Analysis of ultimate uniaxial compressive strength of stiffened panel considering influence of shear load
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摘要:
目的 旨在探究面内剪力对加筋板极限强度的影响规律，以及侧向压力与面内剪力之间是否会产生耦合效应。 方法 建立一系列加筋板有限元模型，采用ABAQUS软件进行面内剪力与纵向轴压载荷联合作用下的数值仿真分析，然后对计算结果进行无量纲化处理，并基于最小二乘法对联合载荷作用下的加筋板极限状态曲线/方程进行拟合。 结果 结果显示，面内剪力对加筋板轴压极限强度的影响规律得以明确，得到了考虑剪切载荷作用的加筋板极限状态方程。 结论 所做研究可为面内剪力作用下加筋板的纵向轴压极限强度修正提供参考。 Abstract:Objective This study aims to explore the law of the critical compression stress of stiffened panels under the influence of in-plane shear load, and whether in-plane shear load combined with lateral pressure will introduce a strong coupling effect. Method To this end, nonlinear finite element (FE) software ABAQUS is used to perform numerical simulation analysis under combined loads on a group of FE models. A limit state equation/curve is then derived from the dimensionless calculation results based on the minimum square error method. Results The results show that the influence law of in-plane shear load on the critical compression stress of stiffened panels is clarified, and a limit state equation of stiffened panels that considers the effect of shear load is obtained. Conclusion The limit state equation in this paper can provide references for modifying the ultimate strength of stiffened panels under the influence of in-plane shear load. -
Key words:
- stiffened panel /
- ultimate strength /
- in-plane shear load /
- lateral pressure /
- combined loads
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图 3 双跨有限元模型边界条件设置图
Figure 3. Illustration of boundary conditions of two-span finiteelement model
图 4 单跨有限元模型边界条件设置图
Figure 4. Illustration of boundary conditions of single-span finiteelement model
图 5 加筋板板周面内剪力加载示意图
Figure 5. Schematic diagram of in-plane shear loads on stiffened plate models
图 6 3种剪切验证算例的剪切极限状态应力云图
Figure 6. Contours of the von Mises stress in shear limit states for three cases
图 7 加筋板失效模式（放大10倍）
Figure 7. Failure modes of stiffened plates obtained under a ten-fold magnification
图 13 联合载荷作用下的加筋板轴压极限状态云图（放大10倍）
Figure 13. Contours of the von Mises stress on stiffened plates in limit state subject to combined loads obtained under a ten-fold magnification
图 14 2种联合载荷施加方法下对应的极限状态曲线及离散点
Figure 14. Limit state curves and discrete points obtained by two methods of applying combined loads
图 15 带板厚为15 mm加筋板在3种载荷联合作用下的应力−应变曲线
Figure 15. Stress-strain curves of stiffened plate with tp = 15 mm under combined loads of lateral pressure, shear and axial compression
表 1 压缩载荷下双跨模型边界条件
Table 1. Boundary conditions of two-span model with compression loads
位置 边界条件 AD Ry = Rz = 0，耦合端部节点并约束Ux一致，施加位移载荷 A1D1 Ry = Rz = 0，耦合端部节点且Ux = 0 AA1，DD1 Rx = Rz = 0，耦合端部节点并约束Uy一致 EF，E1F1，BB1，CC1 Uz = 0 
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表 2 压缩载荷下单跨模型边界条件
Table 2. Boundary conditions of single-span model with compression loads
位置 边界条件 AB Rx = Rz = Uz = 0，耦合端部节点并约束Ux一致，施加位移载荷 A1B1 Rx = Rz = Uz = 0，耦合端部节点并约束Ux = 0 AA1，BB1 Ry = Rz = Uz = 0，耦合端部节点并约束Uy一致
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表 3 单跨模型施加面内剪力时边界条件
Table 3. Boundary conditions of single-span model with in-plane shear loads
位置 边界条件 AB Uz = 0，耦合端部节点并约束Ux一致 A1B1 Uz = 0，耦合端部节点并约束Ux = 0 AA1，BB1 Uz = 0，约束板边节点Rz一致 角点B1 Uy = 0
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表 4 轴压极限强度可靠性验证算例
Table 4. Cases for reliability verification of ultimate strength under axial compression
参数 算例1 算例2 ${t_{\rm{p}} }$/mm 15 18.5 ${h_{\rm{w}} }$/mm 580 235 ${t_{\rm{w}} }$/mm 15 10 ${b_{\rm{f}} }$/mm 150 90 ${t_{\rm{f}} }$/mm 20 15
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表 5 算例计算结果
Table 5. Calculation results of case 1 and case 2
模型 轴压极限强度/MPa 误差/% 本文结果 文献[11]结果 单跨（算例1） 240.96 238.33 1.10 双跨（算例1） 233.09 227.05 2.66 单跨（算例2） 234.45 231.47 1.29 双跨（算例2） 201.25 190.98 5.38
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表 6 剪切极限应力可靠性验证算例
Table 6. Cases for reliability verification of ultimate shear stress
算例 剪切极限应力/MPa 误差/% 本文结果 文献结果 WANG F t10 165.87 163.55 1.42 WANG F t19 175.78 180.23 −2.47 ZHANG S 150.95 149.13 1.22
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表 7 加强筋尺寸参数信息
Table 7. Information of the sizes of stiffeners
尺寸 加强筋尺寸/mm F（$ {h_{\rm{w}}} \times {t_{\rm{w}}} $） A（$ {h_{\rm{w}}} \times {b_{\rm{f}}} \times {t_{\rm{w}}}/{t_{\rm{f}}} $） T（$ {h_{\rm{w}}} \times {t_{\rm{w}}} + {b_{\rm{f}}} \times {t_{\rm{f}}} $） Size 1 $ 250 \times 25 $ $ 235 \times 90 \times 10/15 $ $ 235 \times 10 + 90 \times 15 $ Size 2 $ 350 \times 35 $ $ 383 \times 100 \times 12/17 $ $ 383 \times 12 + 100 \times 17 $ Size 3 $ 550 \times 35 $ $ 580 \times 150 \times 15/20 $ $ 580 \times 15 + 150 \times 20 $
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表 8 按固定比例同时施加压剪载荷时的加筋板极限应力
Table 8. Ultimate stress of stiffened plate obtained by applying compression-shear load simultaneously with fixed proportion
$ {\sigma _x}:{\tau _{xy}} $ 极限状态应力/MPa 8∶2 ${\sigma _{x{\rm{u}} } } = 230.72,{\text{ } }{\tau _{xy} } = 57.68$ 7∶3 ${\sigma _{x{\rm{u}} } } = 214.06,{\text{ } }{\tau _{xy} } = 91.74$ 6∶4 ${\sigma _{x{\rm{u}} } } = 183.18,{\text{ } }{\tau _{xy} } = 122.12$ 4∶6 ${\sigma _{x{\rm{u}} } } = 109.44,{\text{ } }{\tau _{xy} } = 164.16$
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表 9 先施加剪切载荷至指定值后再施加轴压载荷的加筋板极限应力
Table 9. Ultimate stress of stiffened plate as applying shear load to a specified value followed by axial compression load
$ {\tau _{xy}}/{\tau _{y}} $ 极限状态应力/MPa 0.2 ${\sigma _{x{\rm{u}} } } = 238.98,{\text{ } }{\tau _{xy} } = 36.21$ 0.4 ${\sigma _{x{\rm{u}} } } = 225.85,{\text{ } }{\tau _{xy} } = 72.42$ 0.6 ${\sigma _{x{\rm{u}} } } = 198.37,{\text{ } }{\tau _{xy} } = 108.63$ 0.8 ${\sigma _{x{\rm{u}} } } = 153.18,{\text{ } }{\tau _{xy} } = 144.85$
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表 10 3个加筋板算例在3种载荷联合作用下的轴压极限强度值
Table 10. Ultimate strength of three stiffened plates under combined loads of lateral pressure, shear and axial compression
带板厚tp /mm 纯轴压/MPa 侧压/MPa 侧压+轴压/MPa 侧压+剪力(0.2)+轴压/MPa 侧压+剪力(0.4)+轴压/MPa 侧压+剪力(0.6)+轴压/MPa 侧压+剪力(0.8)+轴压/MPa 15.0 226.48 0.10 194.80 (100%) 190.88 (98.0%) 177.12 (90.9%) 146.36 (75.1%) 72.86 (37.4%) 0.15 174.62 (100%) 170.61 (97.7%) 155.41 (89.0%) 122.05 (69.9%) 46.00 (26.3%) 18.5 244.79 0.10 214.97 (100%) 211.11 (98.2%) 197.27 (91.8%) 171.57 (79.8%) 114.30 (53.2%) 0.15 196.08 (100%) 192.67 (98.3%) 179.76 (91.7%) 152.14 (77.6%) 94.39 (48.1%) 25.0 280.42 0.10 251.89 (100%) 248.71 (98.7%) 234.71 (93.2%) 207.46 (82.4%) 157.26 (62.4%) 0.15 237.83 (100%) 230.86 (97.1% 216.91 (91.2%) 192.07 (80.8%) 145.11 (61.0%)
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