Rapid determination method of minimum stable topological plate thickness in topology optimization of complex hull structures
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摘要:
目的 船体结构拓扑优化的设计域通常是基于二维板壳单元，而设计域板厚的取值差异又会对体积分数约束值的设定以及稳定拓扑构型的获得带来了影响，进而制约拓扑优化方法在船体结构设计领域的实用化，故需要开展相关研究予以解决。 方法 以VLCC油船货舱内的横向强框架为优化对象，提出一种设定复杂船体结构体积分数约束值的折衷方法及基于单元统计识别构型并确定最小稳定拓扑板厚的方法。 结果 通过理论分析及相关试算表明，所提方法可以获得较为可靠的体积分数约束值和设计域最小稳定拓扑板厚， 结论 具备有效性和可行性，可为大型油船横向强框架的拓扑优化提供技术支撑，同时还可为其他复杂船体结构的拓扑优化提供参考。 Abstract:Objectives The design domain for the topological optimization of ship structures is usually based on two-dimensional shell elements. However, the thickness difference of the design domain affects the setting of volume fraction constraints and the acquisition of stable topological configuration, restricting the practical application of the topology optimization method in the field of hull structure design. Thus, relevant research needs to be carried out to solve this problem. Methods This paper takes the transverse web frame in the cargo tank of a VLCC (very large crude oil carrier) as the optimization object, and puts forward a compromise method for setting the volume fraction constraint value of the complex hull structure, as well as a method for determining the minimum stable topological plate thickness of the transverse web frame via element statistics. Results Through theoretical analysis and trial calculation, it is found that the volume fraction value and minimum stable topological plate thickness can be obtained more reliably using this method. Conclusions The proposed method possesses validity and feasibility, and is able to provide technical support for the optimization design of the transverse web frames of large oil tankers. It can also provide references for the topology optimization of other complex hull structures. -
图 1 拓扑优化目标横向强框架所在位置
Figure 1. Location of target transverse web frame for topology optimization
图 2 横向强框架拓扑优化设计域
Figure 2. Design domain of transverse web frame for topology optimization
表 1 不同设计域板厚与对应体积分数约束值下的横向强框架拓扑优化结果
Table 1. Topology optimization results of transverse web frame constrained by different plate thickness of design domain and corresponding volume fraction
td/mm Cvf 设计域拓扑优化
单元密度云图拓扑优化结果（x=0.3） 15 0.32 
20 0.21 
23（taver） 0.17 
25 0.14 
30 0.10 
35 0.07 
40 0.04 
注：设计域拓扑优化单元密度云图中，蓝色区域的单元为低密度单元（0~0.1），红色区域的单元为高密度单元（0.9~1），单元密度值越高越接近于红色。 
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表 2 相同体积分数约束值（Cvf = 0.17）下不同设计域板厚所得拓扑优化结果
Table 2. Topology optimization results with different thickness of design domain under the same volume fraction constraint (Cvf = 0.17)
td/mm 设计域拓扑优化
单元相对密度云图拓扑优化结果（x=0.3） 15 
20 
23（taver） 
25 
30 
35 
40 
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表 3 A1_HSM1_S工况下不同设计域板厚所得拓扑优化结果
Table 3. Topology optimization results of different plate thicknesses of design domain in the load case of A1_HSM1_S
td/mm 设计域拓扑优化
单元相对密度云图最终迭代步设计域
等效应力分布云图设计域应力
最大值/MPa10 
379 15 
291 20 
226 25 
241 40 
164
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表 4 A2_BSR1P_S工况下不同设计域板厚所得拓扑优化结果
Table 4. Topology optimization results of different plate thicknesses of design domain in the load case of A2_BSR1P_S
td/mm 设计域拓扑优化
单元相对密度云图最终迭代步设计域等效应力分布云图 设计域应力最大值/MPa 10 
371 15 
272 22 
262 23 
253 24 
235 40 
172
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表 5 4种工况下不同设计域板厚的参数统计结果
Table 5. Statistics of different plate thicknesses of design domain under four load cases
工况 设计域板厚X/mm 单元数量 num_port_X num_mid_X w_port_X w_mid_X A1_HSM1_S 10 15 780 0.16 1.46 14 30 742 0.33 1.39 15（min） 36 728 0.39 1.36 16 38 746 0.41 1.40 20 47 686 0.51 1.28 23 54 656 0.59 1.23 40 92 534 1.00 1.00 A1_FSM2_H 10 28 674 0.10 − 15 40 587 0.14 − 23 227 170 0.79 − 24（min） 267 4 0.93 − 25 274 2 0.95 − 40 287 0 1.00 − A2_BSR1P_S 16 0 776 0.00 3.46 22 169 332 0.78 1.48 23（min） 186 250 0.86 1.12 24 202 234 0.94 1.04 40 216 224 1.00 1.00 A2_HSM1_S 10 172 336 0.65 3.23 11（min） 242 134 0.92 1.29 12 245 124 0.93 1.19 15 250 120 0.95 1.15 23 270 106 1.03 1.02 40 263 104 1.00 1.00 注：min表示该设计域板厚为经本文构型识别法确定的该工况下强框架设计域最小稳定拓扑板厚。
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