posted chapters of bjørn haugen’s 1994 thesis
DESCRIPTION
Posted Chapters of Bjørn Haugen’s 1994 Thesis. Title: Buckling and Stability Problems for Thin Shell Structures Using High Performance Finite Elements. AFEM Ch 31 - Thesis Ch 4: Triangular ANDES Shell Element AFEM Ch 32 - Thesis Ch 5: Quad ANDES Shell Element - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/1.jpg)
![Page 2: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/2.jpg)
Posted Chapters of Bjørn Haugen’s 1994 Thesis
AFEM Ch 31 - Thesis Ch 4: Triangular ANDES Shell ElementAFEM Ch 32 - Thesis Ch 5: Quad ANDES Shell ElementAFEM Ch 33 - Thesis Ch 6-8: Numerical Examples and References
Complete Thesis (in PDF) available on request
Title: Buckling and Stability Problems for Thin Shell Structures Using High Performance Finite Elements
![Page 3: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/3.jpg)
![Page 4: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/4.jpg)
![Page 5: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/5.jpg)
![Page 6: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/6.jpg)
![Page 7: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/7.jpg)
![Page 8: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/8.jpg)
![Page 9: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/9.jpg)
![Page 10: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/10.jpg)
![Page 11: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/11.jpg)
![Page 12: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/12.jpg)
![Page 13: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/13.jpg)
![Page 14: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/14.jpg)
![Page 15: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/15.jpg)
![Page 16: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/16.jpg)
![Page 17: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/17.jpg)
![Page 18: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/18.jpg)
![Page 19: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/19.jpg)
![Page 20: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/20.jpg)
![Page 21: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/21.jpg)
![Page 22: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/22.jpg)
![Page 23: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/23.jpg)
![Page 24: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/24.jpg)
![Page 25: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/25.jpg)
A New Sandwich Design Concept for Ships
Pål G. Bergan
Det Norske Veritas, Høvik, Norwayand
NTNU, Trondheim, Norway
ADMOS 2003, Göteborg, Sweden
![Page 26: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/26.jpg)
Topics of the Lecture
Some examples of challenges in ship modelling and simulationSome general problemsContainer shipLiquid natural gas ship
A new concept for building ships using steel and light-weight concrete design
Some conclusions
![Page 27: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/27.jpg)
Characteristics of Ship Structures“Many pieces of steel welded together”, e.g.
more than 100 000 in a large shipMany types of structural elements:
Outer skins, internal skinsBulkheadsIntegrated ballast tanksGirders, frames, stringers Stiffeners, brackets, lug-plates, cut-outsCutouts, surface grinding and polishing
Numerous stress concentrationsCorrosion serious problem
![Page 28: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/28.jpg)
Particular Considerations for Modeling and Analysis
Enormous scale effects from overall ship beam (e.g. more than 400 meters long) to stress concentrations around weld or crack
Good modeling of ship beam requires inclusion of a significant number of secondary and tertiary structural elements
Fatigue and fracture analysis requires and detailed and accurate analysis of stress concentrations and cracks
Dynamic response analysis integrated with hydrodynamic simulation
Ultimate strength analysis by way of buckling and/or nonlinear simulation
![Page 29: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/29.jpg)
Typical Analysis Steps for Ship Analysis
Wave load analysis
![Page 30: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/30.jpg)
Container shipGlobal structural model
3-and 4-node elementsContainers with low E-modulusModelled in PATRAN/NASTRAN, transferred to
SESAM
![Page 31: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/31.jpg)
Hydrodynamic Model
![Page 32: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/32.jpg)
Hydrodynamic Load Analysis
Dynamic pressures for head sea and max hogging condition
![Page 33: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/33.jpg)
Ultimate load state (ULS) checks
![Page 34: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/34.jpg)
Hot spot stress analysis at hatch corner
![Page 35: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/35.jpg)
Liquid Natural Gas (LNG) Ship
Global finite element model
![Page 36: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/36.jpg)
Stepwise Construction of Global Model
![Page 37: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/37.jpg)
Wave Motion and Pressures
![Page 38: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/38.jpg)
Hot Spots
![Page 39: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/39.jpg)
Structural Problems: Bulk Carrier
![Page 40: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/40.jpg)
Steel – Light-weight Concrete Sandwich
From complex steel structure to
clean sandwich structure
The main idea is to replace stiffened steel panels by steel-concrete sandwich elements for main load carrying structural components
![Page 41: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/41.jpg)
Cellular Sandwich
Steel plate
Thin walled steel
spar box
Light weight
aggregate concrete
Steel plate
The light-weight concrete is filled into the space between the surface steel sheets to completely occupy the internal space and bond to the steel along all sides
The steel sheets provide the major part of the structural strength
The concrete provides some strength and stiffness in compression, but not in tension (conservative assumption)
The concrete provides a stiff spacing between the surface sheets and supports against surface skin buckling
The need for secondary stiffeners is eliminated The concrete has sufficient strength to transfer
relevant transverse shear forces in plates The number of details prone to coating failure
with subsequent corrosion and fatigue is greatly reduced
A concrete with a density below approximately 900 kg/m3 is preferred to keep down the total weight
![Page 42: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/42.jpg)
Using Experience from Other Applications
Steel-concrete sandwich elements have been used successfully for bridge structures, which are also exposed to large dynamic loads and demanding environmental conditions
Composite sandwich structural elements are used in air plane wing structures, wind turbine wings, trains, naval ships, and other severely loaded structures – as a particularly efficient design solution
Shipbuilding should learn from successful experiences in other industries
![Page 43: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/43.jpg)
Panmax Bulk Carrier
![Page 44: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/44.jpg)
Some Characteristics of the Concept
Longitudinal girder stiffened double bottom structureSolid sandwich structure in deckContinuous hatch coaming beam structurePartly hollow sandwich elements in ship sides, transverse bulkheads, and double bottomTraditional fore and aft ship design in the present studyBallast water carried primarily in cargo holdsHT 36 steel throughout cargo areaMinimum steel skin plate thickness 10 millimetreConcrete properties (example)
density 900 kg/m3 compressive cube strength 14 MPa tensile splitting strength 2.5 MPa failure strain in compression 2-2.5 ‰ – similar to yield strain for steel E-modulus 6000 MPa
More than 50 % of concrete strength achieved after a few days
![Page 45: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/45.jpg)
Cross-section of ship beamGlobal and local load cases from DNV Steel Ship RulesInitial scantlings selectedLinear FEM analysis to determine sectional forces – with stiffness contribution of concrete in both compression and tensionScantling optimisation of sections assuming no tensile concrete strength – safety factor 1.4 for concrete compressive strengthDNV Steel Ship Rule longitudinal strength requirements satisfied without including contribution from concreteConfirmation that all local buckling modes are eliminatedDepth of sandwich minimum 70 millimetre to avoid global buckling of deck slab outside the hatch coaming
![Page 46: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/46.jpg)
LNG carrier
Primary barrier
9% Ni Steel or Invar steel
Insulation layere.g. geomaterial
![Page 47: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/47.jpg)
LNG carrier
![Page 48: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/48.jpg)
Tanker for oil or chemicals
Sandwich deck
Easy to cleanballast cells
Stainless steelprimary barrier
Ice strengthenedside structure
![Page 49: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/49.jpg)
Safety and Structural Attributes
Reduced number of fatigue and corrosion prone details
Buckling failure modes virtually eliminatedIncreased hull torsion stiffness Increased energy absorption in case of collision or
groundingIncreased strength to withstand explosions and
accidental loadsIncreased stiffness of aft ship to avoid vibrations and
propeller shaft bearing damages
![Page 50: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/50.jpg)
Safety and Operational Attributes
Increased resistance against damage from cargo handling equipment
Better damping of dynamic stresses and response from hydrodynamic loads
Enhanced damping of noise and vibrations from machinery and propulsion system
Simplified hull structure maintenanceSignificantly reduced coating areaIncreased service lifeHighly fire resistant and insulating hull
![Page 51: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/51.jpg)
Sandwich Application Potential
Sandwich design can be adapted to many different ship types
Sandwich design can be introduced for parts of a shipThe sandwich concept can be used for reinforcement
of existing shipsThe sandwich concept can be used for repair and
strengthening of degradation and damage
![Page 52: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/52.jpg)
Initial Cost and Life Cycle Cost
Building:Price competitive design where 40% of the steel weight is
exchanged with cheaper concrete materialMuch fewer fabrication details and less weldingPotential for automization and modular constructionSignificantly reduced coating area and cost
Operation:Hull maintenance cost expected to be reduced Other operational advantages because of layout?Scrap value uncertain
![Page 53: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/53.jpg)
ConclusionsThere are still major challenges in practical modeling
and simulation of ship structuresThe complexity and mere size of these structures offer
particular difficultiesPractical analyses require coupling of several analysis
toolsA new idea for building ships using a steel -concrete
sandwich concept has been presentedThis concept seems to offer a wide range of advantages,
but further development of the technology is required
![Page 54: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/54.jpg)
Combining High Performance Thin Shell and Surface Crack
Finite Elements For Simulation of Combined Failure Modes
Bjørn Skallerud *Kjell Holthe *
Bjørn Haugen **
*The Norwegian Universitey of Science & Technology Dept. of Structural Engineering, Trondheim, Norway
** FEDEM Technology, USA
![Page 55: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/55.jpg)
Application: free spanning oil/gas pipelines
BM 1 BM 2WM
Crack
![Page 56: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/56.jpg)
Two Bending-Induced Pipeline Failure Modes
Mode 2: Wall crack onthe tensile side
Mode 1: Ovalization &plastic buckling onthe compressive side
![Page 57: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/57.jpg)
Solid FE Modeling of Pipe Wall
3D Solid Model(ANSYS)
Advantages: accurate, no additional modelingneeded. Disadvantages: time consuming as regards preprocessing and simulation
![Page 58: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/58.jpg)
Thin Shell Model of Pipe Wall
Bjørn Haugen’s corotational quad thin shell element used (preferred to triangle since mesh generation is easy for a pipe - all elements are rectangles)
Plastic buckling failure mode: small-strain elastoplasticity (stress resultant or thickness-integrated)
Tensile cracking: fracture mechanics by link elements
![Page 59: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/59.jpg)
Design Rules are Very Conservative for Tension
Solution: use two-parameter fracture mechanics (constraint correction) and direct numerical simulation
![Page 60: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/60.jpg)
Formulation works well for large disp/rot, e.g. inelastic collapse of pinched cylinder
From Haugen’sthesis, note that triangles are used here
![Page 61: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/61.jpg)
Plate bendingScordelis-LoPlate buckling(Q)Plate buckling (R)
Number of integration points over thickness1 2 3 5 7 10 12
1.0 1.23 1.40 1.55 1.75 2.25 2.221.0 1.28 1.38 1.49 1.62 1.85 2.001.0 1.02 1.13 1.29 1.33 1.51 1.751.0 1.22 1.31 1.52 1.80 2.03 2.21
1.0 1.19 1.30 1.46 1.63 1.90 2.05
• Run Ninc up to max load, elastic analysis CPUelast
Run Ninc up to max load, elasti-plastic analysis CPUelast-plast
=> CPUplast= CPUelast-plast - CPUelast
Plasticity model: Integration over thickness (using 5 integr. points) approximately 50% more time consuming than Stress resultant plasticity
A comment on elastic-plastic analysis, stress resultants versus integration
through thickness
![Page 62: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/62.jpg)
Fracture: By Line Spring Finite Element
Reduces 3D crack problem to 2D, has a sound fracture mechanics basis from slip line analysis of the crack ligament
![Page 63: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/63.jpg)
Line spring relationships
![Page 64: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/64.jpg)
Line spring fe discretization, 8 DOF, elongation and rotation (opening of the crack)
![Page 65: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/65.jpg)
Quadrilateral ANDES FE, co-rotated kinematics, consistent tangent
Stress resultants, linear hardening for the shell element, consistent tangent
Rect line spring FE, co-rotated kinematics, power law hardening, alternative stress updates tried (expl, impl euler), yield surface with corners, calculates fracture mechanics quantities such as J-integral, CTOD, T-stress(constraint)
Increm-iterative solution of global eqs using Newton-Raphson and a simplified arc-length method
Summary of Formulation
![Page 66: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/66.jpg)
Some Test Cases
CPU for 3D, half of full model: 60000 secCPU for shell/link fullmodel: 100 sec
ANSYS 3Dbricks
Corotational quad shell + linkelements
![Page 67: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/67.jpg)
Visualisation of J-integral in Crack
![Page 68: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/68.jpg)
CTOD versus Strain
![Page 69: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/69.jpg)
Load-Displacement Response in Bending, D/t=80
![Page 70: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/70.jpg)
Failure Modes: Plastic Buckling vs Fracture
![Page 71: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/71.jpg)
J-Integral versus Load
![Page 72: Posted Chapters of Bjørn Haugen’s 1994 Thesis](https://reader036.vdocuments.site/reader036/viewer/2022081420/56816008550346895dcf080c/html5/thumbnails/72.jpg)
ConclusionsA very feasible tool for assessment of critical compressive
strains and fracture mechanics quantities (by means of two-parameter fract mech)
Mesh generation requires only 6 input parameters (providing automatic meshing of shell and crack)
Needs special treatment for short cracks (a/t < 0.15, which is the most interesting sizes for practical applications and assessments)
Further work: nonlinear hardening for the shell material, ductile tearing of the crack (both a semi-elliptical crack growing through thickness, and further along the circumference as a through crack)