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Wave and earthquake effects on axisymmetric offshore structures

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Abstract

Vertical axisymmetric structures have found a variety of applications in offshore engineering, including oil storage tanks, production platforms and so on. The present paper describes an efficient calculation procedure for determining the interaction of such structures with the surrounding ocean. In particular, numerical calculations are explicated for:

  • - wave forces and runup for a fixed structure,

  • - added-mass and damping coefficients for an oscillating structure,

  • - earthquake loading in terms of base shear and overturning moment,

  • - motions of a floating structure.

The approach used is based on a boundary element method involving an axisymmetric Green's function, and exploits the structure's axisymmetry to provide a highly efficient computational procedure suitable for carrying out on a desk-top computer. Results are presented for surface-piercing conical structures under various loading conditions.

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Abbreviations

A :

matrix coefficients, see eq. (2.14)

a :

added-mass coefficients; cylinder or sphere radius

B :

see eq. (2.13)

b :

damping coefficients

C :

matrix coefficients, see eq. (2.15)

d :

still water depth

F :

wave force

f :

source strength distribution function

G :

Green's function

g :

gravitational constant

H :

wave height

i :

√−1

k :

wave number

L :

segment length

m :

mass matrix coefficients

n :

unit normal vector directed outward from body

R :

runup

r :

radial coordinate

S b :

equilibrium body surface

t :

time

z :

vertical coordinate measured upwards from still water level

α:

see Fig. 1 and Fig. 4

βm :

1 form=0.2i m form≥1

ξ:

z+d

θ:

polar coordinate

ζ:

amplitude of body motion

ρ:

fluid density

ϕ:

velocity potential

ω:

wave angular frequency

References

  1. Fenton, J. D., Wave forces on vertical bodies of revolution, Journal of Fluid Mechanics, Vol. 85, (1978), 241–255.

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  2. Isaacson, M. de St. Q., Fixed and floating axisymmetric structures in wave, Journal of the Waterway, Port, Coastal and Ocean Division, ASCE, Vol. 108, No. WW2, (1982), 180–199.

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  3. Kim, W. D., On a free-floating ship in waves, Journal of Ship Research, Vol. 10, (1966), 182–191, 200.

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  4. Sarpkaya, T. and M. Isaacson, Mechanics of Wave Forces on Offshore Structures, Van Nostrand, Reinhold, New York, (1981).

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of British Columbia, Vancouver, B. C., Canada

    Michael Isaacson

  2. Chongging Jiaotong Institute, Chongqing

    Wu Song-ren

Authors
  1. Michael Isaacson
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  2. Wu Song-ren
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Additional information

Communicated by Wang Zhi-zhong.

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Isaacson, M., Song-ren, W. Wave and earthquake effects on axisymmetric offshore structures. Appl Math Mech 5, 1437–1447 (1984). https://doi.org/10.1007/BF01910434

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  • DOI: https://doi.org/10.1007/BF01910434

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