ntnu puls presentation

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

2Version Slide 330 May 2007

PULS Course Part 1 - Overview

PULS course objective

Motivation for ultimate strength assessment

PULS areas of application

PULS features


PULS Course objective

To gain:

Knowledge and skills related to PULS

General knowledge about buckling and ultimate strength


Motivation

Prevent ship hull collapse disasters

Increased control of available safety margins for ship operations

Safeguard life, properties and the environment


PULS Panel Ultimate Limit State

ls

PULS is a code for bucklingand ULS assessments

of stiffened and unstiffenedpanels


PULS - Element library

Unstiffened plate element (U3): (non-linear)

Stiffened plate element (S3): (non-linear)

Stiffened plate element (T1):(linear, non-regular geometry)


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


PULS - Advanced Viewer


PULS - Advanced Viewer OutputOutput options: ULS-loads, deflections,

stress distribution, interaction curves


PULS - Excel Application


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



Plate buckling

PULS principles

Theoretical basis

PULS solution method


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


Buckling response curves

Linearized buckling theory

Load

Deformation

Eigenvalue




Load

Eigenvalue

Non-linear geometry

Deformation




Load

Eigenvalue

Non-linear geometryNo buckling

Deformation




Load

Eigenvalue

Non-linear geometryNo buckling

Non-linear material

Deformation

10


Buckling concepts

Load

Deformation

Elastic BucklingYielding

Ultimate strength

Pre-buckling

Post-buckling Post-collapse


Slenderness variation

0

1

Slenderness (-)

Load

(-)

Elastic bucklingUltimate strengthSquash yield

11


PULS: Detailed results

0

1

Slenderness (-)

Load

(-)

Stocky

design


0

1

Slenderness (-)

Load

(-)

PULS: Detailed results

Slender

design

12


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

===


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

13


Effect of imperfection shape

Py

Px


Effect of imperfection shape

Capacity envelope

= minimum value

Py

Px

14


Effect of imperfection magnitude

Increasing imperfection magnitude

Load

Deflection


Effect of imperfection magnitude

Load

DeflectionWmax

15


Effect of boundary conditions

Rotational boundary conditions

(linear effect)

In-plane boundary conditions

(nonlinear effect)

Should represent the effect ofsurrounding structure


Simply supported

Clamped

Effect of rotational supportPy

Px

16


PULS principles

PULS design principles for shipstructures

Extreme loads

Accepts elasticbuckling deflections

Do not acceptpermanent sets/buckles

in plates

Ensure strongstiffeners


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

17


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


Energy methodsPrinciple of stationary potential energy:

Intuitively: The structure adjusts itself to the shape that requires theleast energy

P

P

0TU =+=

18



==

==

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


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 + + ...

19


Combined loads - staging

Assume proportional loading(piecewise linear load path)

Reduce number of loadparameters to one

)PP(P)(P 1-sisi

1-sii +=



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

20


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)



PULS U3-element

PULS S3-element

PULS T1-element

PULS Advanced Viewer (AV)

PULS Excel

21


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)


PULS U3-element

Typical buckling modes in unstiffened plates:

a) Axial compression b) Transverse compresson

c) shear c) Axial bendingc) Transverse bending

22


PULS rectangular plate, bi-axial load space

a) b)

c) d) Fixed geometry

Variable shear prestress


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

23


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

ntnu puls presentation

Documents

download puls

puls elementspart

puls demonstration

environmentversion slide

collapseversion slide

puls course contentpart

buckling deflections

puls general knowledge