## Proceedings of the ... International Conference on Offshore Mechanics and Arctic Engineering, Volume 3American Society of Mechanical Engineers, 2001 - Arctic regions |

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Page 341

The method of DQ approximates a partial

respect to a coordinate at a node as a ... by using Lagrange polynomials for

calculating the weighting coefficients for the DQ discretization of any order

The method of DQ approximates a partial

**derivative**of a variable function withrespect to a coordinate at a node as a ... by using Lagrange polynomials for

calculating the weighting coefficients for the DQ discretization of any order

**derivatives**.Page 343

extended GDQ discretization for a partial

point ( a , 0 ) can be expressed by a ( m + ... + P ) 0 DET Oil ( 6 ) abil am ... oup of

variable function and / or its possible

extended GDQ discretization for a partial

**derivative**of order m + ... + p at discretepoint ( a , 0 ) can be expressed by a ( m + ... + P ) 0 DET Oil ( 6 ) abil am ... oup of

variable function and / or its possible

**derivatives**at all nodes ( 4-5 ) . Thus in ...Page 358

XE where x and y are physical coordinates in see and & and n are natural

coordinates in Š . Then the transformations of the first

displacement components ui of element e are 1.y = | J 1-1x ( 19 ) Using equation

( 19 ) , the ...

XE where x and y are physical coordinates in see and & and n are natural

coordinates in Š . Then the transformations of the first

**derivatives**of thedisplacement components ui of element e are 1.y = | J 1-1x ( 19 ) Using equation

( 19 ) , the ...

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### Contents

OMAE2001MAT3010 | 1 |

OMAE2001MAT3011 | 11 |

OMAE2001MAT3013 | 17 |

Copyright | |

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analysis applied assessment bending boundary buckling calculated Charpy compared components compressive considered controlled corrosion crack crack initiation critical CTOD curve cycle defects defined deformation derivatives determined developed direction discrete displacement distribution ductile crack dynamic effect element Engineering equation estimated evaluated experiments factors failure fatigue fatigue cracks field Figure finite element flexible FPSO fracture toughness function geometry grain growth higher impact increase inspection International joints layer length loading material maximum measured mechanical metal method microstructure node notch observed obtained offshore operation parameters performed phase pipe pipeline plastic plate predicted present pressure prestrained problem procedure range region respectively riser shown shows simulated specimens standard steel strain strength stress structures surface Table technique temperature tensile thickness weight weld yield