﻿ HCSR垂向剪力调整方法研究
 舰船科学技术  2022, Vol. 44 Issue (9): 27-32    DOI: 10.3404/j.issn.1672-7649.2022.09.006 PDF
HCSR垂向剪力调整方法研究

Research on vertical shear force adjustment methods in HCSR
HAN Tao, WU Jia-meng, CAI Shi-jian
Marine Design and Research Institute of China, Shanghai 200011, China
Abstract: Vertical shear force adjustment methods in HCSR were researched in this article. Comparing and analyzing the difference between the methods in HCSR version 2019 and version 2020, a new vertical shear force adjustment method was proposed, combined with the problems in actual working. The results of numerical verification showed that compared with HCSR, the new method in this article could not only adjust the vertical shear forces at target positions to target values, but also adjust the reaction forces at both end faces to zero, which would avoid the influence from the reaction forces to target location shear force checking results.
Key words: hull structure     HCSR     vertical shear force adjustment     hull girder loads
0 引　言

1 HCSR垂向剪力调整方法

 图 1 垂向剪力调整基本原理图 Fig. 1 Basic principles of vertical shear force adjustment

 图 2 简化等效施加方法示意图 Fig. 2 Sketch of simplified equivalent application method
1.1 HCSR2019垂向剪力调整方法

 ${M_{{\text{aft}}}} = {M_{{\text{fore}}}} = {{\Delta Q \cdot l} \mathord{\left/ {\vphantom {{\Delta Q \cdot l} 2}} \right. } 2}，$ (1)

 $\Delta Q = \left\{ \begin{gathered} {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}}, \hfill \\ {Q_{{\text{targ - fore}}}} - {Q_{{\text{fwd}}}},\hfill \\ \end{gathered}\right. \begin{array}{l}当调整位置为\text{Bulkhead-aft}时，\\ 当调整位置为\text{Bulkhehead-fore}时。\end{array}$ (2)

 $\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = {{\left( {{Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} + {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}}} \right) \cdot l}/4} ，\hfill \\ {W_1} = {\left( {\Delta {Q_{{\text{aft}}}}\left( {2l - {l_2} - {l_3}} \right) + \Delta {Q_{{\text{fwd}}}}\left( {{l_2} + {l_3}} \right)} \right)} /\hfill \\ \qquad\;\; {\left( {2l - {l_1} - 2{l_2} - {l_3}} \right)} ，\hfill \\ {W_2} = \Delta {Q_{{\text{aft}}}} - \Delta {Q_{{\text{fwd}}}}，\hfill \\ {W_3} = - {\left( {\Delta {Q_{{\text{fwd}}}}\left( {2l - {l_1} - {l_2}} \right) + \Delta {Q_{{\text{aft}}}}\left( {{l_1} + {l_2}} \right)} \right)} /\hfill \\ \qquad\;\;{\left( {2l - {l_1} - 2{l_2} - {l_3}} \right)} ，\end{gathered} \right.$ (3)

 $\begin{split} \Delta {Q_{{\text{fwd}}}} =& - \Delta {Q_{{\text{aft}}}} ={{\left( {{Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} - \left( {{Q_{{\text{targ - aft}}}} - {Q_{{\text{fwd}}}}} \right)} \right)}/ 2}。\end{split}$ (4)
1.2 HCSR2020垂向剪力调整方法

HCSR2020针对除最首最尾区域外的其他区域舱段的垂向剪力调整方法和HCSR2019完全一致，但对于最首和最尾舱段，提出新的调整方法。

 $对于最尾三舱段：\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = {{\Delta Q \cdot l} \mathord{\left/ {\vphantom {{\Delta Q \cdot l} 2}} \right. } 2} - {{M'}_1}，\hfill \\ {{W'}_1} = \Delta Q + {R_{{\text{V}}\_{\text{aft}}}}。\hfill \\ \end{gathered} \right.$ (5)
 $对于最首三舱段：\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = {{\Delta Q \cdot l} \mathord{\left/ {\vphantom {{\Delta Q \cdot l} 2}} \right. } 2} - {{M'}_3}，\hfill \\ {{W'}_3} = \Delta Q + {R_{{\text{V}}\_{\text{fore}}}}。\hfill \\ \end{gathered} \right.$ (6)

 $\left\{ \begin{gathered} {{M'}_1} = (\Delta Q + {R_{{\text{V\_}}aft}}) \cdot {{{l_1}} \mathord{\left/ {\vphantom {{{l_1}} 4}} \right. } 4} ，\hfill \\ {{M'}_3} = (\Delta Q + {R_{{\text{V\_for}}e}}) \cdot {{{l_3}} \mathord{\left/ {\vphantom {{{l_3}} 4}} \right. } 4} 。\hfill \\ \end{gathered} \right.$ (7)

 $\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = ( {Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} +\hfill \\ \qquad\quad {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} ) \times l / 4 - {{M'}_2} ，\hfill \\ {W_1} = {\left( {\Delta {Q_{{\text{aft}}}}\left( {2l - {l_2} - {l_3}} \right) + \Delta {Q_{{\text{fwd}}}}\left( {{l_2} + {l_3}} \right)} \right)} /\hfill \\ \qquad\;\;{\left( {2l - {l_1} - 2{l_2} - {l_3}} \right)} + {{W'}_1}，\hfill \\ {W_2} = \Delta {Q_{{\text{aft}}}} - \Delta {Q_{{\text{fwd}}}}，\hfill \\ {W_3} = - {\left( {\Delta {Q_{{\text{fwd}}}}\left( {2l - {l_1} - {l_2}} \right) + \Delta {Q_{{\text{aft}}}}\left( {{l_1} + {l_2}} \right)} \right)} /\hfill \\ \qquad\;\;{\left( {2l - {l_1} - 2{l_2} - {l_3}} \right)} - {{W'}_3} 。\hfill \\ \end{gathered} \right.$ (8)

 $对于最尾舱段：\left\{ \begin{gathered} {{W'}_1} = N + {R_{{\text{V}}\_{\text{aft}}}} ，\hfill \\ {{M'}_2} = {{{{W'}_1} \cdot {l_1}} \mathord{\left/ {\vphantom {{{{W'}_1} \cdot {l_1}} 4}} \right. } 4} ，\hfill \\ {{W'}_3} = 0 。\hfill \\ \end{gathered} \right.$ (9)
 $对于最首舱段：\left\{ \begin{gathered} {{W'}_3} = N + {R_{{\text{V}}\_{\text{fore}}}} ，\hfill \\ {{M'}_2} = {{{{W'}_3} \cdot {l_3}} \mathord{\left/ {\vphantom {{{{W'}_3} \cdot {l_3}} 4}} \right. } 4} ，\hfill \\ {{W'}_1} = 0。\hfill \\ \end{gathered} \right.$ (10)

 $\begin{split}N =& ( ({Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}})(l - {l_1} - {l_2}) + ({Q_{{\text{targ - fwd}}}} -\\ &{Q_{{\text{fwd}}}})(l - {l_2} - {l_3}) ) / {2l - {l_1} - 2{l_2} - {l_3}}。\end{split}$ (11)
2 HCSR垂向剪力调整原理分析 2.1 HCSR2019垂向剪力调整方法原理

HCSR2019中方法1是通过在模型两端施加大小相等的弯矩MaftMfore，使整体剪力发生变化，从而达到使需要调整处的剪力到达目标值的目的。根据结构力学，控制方程为：

 $\left\{ \begin{gathered} {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} = \Delta Q ，\hfill \\ {M_{{\text{aft}}}} = {M_{{\text{fore}}}} 。\hfill \\ \end{gathered} \right.$ (12)

 $\left\{ \begin{split} &{M_{{\text{aft}}}} = {M_{{\text{fore}}}}，\\ &{{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} / l} + {R_{{\text{va}}}} + {W_1} = {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} ，\\ &{{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} /l} + {R_{{\text{va}}}} + {W_1}{{ - }}{W_2} = {Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} ，\\ & {W_1} + {W_3} = {W_2} ，\\ &{Q_{{\text{targ - aft}}}} - \left( {{Q_{{\text{aft}}}} + {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)}/ l}} \right) = \\ & \qquad- \left( {{Q_{{\text{targ - fwd}}}} - \left( {{Q_{{\text{fwd}}}} + {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} / l}} \right)} \right) 。\end{split} \right.$ (13)

 $\begin{split} {R_{{\text{va}}}} =& \left( {{{W_1} \cdot \left( { - 2l + {l_1} + 2{l_{{\text{end}}}}} \right)} / {2l}} + {{W_2} \cdot \left( {2l - 2{l_1} - {l_2} - 2{l_{{\text{end}}}}} \right)} / \right.\\ & \left. {2l} + {{{W_3} \cdot \left( { - 2l + 2{l_1} + 2{l_2} + {l_3} + 2{l_{{\text{end}}}}} \right)} / {2l}} \right)。\\[-10pt] \end{split}$ (14)

2.2 HCSR2020垂向剪力调整方法原理

 $\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}}，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {R_{{\text{vb}}}} + {R_{{\text{V}}\_{\text{aft}}}} = 0，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {R_{{\text{vb}}}} + {{W'}_1} = \Delta Q。\hfill \\ \end{gathered} \right.$ (15)

 ${R_{{\text{vb}}}} = {{{{W'}_1} \cdot ({l_1} + 2{l_{{\text{end}}}})} \mathord{\left/ {\vphantom {{{{W'}_1} \cdot ({l_1} + 2{l_{{\text{end}}}})} {2l}}} \right. } {2l}} - {W'_1} 。$ (16)

 $\left\{ \begin{split} {M_{{\text{aft}}}} = {M_{{\text{fore}}}}，\hfill \\ &{{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {R_{{\text{va}}}} + {W_1} = {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} ，\hfill \\ &{{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} / l} + {R_{{\text{va}}}} + {W_1} - {W_2} = {Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} ，\hfill \\ &{{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {R_{{\text{va}}}} + {R_{{\text{V}}\_{\text{aft}}}} = 0 ，\hfill \\ &{W_3} = - \left( {{Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} - \left( {{Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}}} \right)} \right) \times \hfill\\ &\qquad\;\; \left( {l - {l_1} - {l_2}} \right) /{\left( {2l - {l_1} - 2{l_2} - {l_3}} \right)}。\end{split} \right.$ (17)

3 垂向剪力调整新方法研究

HCSR2020相对于HCSR2019，对于最首和最尾区域舱段，除了使得目标区域的垂向剪力值到达目标值外，还额外要求最尾舱段的尾端面和最首舱段的首端面的支反力为0，原因是防止端面过大的支反力会影响目标位置的剪力校核结果[7]

 图 3 某散货船最艉舱段垂向剪力调整结果[7] Fig. 3 Vertical shear force adjustment results for aft most cargo holds of a bulk carrier

 图 4 某158 K油船船舯舱段垂向剪力调整结果 Fig. 4 Vertical shear force adjustment results for mid cargo holds of an 158 K oil tanker

1）对于最首最尾舱段，除规范(HCSR2020)要求的端面外，另一处端面的支反力依然存在过大的情况，依然可能会对校核结果产生影响；

2）对于非最首最尾舱段，也存在端面处支反力过大从而影响剪力校核结果的问题。

 $\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}}，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {{R'}_{{\text{vb}}}} + {R_{{\text{V}}\_{\text{aft}}}} = 0，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {{R'}_{{\text{vb}}}} + {{W'}_1} = \Delta Q ，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} \mathord{\left/ {\vphantom {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} l}} \right. } l} + {{R'}_{{\text{vb}}}} + {{W'}_1} + {{W'}_3} + {R_{{\text{V}}\_{\text{fore}}}} = 0。\hfill \\ \end{gathered} \right.$ (18)

 $\begin{split}{R'_{{\text{vb}}}} =& {W'_1} \cdot {{\left( { - 2l + {l_1} + 2{l_{{\text{end}}}}} \right)} / {2l}} + {W'_3} \times\\ &{{\left( { - 2l + 2{l_1} + 2{l_2} + {l_3} + 2{l_{{\text{end}}}}} \right)} / {2l}}。\end{split}$ (19)

 $\left\{ \begin{gathered} {{W'}_1} = \Delta Q + {R_{{\text{V\_aft}}}} ，\hfill \\ {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = \hfill \\ \qquad\quad \left( \begin{gathered} {{\Delta Q \cdot \left( {{l_1} + 2{l_2} + {l_3}} \right)} /4} - {{{R_{{\text{V\_aft}}}} \times \left( {{l_1} + 2{l_{{\text{end}}}}} \right)} /4} \hfill \\ - {{{R_{{\text{V}}\_{\text{fore}}}} \cdot \left( {2l - 2{l_1} - 2{l_2} - {l_3} - 2{l_{{\text{end}}}}} \right)} / 4} \hfill \\ \end{gathered} \right)，\hfill \\ {{W'}_3} = - {R_{{\text{V}}\_{\text{fore}}}} - \Delta Q 。\hfill\\ \end{gathered} \right.$ (20)

 $\left\{ \begin{gathered} {M_{{\text{aft}}}} = {M_{{\text{fore}}}} ，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} /l} + {R_{{\text{va}}}} + {W_1} = {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} ，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} / l} + {R_{{\text{va}}}} + {W_1}{\text{ - }}{W_2}= {Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}} ，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} /l} + {R_{{\text{va}}}} + {R_{{\text{V}}\_{\text{aft}}}} = 0 ，\hfill \\ {{\left( {{M_{{\text{aft}}}} + {M_{{\text{fore}}}}} \right)} /l} + {R_{{\text{va}}}} + {W_1}{{ - }}{W_2} + {W_3} + {R_{{\text{V}}\_{\text{fore}}}} = 0 。\end{gathered} \right.$ (21)

 $\left\{ \begin{gathered} {W_1} = {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} + {R_{{\text{V}}\_{\text{aft}}}} ，\hfill \\ {W_2} = {Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}} - ({Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}})，\hfill \\ {W_3} = - {R_{{\text{V}}\_{\text{fore}}}} - ({Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}}) ，\hfill \\ {M_{{\text{aft}}}} = {M_{{\text{fore}}}} = \left( \begin{gathered} {{({Q_{{\text{targ - aft}}}} - {Q_{{\text{aft}}}}) \times \left( {{l_1} + {l_2}} \right)} / 4} + \hfill \\ {{({Q_{{\text{targ - fwd}}}} - {Q_{{\text{fwd}}}}) \times \left( {{l_2} + {l_3}} \right)} / 4} \hfill \\ - {{{R_{{\text{V}}\_{\text{aft}}}} \cdot \left( {{l_1} + 2{l_{{\text{end}}}}} \right)} / 4} - {R_{{\text{V}}\_{\text{fore}}}} \times \hfill \\ \left( {2l - 2{l_1} - 2{l_2} - {l_3} - 2{l_{{\text{end}}}}} \right)/ 4 \hfill \\ \end{gathered} \right) 。\end{gathered} \right.$ (22)
4 垂向剪力调整方法数值验证

 图 5 理想模型及局部载荷加载示意图 Fig. 5 Idea model and the application of local loads

 图 7 HCSR2019和HCSR2020的方法1对比结果 Fig. 7 Comparison results between HCSR2019 and HCSR2020 in method1

 图 10 HCSR2020和本文新方法的方法2对比结果 Fig. 10 Comparison results between HCSR2020 and new method of the article in method2

 图 8 HCSR2019和HCSR2020的方法2对比结果 Fig. 8 Comparison results between HCSR2019 and HCSR2020 in method2

 图 9 HCSR2020和本文新方法的方法1对比结果 Fig. 9 Comparison results between HCSR2020 and new method of the article in method1
5 结　语

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