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**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 AFEM Ch 33 - Thesis Ch 6-8: Numerical Examples and References Complete Thesis (in PDF) available on request

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**A New Sandwich Design Concept for Ships**

ADMOS 2003, Göteborg, Sweden A New Sandwich Design Concept for Ships Pål G. Bergan Det Norske Veritas, Høvik, Norway and NTNU, Trondheim, Norway

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Topics of the Lecture Some examples of challenges in ship modelling and simulation Some general problems Container ship Liquid natural gas ship A new concept for building ships using steel and light-weight concrete design Some conclusions

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**Characteristics of Ship Structures**

“Many pieces of steel welded together”, e.g. more than in a large ship Many types of structural elements: Outer skins, internal skins Bulkheads Integrated ballast tanks Girders, frames, stringers Stiffeners, brackets, lug-plates, cut-outs Cutouts, surface grinding and polishing Numerous stress concentrations Corrosion serious problem

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**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

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**Typical Analysis Steps for Ship Analysis**

Wave load analysis

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**Container ship Global structural model 3-and 4-node elements**

Containers with low E-modulus Modelled in PATRAN/NASTRAN, transferred to SESAM

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Hydrodynamic Model

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**Hydrodynamic Load Analysis**

Dynamic pressures for head sea and max hogging condition

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**Ultimate load state (ULS) checks**

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**Hot spot stress analysis at hatch corner**

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**Liquid Natural Gas (LNG) Ship**

Global finite element model

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**Stepwise Construction of Global Model**

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**Wave Motion and Pressures**

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Hot Spots

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**Structural Problems: Bulk Carrier**

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**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

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**Light weight aggregate concrete**

Cellular Sandwich 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 Steel plate Light weight aggregate concrete Steel plate Thin walled steel spar box

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**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

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Panmax Bulk Carrier

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**Some Characteristics of the Concept**

Longitudinal girder stiffened double bottom structure Solid sandwich structure in deck Continuous hatch coaming beam structure Partly hollow sandwich elements in ship sides, transverse bulkheads, and double bottom Traditional fore and aft ship design in the present study Ballast water carried primarily in cargo holds HT 36 steel throughout cargo area Minimum steel skin plate thickness 10 millimetre Concrete properties (example) density 900 kg/m3 compressive cube strength 14 MPa tensile splitting strength 2.5 MPa failure strain in compression ‰ – similar to yield strain for steel E-modulus 6000 MPa More than 50 % of concrete strength achieved after a few days

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**Cross-section of ship beam**

Global and local load cases from DNV Steel Ship Rules Initial scantlings selected Linear FEM analysis to determine sectional forces – with stiffness contribution of concrete in both compression and tension Scantling optimisation of sections assuming no tensile concrete strength – safety factor 1.4 for concrete compressive strength DNV Steel Ship Rule longitudinal strength requirements satisfied without including contribution from concrete Confirmation that all local buckling modes are eliminated Depth of sandwich minimum 70 millimetre to avoid global buckling of deck slab outside the hatch coaming

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**9% Ni Steel or Invar steel**

LNG carrier Primary barrier 9% Ni Steel or Invar steel Insulation layer e.g. geomaterial

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LNG carrier

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**Tanker for oil or chemicals**

Sandwich deck Easy to clean ballast cells Ice strengthened side structure Stainless steel primary barrier

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**Safety and Structural Attributes**

Reduced number of fatigue and corrosion prone details Buckling failure modes virtually eliminated Increased hull torsion stiffness Increased energy absorption in case of collision or grounding Increased strength to withstand explosions and accidental loads Increased stiffness of aft ship to avoid vibrations and propeller shaft bearing damages

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**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 maintenance Significantly reduced coating area Increased service life Highly fire resistant and insulating hull

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**Sandwich Application Potential**

Sandwich design can be adapted to many different ship types Sandwich design can be introduced for parts of a ship The sandwich concept can be used for reinforcement of existing ships The sandwich concept can be used for repair and strengthening of degradation and damage

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**Initial Cost and Life Cycle Cost**

Building: Price competitive design where 40% of the steel weight is exchanged with cheaper concrete material Much fewer fabrication details and less welding Potential for automization and modular construction Significantly reduced coating area and cost Operation: Hull maintenance cost expected to be reduced Other operational advantages because of layout? Scrap value uncertain

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Conclusions There are still major challenges in practical modeling and simulation of ship structures The complexity and mere size of these structures offer particular difficulties Practical analyses require coupling of several analysis tools A new idea for building ships using a steel -concrete sandwich concept has been presented This concept seems to offer a wide range of advantages, but further development of the technology is required

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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

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**Application: free spanning oil/gas pipelines**

BM 1 BM 2 WM Crack

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**Two Bending-Induced Pipeline Failure Modes**

Mode 1: Ovalization & plastic buckling on the compressive side Mode 2: Wall crack on the tensile side

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**Solid FE Modeling of Pipe Wall**

Advantages: accurate, no additional modeling needed. Disadvantages: time consuming as regards preprocessing and simulation 3D Solid Model (ANSYS)

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**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

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**Design Rules are Very Conservative for Tension**

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

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**Formulation works well for large disp/rot, e. g**

Formulation works well for large disp/rot, e.g. inelastic collapse of pinched cylinder From Haugen’s thesis, note that triangles are used here

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**A comment on elastic-plastic analysis, **

stress resultants versus integration through thickness Run Ninc up to max load, elastic analysis CPUelast Run Ninc up to max load, elasti-plastic analysis CPUelast-plast => CPUplast= CPUelast-plast - CPUelast Number of integration points over thickness Plate bending Scordelis-Lo Plate buckling(Q) Plate buckling (R) Plasticity model: Integration over thickness (using 5 integr. points) approximately 50% more time consuming than Stress resultant plasticity

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**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

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**Line spring relationships**

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

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**Summary of Formulation**

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

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**Some Test Cases ANSYS 3D bricks Corotational quad shell + link**

elements CPU for 3D, half of full model: sec CPU for shell/link full model: 100 sec

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**Visualisation of J-integral in Crack**

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CTOD versus Strain

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

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**Failure Modes: Plastic Buckling vs Fracture**

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**J-Integral versus Load**

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Conclusions A 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)

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