of Plates Model
$
$ \201 202 203 204 205 206 207 208 209 210 211
$ Y \*----*----*----*----*----*----*----*----*----*----*
$ ^ \| | | | | | | | | | |
$ | \| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
$ | \| | | | | | | | | | |
$ +--->X \*----*----*----*----*----*----*----*----*----*----*
$ \101 102 103 104 105 106 107 108 109 110 111
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
PARAM LGDISP 1
$
$
NLPARM 1 5 ITER 1
NLPARM 2 2 ITER 1
EIGRL 10 3
GRID 101 0. 0. 0. 123456
GRID 102 1. 0. 0.
GRID 201 0. 1. 0. 123456
GRID 202 1. 1. 0.
$
CQUAD4 1 1 101 102 202 201
MAT1 1 10.5E6 .3 2.588-4 1.E-6 0.
PSHELL 1 1 .1 1
$.......2.......3.......4.......5.......6.......7.......8.......9.......
$FORCE SID G CID F N1 N2 N3
FORCE 91 111 20.00 -1.0 0. 0.
FORCE 91 211 20.00 -1.0 0. 0.
$
FORCE 92 111 10.00 -1.0 0. 0.
FORCE 92 211 10.00 -1.0 0. 0.
$
FORCE 93 111 10.50 -1.0 0. 0.
FORCE 93 211 10.50 -1.0 0. 0.
$
FORCE 94 111 11.00 -1.0 0. 0.
FORCE 94 211 11.00 -1.0 0. 0.
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
ENDDATA

Run 2: Applied load is 20 lb. This load is applied in two cases with magnitude as 95% + 5%. In this run we get the exact critical load.

SOL 106 $ Nonlinear Statics
CEND
$
TITLE = CANTILEVERED BEAM MADE OF PLATES MODEL / Linear PCRIT = 21.59
$
$
oload = all
SUBCASE 101
LABEL = Total Load = 19.0 Lbs (0 to 19 lbs)
LOAD = 91
NLPARM = 1
SUBCASE 102
LABEL = Total Load = 20.0 Lbs (19 to 20 lbs)
LOAD = 92
NLPARM = 2
param, buckle,2
method = 10
force = all
spcforce = all
disp = all
oload = all
BEGIN BULK
$
$ Cantilevered Beam Made of Plates Model
$
$ \201 202 203 204 205 206 207 208 209 210 211
$ Y \*----*----*----*----*----*----*----*----*----*----*
$ ^ \| | | | | | | | | | |
$ | \| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
$ | \| | | | | | | | | | |
$ +--->X \*----*----*----*----*----*----*----*----*----*----*
$ \101 102 103 104 105 106 107 108 109 110 111
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
PARAM LGDISP 1
$
$
NLPARM 1 5 ITER 1
NLPARM 2 2 ITER 1
EIGRL 10 3
GRID 101 0. 0. 0. 123456
GRID 102 1. 0. 0.
GRID 201 0. 1. 0. 123456
GRID 202 1. 1. 0.
CQUAD4 1 1 101 102 202 201
MAT1 1 10.5E6 .3 2.588-4 1.E-6 0.
PSHELL 1 1 .1 1
$
FORCE 91 111 9.500 -1.0 0. 0.
FORCE 91 211 9.500 -1.0 0. 0.
$
FORCE 92 111 10.00 -1.0 0. 0.
FORCE 92 211 10.00 -1.0 0. 0.
$
FORCE 93 111 10.50 -1.0 0. 0.
FORCE 93 211 10.50 -1.0 0. 0.
$
FORCE 94 111 11.00 -1.0 0. 0.
FORCE 94 211 11.00 -1.0 0. 0.
$
$.......2.......3.......4.......5.......6.......7.......8.......9.......0
ENDDATA