| 负压激励下含椭圆孔高弹体的屈曲分析 |
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| 引用本文： | 梁观坡,傅禹鑫,娄本亮,谢宇新.负压激励下含椭圆孔高弹体的屈曲分析[J].应用数学和力学,2021,42(12):1221-1228. |
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| 作者姓名： | 梁观坡 傅禹鑫 娄本亮 谢宇新 |
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| 作者单位： | 天津大学 机械工程学院，天津 300350 |
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| 基金项目： | 国家自然科学基金(12072225； 11532001； 11991031； 11991032； 12021002) |
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| 摘 要： | 基于数值模拟与理论分析，研究了含周期性椭圆孔二维结构的屈曲行为。针对不同的屈曲模态，建立理论模型进行模态分析。结果表明，改变孔的几何参数，椭圆孔结构的屈曲模态会随之发生转换，理论分析与数值结果吻合良好。此外，在数值模拟中，与位移加载不同，负压激励下的单胞需要考虑力边界条件的修正，以确保其满足完备性条件。已有工作在单胞选择中常存在问题，导致错误结果。针对上述问题研究了不同单胞所对应的边界条件，并结合有限结构进行了分析与讨论。
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| 关 键 词： | 负压激励 多孔高弹体 超材料 屈曲 |
| 收稿时间： | 2021-04-16 |
Buckling Behaviors of Elastomers With Periodic Elliptical Holes Under Negative Pressure Activation |
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| Affiliation: | School of Mechanical Engineering, Tianjin University, Tianjin 300350, P.R.China |
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| Abstract: | The buckling behaviors of 2D structures with periodic elliptical holes were studied through numerical simulations and theoretical analysis. A theoretical model was established for the modal analysis corresponding to different buckling modes. The analysis results indicate that, there is a transformation between the buckling modes of the 2D structure with elliptical holes, with the change of the geometrical parameters of the holes. The theoretical analysis and the numerical results match up. Furthermore, in the numerical simulation, a modified force boundary condition for a unit cell under negative pressure activation, being different from the displacement loading, should be considered to ensure the completeness conditions are fulfilled. The confusion in the application of appropriate boundary conditions for the unit cell will result in errors. The choice of the unit cell and the derivation of correct boundary conditions, combined with finite structures, were discussed. |
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