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

A New Sandwich Design Concept for Ships

Pål G. Bergan

Det Norske Veritas, Høvik, Norwayand

NTNU, Trondheim, Norway

ADMOS 2003, Göteborg, Sweden

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

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

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

Typical Analysis Steps for Ship Analysis

Wave load analysis

Container shipGlobal structural model

3-and 4-node elementsContainers with low E-modulusModelled in PATRAN/NASTRAN, transferred to

SESAM

Hydrodynamic Model

Hydrodynamic Load Analysis

Dynamic pressures for head sea and max hogging condition

Ultimate load state (ULS) checks

Hot spot stress analysis at hatch corner

Liquid Natural Gas (LNG) Ship

Global finite element model

Stepwise Construction of Global Model

Wave Motion and Pressures

Hot Spots

Structural Problems: Bulk Carrier

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

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

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

Panmax Bulk Carrier

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

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

LNG carrier

Primary barrier

9% Ni Steel or Invar steel

Insulation layere.g. geomaterial

LNG carrier

Tanker for oil or chemicals

Sandwich deck

Easy to cleanballast cells

Stainless steelprimary barrier

Ice strengthenedside structure

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

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

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

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

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

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

Application: free spanning oil/gas pipelines

BM 1 BM 2WM

Crack

Two Bending-Induced Pipeline Failure Modes

Mode 2: Wall crack onthe tensile side

Mode 1: Ovalization &plastic buckling onthe compressive side

Solid FE Modeling of Pipe Wall

3D Solid Model(ANSYS)

Advantages: accurate, no additional modelingneeded. Disadvantages: time consuming as regards preprocessing and simulation

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

Design Rules are Very Conservative for Tension

Solution: use two-parameter fracture mechanics (constraint correction) and direct numerical simulation

Formulation works well for large disp/rot, e.g. inelastic collapse of pinched cylinder

From Haugen’sthesis, note that triangles are used here

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

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

Line spring relationships

Line spring fe discretization, 8 DOF, elongation and rotation (opening of the crack)

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

Some Test Cases

CPU for 3D, half of full model: 60000 secCPU for shell/link fullmodel: 100 sec

ANSYS 3Dbricks

Corotational quad shell + linkelements

Visualisation of J-integral in Crack

CTOD versus Strain

Load-Displacement Response in Bending, D/t=80

Failure Modes: Plastic Buckling vs Fracture

J-Integral versus Load

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)