| 图十二 壳单元模型
所示是壳单元模型底部36个节点的节点力Fxnode值，本文取前十个分析步的结果为例。将底部所有节点的节点力Fxnode值累加，得到壳单元模型底部的总支反力Fx。从表中可以看出，壳单元和梁单元所得的结果是精确相等，这也验证了采用如本文所假设的载荷分布方式满足目前规范的要求。
表六 两种单元类型的计算结果
|
|
STEP1
|
STEP2
|
STEP3
|
STEP4
|
STEP5
|
STEP6
|
STEP7
|
STEP8
|
STEP9
|
STEP10
|
|
NODE1
|
3.252E-02
|
2.330E-02
|
1.391E-02
|
4.369E-03
|
-5.278E-03
|
-1.500E-02
|
-2.458E-02
|
-3.409E-02
|
-4.356E-02
|
-5.296E-02
|
|
NODE2
|
3.101E-02
|
2.219E-02
|
1.321E-02
|
4.094E-03
|
-5.129E-03
|
-1.442E-02
|
-2.358E-02
|
-3.267E-02
|
-4.173E-02
|
-5.071E-02
|
|
NODE3
|
2.666E-02
|
1.900E-02
|
1.121E-02
|
3.301E-03
|
-4.700E-03
|
-1.276E-02
|
-2.071E-02
|
-2.860E-02
|
-3.645E-02
|
-4.424E-02
|
|
NODE4
|
1.999E-02
|
1.412E-02
|
8.149E-03
|
2.087E-03
|
-4.041E-03
|
-1.022E-02
|
-1.630E-02
|
-2.235E-02
|
-2.836E-02
|
-3.433E-02
|
|
NODE5
|
1.181E-02
|
8.133E-03
|
4.392E-03
|
5.988E-04
|
-3.233E-03
|
-7.089E-03
|
-1.090E-02
|
-1.468E-02
|
-1.844E-02
|
-2.217E-02
|
|
NODE6
|
3.110E-03
|
1.760E-03
|
3.944E-04
|
-9.840E-04
|
-2.370E-03
|
-3.760E-03
|
-5.142E-03
|
-6.514E-03
|
-7.876E-03
|
-9.220E-03
|
|
NODE7
|
-5.068E-03
|
-4.228E-03
|
-3.361E-03
|
-2.470E-03
|
-1.558E-03
|
-6.288E-04
|
2.699E-04
|
1.161E-03
|
2.056E-03
|
2.952E-03
|
|
NODE8
|
-1.174E-02
|
-9.111E-03
|
-6.423E-03
|
-3.681E-03
|
-8.946E-04
|
1.925E-03
|
4.683E-03
|
7.420E-03
|
1.016E-02
|
1.288E-02
|
|
NODE9
|
-1.609E-02
|
-1.230E-02
|
-8.421E-03
|
-4.472E-03
|
-4.630E-04
|
3.590E-03
|
7.562E-03
|
1.150E-02
|
1.544E-02
|
1.935E-02
|
|
NODE10
|
-1.760E-02
|
-1.340E-02
|
-9.119E-03
|
-4.754E-03
|
-3.241E-04
|
4.154E-03
|
8.543E-03
|
1.290E-02
|
1.725E-02
|
2.157E-02
|
|
NODE11
|
-1.607E-02
|
-1.230E-02
|
-8.433E-03
|
-4.497E-03
|
-5.004E-04
|
3.540E-03
|
7.500E-03
|
1.143E-02
|
1.535E-02
|
1.925E-02
|
|
NODE12
|
-1.171E-02
|
-9.110E-03
|
-6.447E-03
|
-3.730E-03
|
-9.683E-04
|
1.827E-03
|
4.561E-03
|
7.274E-03
|
9.985E-03
|
1.268E-02
|
|
NODE13
|
-5.032E-03
|
-4.228E-03
|
-3.397E-03
|
-2.542E-03
|
-1.666E-03
|
-7.725E-04
|
9.059E-05
|
9.463E-04
|
1.807E-03
|
2.668E-03
|
|
NODE14
|
3.156E-03
|
1.761E-03
|
3.487E-04
|
-1.076E-03
|
-2.509E-03
|
-3.944E-03
|
-5.372E-03
|
-6.790E-03
|
-8.196E-03
|
-9.584E-03
|
|
NODE15
|
1.187E-02
|
8.134E-03
|
4.337E-03
|
4.890E-04
|
-3.398E-03
|
-7.309E-03
|
-1.117E-02
|
-1.501E-02
|
-1.882E-02
|
-2.260E-02
|
|
NODE16
|
2.005E-02
|
1.412E-02
|
8.087E-03
|
1.963E-03
|
-4.228E-03
|
-1.046E-02
|
-1.661E-02
|
-2.272E-02
|
-2.880E-02
|
-3.482E-02
|
|
NODE17
|
2.672E-02
|
1.901E-02
|
1.115E-02
|
3.166E-03
|
-4.902E-03
|
-1.303E-02
|
-2.104E-02
|
-2.900E-02
|
-3.692E-02
|
-4.478E-02
|
|
NODE18
|
3.108E-02
|
2.219E-02
|
1.314E-02
|
3.953E-03
|
-5.341E-03
|
-1.471E-02
|
-2.394E-02
|
-3.310E-02
|
-4.222E-02
|
-5.127E-02
|
|
NODE19
|
3.259E-02
|
2.330E-02
|
1.383E-02
|
4.226E-03
|
-5.493E-03
|
-1.529E-02
|
-2.494E-02
|
-3.452E-02
|
-4.406E-02
|
-5.353E-02
|
|
NODE20
|
3.108E-02
|
2.219E-02
|
1.314E-02
|
3.953E-03
|
-5.341E-03
|
-1.471E-02
|
-2.394E-02
|
-3.310E-02
|
-4.222E-02
|
-5.127E-02
|
|
NODE21
|
2.672E-02
|
1.901E-02
|
1.115E-02
|
3.166E-03
|
-4.902E-03
|
-1.303E-02
|
-2.104E-02
|
-2.900E-02
|
-3.692E-02
|
-4.478E-02
|
|
NODE22
|
2.005E-02
|
1.412E-02
|
8.087E-03
|
1.963E-03
|
-4.228E-03
|
-1.046E-02
|
-1.661E-02
|
-2.272E-02
|
-2.880E-02
|
-3.482E-02
|
|
NODE23
|
1.187E-02
|
8.134E-03
|
4.337E-03
|
4.890E-04
|
-3.398E-03
|
-7.309E-03
|
-1.117E-02
|
-1.501E-02
|
-1.882E-02
|
-2.260E-02
|
|
NODE24
|
3.156E-03
|
1.761E-03
|
3.487E-04
|
-1.076E-03
|
-2.509E-03
|
-3.944E-03
|
-5.372E-03
|
-6.790E-03
|
-8.196E-03
|
-9.584E-03
|
|
NODE25
|
-5.032E-03
|
-4.228E-03
|
-3.397E-03
|
-2.542E-03
|
-1.666E-03
|
-7.725E-04
|
9.059E-05
|
9.463E-04
|
1.807E-03
|
2.668E-03
|
|
NODE26
|
-1.171E-02
|
-9.110E-03
|
-6.447E-03
|
-3.730E-03
|
-9.683E-04
|
1.827E-03
|
4.561E-03
|
7.274E-03
|
9.985E-03
|
1.268E-02
|
|
NODE27
|
-1.607E-02
|
-1.230E-02
|
-8.433E-03
|
-4.497E-03
|
-5.004E-04
|
3.540E-03
|
7.500E-03
|
1.143E-02
|
1.535E-02
|
1.925E-02
|
|
NODE28
|
-1.760E-02
|
-1.340E-02
|
-9.119E-03
|
-4.754E-03
|
-3.241E-04
|
4.154E-03
|
8.543E-03
|
1.290E-02
|
1.725E-02
|
2.157E-02
|
|
NODE29
|
-1.609E-02
|
-1.230E-02
|
-8.421E-03
|
-4.472E-03
|
-4.630E-04
|
3.590E-03
|
7.562E-03
|
1.150E-02
|
1.544E-02
|
1.935E-02
|
|
NODE30
|
-1.174E-02
|
-9.111E-03
|
-6.423E-03
|
-3.681E-03
|
-8.946E-04
|
1.925E-03
|
4.683E-03
|
7.420E-03
|
1.016E-02
|
1.288E-02
|
|
NODE31
|
-5.068E-03
|
-4.228E-03
|
-3.361E-03
|
-2.470E-03
|
-1.558E-03
|
-6.288E-04
|
2.699E-04
|
1.161E-03
|
2.056E-03
|
2.952E-03
|
|
NODE32
|
3.110E-03
|
1.760E-03
|
3.944E-04
|
-9.840E-04
|
-2.370E-03
|
-3.760E-03
|
-5.142E-03
|
-6.514E-03
|
-7.876E-03
|
-9.220E-03
|
|
NODE33
|
1.181E-02
|
8.133E-03
|
4.392E-03
|
5.988E-04
|
-3.233E-03
|
-7.089E-03
|
-1.090E-02
|
-1.468E-02
|
-1.844E-02
|
-2.217E-02
|
|
NODE34
|
1.999E-02
|
1.412E-02
|
8.149E-03
|
2.087E-03
|
-4.041E-03
|
-1.022E-02
|
-1.630E-02
|
-2.235E-02
|
-2.836E-02
|
-3.433E-02
|
|
NODE35
|
2.666E-02
|
1.900E-02
|
1.121E-02
|
3.301E-03
|
-4.700E-03
|
-1.276E-02
|
-2.071E-02
|
-2.860E-02
|
-3.645E-02
|
-4.424E-02
|
|
NODE36
|
3.101E-02
|
2.219E-02
|
1.321E-02
|
4.094E-03
|
-5.129E-03
|
-1.442E-02
|
-2.358E-02
|
-3.267E-02
|
-4.173E-02
|
-5.071E-02
|
|
SHELL
|
2.694E-01
|
1.781E-01
|
8.537E-02
|
-8.510E-03
|
-1.032E-01
|
-1.984E-01
|
-2.926E-01
|
-3.862E-01
|
-4.792E-01
|
-5.712E-01
|
|
BEAM
|
2.694E-01
|
1.781E-01
|
8.537E-02
|
-8.510E-03
|
-1.032E-01
|
-1.984E-01
|
-2.926E-01
|
-3.862E-01
|
-4.792E-01
|
-5.712E-01
|
5 结论分析
本文总结了基于Morison公式的小直径桩柱（包括直立桩柱和倾斜桩柱）上波浪力的计算方法，开发了相应的ABAQUS USER SUBROUTINE进行有限元分析，进而结合流体力学知识，将该程序从梁单元推广到了壳单元上。通过与相关实验数据的对比，证明该方法计算工程实际问题是可行的。
参考文献
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[2]竺艳蓉.海洋工程波浪力学[M].天津：天津大学出版社，1991：63
[3]DNV. DNV-OS-J101―2007 Design of offshore wind turbinestructures[S].Norway
[4]庄茁.基于ABAQUS的有限元分析和应用[M].北京：清华大学出版社，2009：505
[5]Alexandra Techet. Design Principles for Ocean Vehicles [M].Massachusetts. MIT
[6]兰梅雅.桩基结构物的波流作用力研究[D].上海：上海交通大学，2006
[7]姚文伟.桩基结构波浪力的工程计算方法[D].上海；上海交通大学，2009.
[8]严磊.风力发电机支撑体系结构设计研究[D].天津；天津大学，2008.
[9]聂武，孙丽萍，李治彬，曾志强.海洋工程钢结构设计[M].哈尔滨：哈尔滨工程大学出版社，1994
[10]中国船级社．GD 04-2005―2005 海上平台状态评定指南[S]．北京：人民交通出版社，2005.
[11]孙东昌，潘斌.海洋自升式移动平台设计与研究[M].上海：上海交通大学出版社，2008：63
[12]交通部第一航务工程勘察设计院等.海港水工规范[S]. 北京：人民交通出版社，1998
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