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Approximate calculation method of buckling load on integral sub-stiffened panel
XU Yuanming , LI Songze
School of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:To calculate the integral sub-stiffened panel buckling load in the preliminary design stage quickly, a simplifying approximate calculation method based on some reasonable assumptions was proposed. The perfect rectangular sub-stiffened panel simply supported on four sizes was used as investigation object. This structure has 3 instability forms, and the corresponding buckling loads were obtained by using the traditional stiffened plate theory. The minimum buckling load of the 3 instability forms was regarded as the approximate buckling load of the integral sub-stiffened panel. The buckling linear perturbation step method of ABAQUS was used to calculate the two sets of finite element (FE) models respectively: one set was used to validate the accuracies of the theoretical formulas for failure modes, and the other set was integral sub-stiffened panel finite element models which were used to verify the applicability of proposed calculation method of sub-stiffened panel buckling load. Only two load cases were considered in the research above: the longitudinal compression load and the combination of compression and shear load. The results indicate that the theoretical approximate calculation method can calculate the buckling load of sub-stiffened panel, which count for engineering application to some extent.
Key words: integral sub-stiffened panel     combined load     approximate formula     buckling load     finite element analysis

 图 1 传统加筋板和次加筋板的比较Fig. 1 Comparison between traditional stiffened panel and sub-stiffened panels
 t—平板厚度；a—次加筋板长度； b—带板宽度；bi—次筋条之间平板宽度; hp,hs—主、次加筋的高度;tp,ts—主、次加筋条的厚度. 图 2 次加筋板的主要尺寸与载荷的示意图 Fig. 2 Schematic diagram of primary dimensions and load of sub-stiffened panel

 图 3 次加筋板失稳模式示意图Fig. 3 Schematic diagram of buckling forms of sub-stiffened panel
1.2.1 次筋条之间的平板失稳[11]

 图 4 准确度验证有限元模型Fig. 4 Finite element models for accuracy verification
2.2 结果与讨论

 失效形式 压剪载荷比例 有限元计算/105 Pa 理论计算/105 Pa 误差/% Nx Nxy Nx Nxy 1 1 : 0 28.0 0 28.1 0 0.4 2 8.92 0 9.77 0 9.5 3 1.96 0 2.10 0 6.9 1 1 : 0.5 25.4 12.7 25.3 12.6 0.4 2 1.69 0.85 1.74 0.87 2.7

 图 5 次加筋板的有限元模型(次筋条数可以不同)Fig. 5 Finite element model of sub-stiffened panel (sub-stiffener numbers may be different)

 模型编号 板长/mm 带板宽度 次筋条数 次筋高度/mm 1 300 300 5 10 2 500 300 5 10 3 700 300 5 10 4 1 200 300 5 10 5 590 167 5 8 6 590 167 5 10 7 590 167 5 20 8 590 167 3 10 9 590 167 7 10
3.2 结果与讨论

 压剪载荷比 模型编号 有限元结果/kPa 理论结果/kPa 失效形式 误差/% 1∶0 1 99.2 93.5 3 5.8 2 57.0 53.5 3 6.0 3 55.1 54.3 3 1.5 4 54.8 51.6 3 5.7 1∶0.5 1 96.3 89.8 3 6.8 2 53.6 49.3 3 8.2 3 49.7 46.7 3 6.0 4 40.3 44.5 3 10.4

 图 6 模型8的屈曲模态Fig. 6 Buckling modal of model 8

 压剪载荷比 模型编号 有限元结果/kPa 理论结果/kPa 失效形式 误差/% 1∶0 5 163 155 3 4.6 6 200 210 3 4.7 7 265 244 2 8.0 1∶0.5 5 139 135 3 2.4 6 169 174 3 2.8 7 248 244 2 1.4

 压剪载荷比 模型编号 有限元结果/kPa 理论结果/kPa 失效形式 误差/% 1∶0 6 200 210 3 4.7 8 168 182 3 8.5 9 199 233 3 17.4 1∶0.5 6 169 174 3 2.8 8 142 130 3 8.0 9 179 190 3 6.4

 压剪载荷比 有限元结果/kPa 理论结果/kPa 失效模式 误差/% 1∶0 200 210 3 4.7 1∶0.2 194 202 3 4.2 1∶0.5 169 174 3 2.8 1∶0.8 143 145 3 1.7

1) 本文提出的棱柱形整体次加筋板计算公式仅适用于主筋条间次筋条个数大于2个的情况,且次加筋板不会发生整体失稳.否则,将会产生较大误差.

2) 针对3种失效形式而提出的计算公式,无论在纵向压缩载荷作用下还是压剪组合载荷作用下,公式计算结果与有限元结果的误差都不大于10%,有较高的准确度.

3) 针对不同的次加筋带板的长宽比、次筋条的高厚比,以及不同压剪载荷比例,本文提出的计算方法与有限元仿真的结果符合得较好,反映出该方法具有较为广泛的适用性,非常适合用于结构的初步设计阶段进行近似计算,以及加快棱柱形次加筋板的优化速度.

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#### 文章信息

XU Yuanming, LI Songze

Approximate calculation method of buckling load on integral sub-stiffened panel

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 369-374.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0240