DNVGL-RP-C208 Determination of structural capacity by non-linear finite element analysis methods

125 Pages·2016·12.298 MB·English

RECOMMENDED PRACTICE
DNVGL-RP-C208 Edition September 2016
Determination of structural capacity by
non-linear finite element analysis methods
The electronic pdf version of this document found through http://www.dnvgl.com is the officially binding version.
The documents are available free of charge in PDF format.
DNV GL AS
FOREWORD
DNV GL recommended practices contain sound engineering practice and guidance.
© DNV GL AS September 2016
Any comments may be sent by e-mail to [email protected]
This service document has been prepared based on available knowledge, technology and/or information at the time of issuance of this document. The use of this
document by others than DNV GL is at the user's sole risk. DNV GL does not accept any liability or responsibility for loss or damages resulting from any use of
this document.
CHANGES – CURRENT t
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General r
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This document supersedes DNV-RP-C208, June 2013.
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Text affected by the main changes in this edition is highlighted in red colour. However, if the changes

involve a whole chapter, section or sub-section, normally only the title will be in red colour. s
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Main changes September 2016
• Sec.4 Requirements to finite element analysis
— In [4.3.4] new section has been added. Previous text rearranged and moved to [4.5].
— In [4.5] title has been changed and text rearranged. Comment on drilling stiffness added.
— In [4.6] new material curves have been added, modified text regarding strain rate.
— In [4.9] new text on contact modelling has been added.
• Sec.5 Representation of different failure modes
— In [5.1] criteria have been revised.
— In [5.2] thickness effect has been included.
• Sec.7 Commentary (previously Appendix A)
— In [7.3] new material curves have been added.
— In [7.6] new comment has been added.
— In [7.7] new comment has been added.
— In [7.8] text revised and mean curves have been added.
— In [7.11] new comment has been added.
• Sec.8 Examples
— In [8.1] example has been updated.
— In [8.6] new example has been added.
— In [8.7] new example has been added.
— In [8.8] new example has been added.
— In [8.9] numbers have been updated.
• App.A Structural models for ship collision analysis
— App.A Structural models for ship collision analysis has been added.
Editorial corrections
In addition to the above stated main changes, editorial corrections may have been made.
Recommended practice, DNVGL-RP-C208 – Edition September 2016 Page 3
DNV GL AS
Acknowledgements t
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This recommended practice is prepared based on results from two joint industry projects. The first joint r
r
industry project was sponsored by the following companies and institutions (in alphabetic order): u
c
ConocoPhillips Skandinavia AS
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Det Norske Veritas AS
s
Mærsk Olie og Gas AS e
g
Petroleum Safety Authority Norway n
a
Statoil ASA
h
C
Total E&P Norge AS

A follow-up project was sponsored by the following companies and institutions (in alphabetic order):

ConocoPhillips Norge
DNV GL AS
DYNAmore Nordic AB
EDRMedeso AS
Force Technology Norway AS
Lundin Norway AS
Maersk Olie og Gas A/S
Petroleum Safety Authority Norway
Rambøll
Statoil ASA
Total E&P Norge
In addition to their financial support, the above companies are also acknowledged for their technical
contributions through their participation in the project.
Recommended practice, DNVGL-RP-C208 – Edition September 2016 Page 4
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CONTENTS
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CHANGES – CURRENT .................................................................................................. 3
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Sec.1 Introduction.................................................................................................. 7
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1.1 General...................................................................................................7 C

1.2 Objective................................................................................................7

1.3 Scope.....................................................................................................7

1.4 Validity...................................................................................................7
1.5 Definitions .............................................................................................8
Sec.2 Basic considerations ................................................................................... 10
2.1 Limit state safety format......................................................................10
2.2 Characteristic resistance......................................................................11
2.3 Types of failure modes.........................................................................11
2.4 Use of linear and non-linear analysis methods.....................................11
2.5 Empirical basis for the resistance.........................................................11
2.6 Ductility................................................................................................12
2.7 Serviceability limit states.....................................................................12
2.8 Permanent deformations......................................................................12
Sec.3 General requirements ................................................................................. 13
3.1 Definition of failure..............................................................................13
3.2 Modelling strategy................................................................................13
3.3 Modelling accuracy...............................................................................13
3.4 Determination of characteristic resistance taking into account
statistical variation ..............................................................................13
3.5 Requirement to the software................................................................14
3.6 Requirements to the user.....................................................................14
Sec.4 Requirements to finite element-analysis .................................................... 15
4.1 General.................................................................................................15
4.2 Selection of software for finite element analysis..................................15
4.3 Selection of analysis method ...............................................................15
4.4 Geometry modelling.............................................................................17
4.5 Mesh ....................................................................................................17
4.6 Material modelling................................................................................19
4.7 Boundary conditions.............................................................................24
4.8 Load application...................................................................................24
4.9 Contact modelling ................................................................................24
4.10 Application of safety factors.................................................................25
4.11 Execution of non-linear finite element analyses, quality control ..........25
4.12 Requirements to documentation of the finite element analysis............26
Sec.5 Representation of different failure modes................................................... 27
5.1 Design against tensile failure...............................................................27
5.2 Failure due to repeated yielding (low cycle fatigue).............................31
5.3 Accumulated strain (ratcheting) ..........................................................36
5.4 Buckling...............................................................................................36
5.5 Repeated buckling................................................................................41
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Sec.6 Bibliography................................................................................................ 43 s
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Sec.7 Commentary................................................................................................ 45 n
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7.1 Comments to [4.1] General..................................................................45
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7.2 Comments to [4.5.2] Selection of element...........................................45
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7.3 Comments to [4.6.6] Recommendations for steel material qualities C
(low fractile)........................................................................................45

7.4 Comment to [4.6.8] Strain rate effects.................................................46

7.5 Comments to [5.1.1] General...............................................................46

7.6 Comments to [5.1.3] Tensile failure in base material - simplified
approach for plane plates.....................................................................47
7.7 Comments to [5.1.5] Failure of welds ..................................................47
7.8 Comment to [5.1.6] Simplified tensile failure criteria in case low
capacity is unfavourable.......................................................................47
7.9 Comment to [5.2.3] Determination of cyclic loads................................49
7.10 Comment to [5.2.4] Cyclic stress strain curves....................................49
7.11 Comment to [5.2.6] Low cycle fatigue of base material........................49
7.12 Comment to [5.2.5.1] Accumulated damage criterion .........................49
7.13 Comments to [5.2.7] Shake down check ..............................................50
7.14 Comments to [5.4.1] General...............................................................50
7.15 Comments to [5.4.5] Strain limits to avoid accurate check of local
stability for plates and tubular sections yielding in compression..........50
Sec.8 Examples..................................................................................................... 51
8.1 Example: Strain limits for tensile failure due to gross yielding of
plane plates (uniaxial stress state)......................................................51
8.2 Example: Convergence test of linearized buckling of frame corner.......56
8.3 Example: Determination of buckling resistance by use of linearized
buckling values ....................................................................................59
8.4 Example: Determination of buckling resistance from non-linear
analysis using standard defined equivalent tolerances.........................63
8.5 Example: Determination of buckling resistance from non-linear
analysis that are calibrated against standard formulations or tests.....65
8.6 Example: Buckling check of jacket frame structure during deck
installation...........................................................................................71
8.7 Example: Joint of rectangular hollow section (RHS) and circular
hollow section (CHS) under tension loading.........................................82
8.8 Example: Check of stiffened plate exposed to blast loads...................101
8.9 Example: Low cycle fatigue analysis of tubular joint subjected to out
of plane loading..................................................................................117
8.10 Example: Low cycle fatigue analysis of plate with circular hole..........121
App. A Structural models for ship collision analyses............................................. 124
Recommended practice, DNVGL-RP-C208 – Edition September 2016 Page 6
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SECTION 1 INTRODUCTION

1.1 General

This document is intended to give guidance on how to establish structural resistance by use of non-linear
finite element (FE) methods. It deals with determining the characteristic resistance of a structure or part of
a structure in a way that fulfils the requirements to ultimate strength in DNV GL standards.
Non-linear effects that may be included in the analyses are material and geometrical non-linearity, contact
problems, etc.
The characteristic resistance should represent a value that meets the requirement that there is less than
5% probability that the resistance is less than this value. This definition of characteristic resistance is similar
to what is required by many other structural standards that use the limit state safety format.
Recommendations in this document are expected to be valid for determination of capacities to be used with
such standards.
1.2 Objective
The objective of this recommended practice is that analyses carried out according to the recommendations
given in this document will lead to a structure that meets the requirements to the minimum safety margin
in the governing structural standard.
This document is not intended to replace formulas for resistance in design standards for the cases where
they are applicable and accurate, but to present methods that allow for using non-linear FE-methods to
determine resistance for cases that is not covered by traditional standards.
1.3 Scope
This recommended practice is meant to supplement structural design standards for offshore steel structures
and gives recommendation on how to determine the structural capacity by the use of non-linear finite
element analysis.
1.4 Validity
The document is valid for marine structures made from structural steels meeting requirements to offshore
structures with yield strength of up to 500 MPa.
The recommendations presented herein are adapted to typical offshore steels that fulfil the requirements
specified in DNVGL-OS-C101 /9/ or an equivalent offshore design standard. The specified requirements are
made under the assumption that the considered structure is operating under environmental conditions that
are within the specifications of the applied offshore standard. If the offshore unit is operating outside these
specifications, the failure criterion presented in this recommended practice can only be utilized if it can be
documented that both the weld and parent material have sufficient toughness in the actual environmental
conditions.
This recommended practice is concerned only with failure associated with extreme loads. Failure due to
repeated loading from moderate loads (fatigue) needs to be checked separately. See DNVGL-RP-C203 /11/.
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1.5 Definitions

1.5.1 Definition of terms

This recommended practice use terms as defined in DNVGL-OS-C101 /9/. The following additional terms
are defined below:
Table 1-1 Definition of terms
Term Definition
characteristic resistance the resistance that for a particular failure mode is meeting the requirement of having a
prescribed probability that the resistance falls below a specified value, usually the 5% fractile
conservative load load that maintains its orientation when the structure deforms, e.g. gravity loads
dimensioning event the extreme load or sequence of loads that are the most unfavourable with respect to the
structural capacity
ductility the ability to deform beyond the proportionality limit without significant reduction in the
capacity due to fracture or local buckling
Note: Originally, ductility refers to the behaviour of the material, but is here also used for the
behaviour of structures and structural details
engineering shear strain (cid:2011) =2 × (cid:2013) (cid:2011) =2 × (cid:2013) (cid:2011) =2 × (cid:2013)
(cid:1876)(cid:1877) (cid:1876)(cid:1877) (cid:1876)(cid:1878) (cid:1876)(cid:1878) (cid:1877)(cid:1878) (cid:1877)(cid:1878)
equivalent strain
1 1
2 2
(cid:2013) = (cid:3496) (cid:4674)(cid:3435)(cid:2013) −(cid:2013) (cid:3439) +(cid:3435)(cid:2013) −(cid:2013) (cid:3439) +((cid:2013) −(cid:2013) )2(cid:4675)+3(cid:3435)(cid:2013) 2+(cid:2013) 2+(cid:2013) 2(cid:3439)
(cid:1857)(cid:1869) 1+(cid:2021) 2 (cid:1876)(cid:1876) (cid:1877)(cid:1877) (cid:1877)(cid:1877) (cid:1878)(cid:1878) (cid:1878)(cid:1878) (cid:1876)(cid:1876) (cid:1876)(cid:1877) (cid:1877)(cid:1878) (cid:1876)(cid:1878)
expected resistance the resistance having 50% probability of being exceeded
follower load load that changes direction with the structure, e.g. hydrostatic pressure
gross yielding yielding across larger parts of a structural detail.
low-cycle fatigue the progressive and localised damage caused by repeated plastic strain in the material
Note: Low-cycle fatigue assessments are carried out by considering the cyclic strain level.
net area area of a cross section or part of a cross section where the area of holes and openings are
subtracted
net section ratio the ratio between the net area and the gross area of the tension part of a cross section
redundant structure a structure in which loss of capacity in one of its structural elements will lead to little or no
reduction in the overall load-carrying capacity due to load redistribution
shake down a state in which a structure after being loaded into the elasto-plastic range will behave
essentially linear for all subsequent cycles
1.5.2 Symbols
b span of plate
c flange outstand, speed of sound
C damping matrix
C resistance knock down factor
FEM
D outer diameter of tubular sections
E modulus of elasticity
Ep1 stress-strain curve parameter
Ep2 stress-strain curve parameter
Fext external forces
Fint internal forces
fy yield stress/yield strength
K Ramberg-Osgood parameter
kg eigenvalue for governing buckling mode
Ls characteristic element size of smallest element
l length of yielding zone
yz
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M mass matrix

N number of cycles to failure

Rd design resistance
Rk characteristic resistance
Sd design action effect
Sd characteristic action effect
t time, thickness
u displacement vector
ε strain
ε critical strain
cr
ε engineering (nominal) strain
eng
ε equivalent strain
eq
ε gross yielding strain limit
crg
(cid:2013)′ fatigue ductility coefficient
(cid:1858)
ε stress-strain curve parameter
p_ult
ε stress-strain curve parameter
p_y1
ε true (logarithmic) strain
true
Δε fully reversible maximum principal hot spot strain range
hs
Δε fully reversible local maximum principal strain range
l
Δt time step
γ material factor
M
γ partial factor for actions
f
(cid:2019)̅ reduced slenderness
ν Poisson’s ratio = 0.5 for plastic strain
ρ density
σ,σ principal stresses
1 2
σ representative stress
Rep
σ engineering (nominal) stress
eng
(cid:2026)′ fatigue strength coefficient
(cid:1858)
σ critical buckling stress
ki
σ linearized buckling stress disregarding local buckling modes
kig
σ linearized local buckling stress
kil
σ stress-strain curve parameter
prop
σ true (Cauchy) stress
true
σ stress-strain curve parameter
ult
σ stress-strain curve parameter
yield
σ stress-strain curve parameter
yield2
1.5.3 Verbal forms
Table 1-2 Definition of verbal forms
Term Definition
shall verbal form used to indicate requirements strictly to be followed in order to conform to the document
should verbal form used to indicate that among several possibilities one is recommended as particularly suitable,
without mentioning or excluding others, or that a certain course of action is preferred but not necessarily
required
may verbal form used to indicate a course of action permissible within the limits of the document
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SECTION 2 BASIC CONSIDERATIONS

2.1 Limit state safety format

A limit state can be defined as: A state beyond which the structure no longer satisfies the design
performance requirements. See e.g. /1/.
Limit states can be divided into the following groups:
Ultimate limit states (ULS) corresponding to the ultimate resistance for carrying loads.
Fatigue limit states (FLS) related to the possibility of failure due to the effect of cyclic loading.
Accidental limit states (ALS) corresponding to failure due to an accidental event or operational failure.
Serviceability limit states (SLS) corresponding to the criteria applicable to normal use or durability.
This recommended practice deals with limit states that can be grouped to ULS and ALS. It also addresses
failure modes from cyclic loading for cases that cannot adequately be checked according to the methods
used in standards for check of FLS. This is relevant for situations where the structure is loaded by a cyclic
load at a high load level, but only for a limited number of cycles (low-cycle fatigue).
The safety format that is used in limit state standards is schematically illustrated in Figure 2-1.
Figure 2-1 Illustration of the limit state safety format
The requirement can be written as:
S ≤ R (1)
d d
S = S γ design action effect
d k f
R = R /γ design resistance
d k M
S = characteristic action effect
k
γ = partial factor for actions
f
R = characteristic resistance
k
γ = material factor
M
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