Deformation Mode of Hemispherical Shell under Static Load
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摘要: 采用顶点及平板下压加载的加载方式对半球壳的准静态压缩进行了实验研究，获得了半球壳的变形模态及力-位移曲线。通过准静态压缩实验观察在不同加载方式下球壳变形模式随压缩深度的变化，发现半球壳出现了轴对称和非轴对称变形形式。利用ABAQUS有限元软件对球壳准静态压缩过程进行数值模拟，分析加载方式与球壳尺寸等对变形行为的影响。结果表明：球壳在压缩下的变形可分为加载点附近局部压平、轴对称凹陷以及形成非对称多边形3个阶段。其中，在压平向凹陷转变时，小截面平头加载的接触力-位移曲线产生了突跳现象，但在半球头与平板加载时未出现，且凹陷之后，半球头加载下接触力的增加速率减小，而平板加载下接触力的增加速率几乎保持不变。壳的径厚比越大，后期的变形程度越复杂；径厚比越小，由压平到凹陷转变时的临界荷载越大，球壳承载力越大。计算表明，在本研究范围内球壳凹陷前后接触力的大小以及增加速率只与厚度有关，而与半径的相关性则较小。Abstract: Axial compression on stainless steel spherical shells was performed under different loading styles by quasi-static tests, and the deformation energy of spherical shell was calculated.The stress distribution was observed through the photo elastic experiment so as to analyze the deformation model of hemispherical shell under static load.It can be seen that, the maximum stress occur near the loading point at the beginning, and extends outward in a circular form with the compression depth increases, eventually larger stresses distribute near polygon vertex, loading point and the region between them.It's also simulated by ABAQUS software to analysis the influence of loading method and hemispherical shell size on deformation mode.The result shows:The ability to resist deformation of spherical shell decreases along with the R/t increase; under flat nosed compression, the contact force of spherical shell decreases after reaching the peak, but it doesn't under other loadings; the increasing ratio of contact force is only related with thickness, but not with radius.
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Key words:
- quasi-static compression /
- hemispherical shell /
- deformation model /
- deformation energy
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图 1 实验装置及半球壳变形简化示意图
Figure 1. Experimental device and simplified schematic of hemispherical shell's deformation
(a) Experimental device picture (b) Simplified schematic of hemispherical shell's deformation
图 3 不同厚度壳体、不同加载方式的载荷-位移实验曲线
Figure 3. The force-displacement curves of shell compressed by different loading styles or with different thickness
(a) Different thickness (b) Different loading styles
图 5 模拟所得的变形模态以及实验与模拟的接触力-位移曲线
Figure 5. Deformation mode in simulation and force-deformation curve
图 6 内空半球壳凹陷区翻转变形(镜像图)(R=80)
Figure 6. Inward dimpling reflection of single-layer empty spherical shell (R=80)
图 7 平头加载下不同半径球壳的接触力-位移曲线
Figure 7. Contact force-displacement curves of different shell diameters under flat nosed loading
图 8 平头加载下不同厚度球壳的接触力-位移曲线
Figure 8. Contact force-displacement curves of the different shell thickness under flat nosed loading
图 9 平板加载下不同厚度球壳的荷载-位移曲线
Figure 9. Contact force-displacement curves of the different shell thickness under board loading
图 10 半球头加载下不同厚度球壳的荷载-位移曲线
Figure 10. Contact force-displacement curves of the different shell thickness under ball-head loading
图 11 不同加载方式下壳体的接触力-位移曲线
Figure 11. Contact force-displacement curves of the shell under different loading methods
表 1 试件尺寸及结果
Table 1. Geometry and result of specimen
Specimen No. Type of
shellType of
indenterδ/
(mm)R/
(mm)$\frac{R}{\delta}$ Experimental results 2h/(mm) a/(mm) Shape S1 Hemispherical Flat nose 1.2 50 41.67 30 31.1 Ring S2 Entire spherical Flat nose 0.8 47.5 59.38 30 37.2 4-lobes S3 Hemispherical Flat nose 1.5 60 40.00 30 27.7 Ring S4 Entire spherical Flat nose 0.8 55 68.75 30 42.7 4-lobes S5 Hemispherical Plates 1.2 50 41.67 46 48.4 Ring S6 Hemispherical Flat nose 0.7 50 71.43 30 36.7 3-lobes S7 Hemispherical Plates 0.7 50 71.43 50 49.1 5-lobes 
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表 2 半球壳的几何尺寸
Table 2. Geometric dimensions of the hemispherical shell
Specimen No. R/(mm) δ/(mm) R/δ p-100-0.7 50 0.7 71.43 p-100-1.0 50 1.0 50.00 p-100-1.2 50 1.2 41.67 p-120-1.2 60 1.2 50.00 p-150-1.2 75 1.2 62.50 b-100-0.7 50 0.7 71.43 b-100-1.2 50 1.2 41.67 q-100-0.7 50 0.7 71.43 q-100-1.2 50 1.2 41.67 Note：The meaning of specimen No. is loading type, external diameter, thickness of shell; p means blunt indenter; b means plate; q means hemispherical indenter.
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