NTNU PULS Presentation
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Transcript of NTNU PULS Presentation
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1PULS Course 2007
Department of Marine Technology, NTNU
Lars Brubak27.04.2007
Version Slide 230 May 2007
PULS Course contentPart 1: General introduction
Part 2: Theory and principles
Part 3: PULS elements
Part 4: Comparison with FEM and buckling-codes
Part 5: PULS demonstration and exercises
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2Version Slide 330 May 2007
PULS Course Part 1 - Overview
PULS course objective
Motivation for ultimate strength assessment
PULS areas of application
PULS features
Version Slide 430 May 2007
PULS Course objective
To gain:
Knowledge and skills related to PULS
General knowledge about buckling and ultimate strength
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3Version Slide 530 May 2007
Motivation
Prevent ship hull collapse disasters
Increased control of available safety margins for ship operations
Safeguard life, properties and the environment
Version Slide 630 May 2007
PULS Panel Ultimate Limit State
ls
PULS is a code for bucklingand ULS assessments
of stiffened and unstiffenedpanels
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4Version Slide 730 May 2007
PULS - Element library
Unstiffened plate element (U3): (non-linear)
Stiffened plate element (S3): (non-linear)
Stiffened plate element (T1):(linear, non-regular geometry)
Version Slide 830 May 2007
PULS - Software implementation
Stand alone software: Excel spreadsheet
Advanced Viewer (commercial code)
Nauticus Hull rule package (Ship Rules): Section Scantling - longitudinal strength check
Automatic Buckling Check (ABC); Rule check of FE mid-ship model
Nauticus Hull FPSO rule package (RP-C201): Section Scantling, longitudinal strength check
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5Version Slide 930 May 2007
PULS - Advanced Viewer
Version Slide 1030 May 2007
PULS - Advanced Viewer OutputOutput options: ULS-loads, deflections,
stress distribution, interaction curves
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6Version Slide 1130 May 2007
PULS - Excel Application
Version Slide 1230 May 2007
PULS 2.06 download and installation
Go to the internet page:
www.dnv.com/software/nauticus/nauticushull/bucklingassessment.asp
Click on Download PULS
Unpack .zip-file
Install (setup.exe)
Execute PULS from the Start-meny
Included in download:- Installation instructions- User manual
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7Version Slide 1330 May 2007
PULS Course Part 2 - Overview
Plate buckling
PULS principles
Theoretical basis
PULS solution method
Version Slide 1430 May 2007
Plate buckling
Buckling deflections tend to be regular and periodic
Representation by trigonometricseries:
- Need very few degrees of freedomcompared to FEM
- Any shape can be represented by applying sufficiently many termsDeflection due toaxial compression
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8Version Slide 1530 May 2007
Buckling response curves
Linearized buckling theory
Load
Deformation
Eigenvalue
Version Slide 1630 May 2007
Buckling response curves
Linearized buckling theory
Load
Eigenvalue
Non-linear geometry
Deformation
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9Version Slide 1730 May 2007
Buckling response curves
Linearized buckling theory
Load
Eigenvalue
Non-linear geometryNo buckling
Deformation
Version Slide 1830 May 2007
Buckling response curves
Linearized buckling theory
Load
Eigenvalue
Non-linear geometryNo buckling
Non-linear material
Deformation
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10
Version Slide 1930 May 2007
Buckling concepts
Load
Deformation
Elastic BucklingYielding
Ultimate strength
Pre-buckling
Post-buckling Post-collapse
Version Slide 2030 May 2007
Slenderness variation
0
1
Slenderness (-)
Load
(-)
Elastic bucklingUltimate strengthSquash yield
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11
Version Slide 2130 May 2007
PULS: Detailed results
0
1
Slenderness (-)
Load
(-)
Stocky
design
Version Slide 2230 May 2007
0
1
Slenderness (-)
Load
(-)
PULS: Detailed results
Slender
design
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12
Version Slide 2330 May 2007
Combined loads capacity surface
Combined loads load history in load space
Capacity boundary/surface
in load space:
Sig1
Sig2
Sig3
Proportional load history:
Sig1
Sig2
tau = 0
tau = fixedSig1E
Sig2E
303202
101
SigUSigSigUSigSigUSig
U
U
U
===
Version Slide 2430 May 2007
Imperfections Imperfections:
- Geometrical imperfections (initial deformation)- Material imperfections (residual stress)
In real life: Imperfections introduced during fabrication (welding) and operation
In calculation model: Initial deformations are introduced to account for geometrical and material deformations
Initial deflections characterized by:- Deflection shape- Deflection magnitude
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13
Version Slide 2530 May 2007
Effect of imperfection shape
Py
Px
Version Slide 2630 May 2007
Effect of imperfection shape
Capacity envelope
= minimum value
Py
Px
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14
Version Slide 2730 May 2007
Effect of imperfection magnitude
Increasing imperfection magnitude
Load
Deflection
Version Slide 2830 May 2007
Effect of imperfection magnitude
Load
DeflectionWmax
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15
Version Slide 2930 May 2007
Effect of boundary conditions
Rotational boundary conditions
(linear effect)
In-plane boundary conditions
(nonlinear effect)
Should represent the effect ofsurrounding structure
Version Slide 3030 May 2007
Simply supported
Clamped
Effect of rotational supportPy
Px
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Version Slide 3130 May 2007
PULS principles
PULS design principles for shipstructures
Extreme loads
Accepts elasticbuckling deflections
Do not acceptpermanent sets/buckles
in plates
Ensure strongstiffeners
Version Slide 3230 May 2007
PULS Theoretical basis
von Karman and Marguerres geometric non-linear plate theory
Establish non-linear elastic equilibrium equations - Energy methods, virtual work/stationary potential energy
- Raleigh-Ritz discretization of deflections (Fourier series)
Solves non-linear elastic equilibrium equations: - Incremental perturbation procedure with arc length control
- Stepping along equilibrium curve
Solve local stress limit state functions - Trace redistributed stresses in plate and stiffeners
- Check of material yield in internal critical hot spot positions
Moderate large deflections
Load
Deflection
Ultimate load
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17
Version Slide 3330 May 2007
Nonlinear plate theory
Geometrical non-linearity
Membrane strain-displacement relation (kinematic relations)
)wwww(21)ww(
21)uu(
21
ww w21 u
ww w21 u
1,02,2,01,2,1,1,22,112
2,02,2
2,2,222
1,01,2
1,1,111
++++=
++=
++=
von Karman, 1930
Perfect plate
Marguerre, 1938
Imperfect plate
Version Slide 3430 May 2007
Energy methodsPrinciple of stationary potential energy:
Intuitively: The structure adjusts itself to the shape that requires theleast energy
P
P
0TU =+=
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Version Slide 3530 May 2007
PULS solution method
==
==
m21
nmn
021i0i0
m21
nmn21ii
)xb
nsin()xa
msin( A)x,x(fqw
)xb
nsin()xa
msin( A)x,x(fqwDeflections:
Potential energy:
Stationary pot energy, equilibrium equations:
w
Non-linear equilib. eq., cubic in Amn
##
0)P,....,A,A(fVA
0)P,....,A,A(fVA
12111212
12111111
==
==
)Ainquartic(;)P,.....,A,A(V
uPdV21V
1211
ijij
==
mn
Version Slide 3630 May 2007
PULS theory
w,Aij
w
Solves incrementally
Load, P
Equil. eq. on incremental form (linearization) perturbation (Taylor) expansion
KA + G = 0As+1 = As + +...s+1 = s + + ...
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19
Version Slide 3730 May 2007
Combined loads - staging
Assume proportional loading(piecewise linear load path)
Reduce number of loadparameters to one
)PP(P)(P 1-sisi
1-sii +=
Version Slide 3830 May 2007
PULS solution method
Ultimate capacity assessment:Stops load incrementation at first von Mises yield in hot spot stress location
Deflection
Load
Elastic buckling load
Ultimate load
Overcritical strength
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20
Version Slide 3930 May 2007
Summary of the model theoryRepresent deflections by shape functions
Nonlinear plate theory (elastic deflections accepted)
Principle of minimum potential energy
Incremental solution procedure
Hot spot stress control (plastic deformations not accepted)
Version Slide 4030 May 2007
PULS Course Part 3 - Overview
PULS U3-element
PULS S3-element
PULS T1-element
PULS Advanced Viewer (AV)
PULS Excel
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21
Version Slide 4130 May 2007
PULS U3-element
U3 element usage:
For plates with sufficient lateral support at all edges
Validity range: Geometric requirements with respect to aspect ratio and slenderness
Aspect ratio limit: L1/L2 < 20 for L1 > L2 (or equivalent L2/L1 < 20 for L1 < L2) Plate slenderness ratio: Li/tp < 200 (Li = minimum of L1 and L2)
Version Slide 4230 May 2007
PULS U3-element
Typical buckling modes in unstiffened plates:
a) Axial compression b) Transverse compresson
c) shear c) Axial bendingc) Transverse bending
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Version Slide 4330 May 2007
PULS rectangular plate, bi-axial load space
a) b)
c) d) Fixed geometry
Variable shear prestress
Version Slide 4430 May 2007
PULS square plate bi axial load space
10 mm plate, ULS capacity curves 50 mm plate Von Mises yield
Bi-axial load space,
Variable Shear pre-stress
Slender
design
Stocky
design
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Version Slide 4530 May 2007
PULS S3 element
S3 element usage: For regularly stiffened plates, supported by frames or bulkheads
Validity limits:Web slenderness for flat bar stiffeners: 35Web slenderness for L or T profiles: 80Free flange for L or T profiles: 10t/f ff