Multivariable optimization design method of composite stiffener based on critical stiffness
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摘要: 以船舶结构优化设计为背景，针对目前结构安全余量过高导致加筋板板筋刚度过匹配现状，提出板筋刚度匹配临界刚度的概念，推导了板筋刚度比关系式。以T型复合材料筋材为对象，建立优化模型，基于Isight软件平台对设计变量进行灵敏度分析，简化设计变量。采用多岛遗传算法对筋材开展多变量优化设计，结合工程实际在筋材优化结果基础上确定设计方案，并开展复合材料加筋板力学性能试验研究，验证了多变量优化设计方法的可行性。研究表明：利用提出的加筋板板筋刚度比关系式，可以指导板筋刚度匹配设计；对T型复合材料筋材进行优化设计时，提升腹板高度对优化目标影响最明显；在等刚度约束前提下，提出的T型筋材优化设计方案能够较好地实现优化目标，同时保证了较优的经济性。Abstract: Based on the optimization design of ship structure, in view of the current situation that the structural safety margin is too high and the stiffener of stiffened plate is over matched, the concept of the critical stiffness of the stiffener matching was proposed, and the relationship between the stiffness ratio of plate and stiffener was derived. The optimization model of T-type composite stiffener was established. Based on Isight software platform, sensitivity analysis of design variables was carried out to simplify design variables. The Multi-Island genetic algorithm was used to carry out the multivariable optimization design of stiffener. Then, combined with the engineering practice, the design scheme was determined on the basis of the stiffener optimization results. The feasibility of the multivariable optimization design method was verified by the experimental study on the mechanical properties of composite stiffened plates. Research shows that the stiffness ratio formula of the stiffened plate can be used to guide the design of stiffener stiffness matching. In the optimization design of T-type composite reinforcement, the effect of web height on the optimization target is the most obvious. Under the condition of equal stiffness constraint, the optimal design scheme of T-type stiffener can achieve the optimization goal and ensure the better economy.
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Key words:
- composites /
- stiffener /
- critical stiffness /
- multivariable /
- optimal design
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图 1 筋材及其带板示意图
Figure 1. Schematic diagram of stiffener and attached plate
Eq1, Eq2—Equivalent modulus of elasticity of stiffener and attached plate; d— Thickness of the attached plate; h—Height of the stiffener; b—Width of the stiffener; O—Neutral axis of the attached plate
图 2 板筋刚度比函数曲线(
$b' = 1$ 、$\nu = 0.05$ )Figure 2. Function curves of stiffness ratio between reinforcement and plate (
$b' = 1$ ,$\nu = 0.05$ )
图 3 常用复合材料T型筋材示意图
Figure 3. Schematic diagram of common composite T-type stiffener
B—Spacing of stiffener; L—Span; t—Thickness of the skin of web; t1—Thickness of table; h1—Height of web; T—Total thickness; b1—Width of core; b2—Width of panel; b'—Width of attached plate
图 8 优化目标单位长度筋材的质量M的灵敏度
Figure 8. Sensitivity of optimization objective mass of the stiffener M
图 7 优化目标筋材截面积S的灵敏度
Figure 7. Sensitivity of optimization objective cross sectional area S
图 11 碳纤维增强环氧树脂复合材料加筋板剖面图
Figure 11. Section of carbon fiber reinforced epoxy stiffened plate
图 12 碳纤维增强环氧树脂复合材料加筋板仿真模型
Figure 12. Simulation model of carbon fiber reinforced epoxy stiffened plate
表 1 材料性能参数
Table 1. Material performance parameters
Material Young's modulus/GPa Shear strength/MPa Compressive strength/MPa Tensile strength/MPa Density/
(g∙cm−3)Poisson's
ratioBuoyancy material 1.1 3 20 — 0.65 0.4 T700/350 58.7 47.2 424 797 1.46 0.045 
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表 2 碳纤维增强环氧树脂复合材料T型筋材优化结果
Table 2. Optimization results of carbon fiber reiforced epoxy T-type stiffener
Number of cycles b1 t t1 h1 M S Design feasibility 21 36.20 3.51 19.51 102.75 4633.38 5284.24 9 125 35.98 3.51 19.51 102.75 4612.59 5257.16 9 325 35.98 3.51 19.51 102.75 4612.48 5257.09 9 328 35.97 3.51 19.53 102.75 4612.33 5256.24 9 393 33.32 4.10 16.22 109.98 4612.75 5239.33 9 494 33.32 4.10 16.22 109.94 4611.48 5237.75 9 692 33.32 4.10 16.22 109.94 4611.00 5237.09 9 693 33.24 4.10 16.22 109.94 4603.67 5227.24 9 800 33.24 4.10 16.22 109.94 4603.64 5227.20 9 892 33.24 4.09 16.22 109.94 4602.55 5226.44 9 Notes: M—Mass of the stiffener; S—Cross sectional area.
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表 3 碳纤维增强环氧树脂复合材料加筋板测点试验值与仿真值(载荷为100 kPa)
Table 3. Experimental values and simulation values of carbon fiber reinforced epoxy stiffened plate (Load is 100 kPa)
Measuring point Test value Simulation value Error/% Strain Ⅰ#/10−6 219.3 238.9 8.9 Strain Ⅱ#/10−6 535.6 579.8 8.3 Displacement 1#/mm 0.36 0.34 5.6 Displacement 2#/mm 0.23 0.22 5.7
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