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负压激励下含椭圆孔高弹体的屈曲分析

梁观坡 傅禹鑫 娄本亮 谢宇新

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 doi: 10.21656/1000-0887.420100
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 doi: 10.21656/1000-0887.420100
LIANG Guanpo, FU Yuxin, LOU Benliang, XIE Yuxin. Buckling Behaviors of Elastomers With Periodic Elliptical Holes Under Negative Pressure Activation[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1221-1228. doi: 10.21656/1000-0887.420100
Citation: LIANG Guanpo, FU Yuxin, LOU Benliang, XIE Yuxin. Buckling Behaviors of Elastomers With Periodic Elliptical Holes Under Negative Pressure Activation[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1221-1228. doi: 10.21656/1000-0887.420100

负压激励下含椭圆孔高弹体的屈曲分析

doi: 10.21656/1000-0887.420100
基金项目: 国家自然科学基金(12072225; 11532001; 11991031; 11991032; 12021002)
详细信息
    作者简介:

    梁观坡(1995—),男,硕士生 (E-mail:254092944@qq.com)

    谢宇新(1974—),男,副教授,博士 (通讯作者. E-mail:xyx@tju.edu.cn)

  • 中图分类号: O343.9

Buckling Behaviors of Elastomers With Periodic Elliptical Holes Under Negative Pressure Activation

  • 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。

  • 图  1  二维正方排布椭圆孔周期结构的不同单胞取法

    Figure  1.  Various methods of selecting unit cells for the periodic structure with elliptical holes in 2D tetragonal lattice arrangement

    图  2  单胞a、单胞b与修正后的单胞b在负压加载下的临界压力

    Figure  2.  Critical pressures of unit cell a, unit cell b and modified unit cell b under the negative pressure

    图  3  单胞a与单胞b在单轴位移加载下的临界应变

    Figure  3.  Critical strains of unit cell a and unit cell b under the loading of uniaxial displacement

    图  4  有限结构与单胞a在条带截面的法向合力

    Figure  4.  Normal resultant forces of the finite structure and unit cell a at the strip section

    图  5  有限结构大小对其临界力的影响

    Figure  5.  The influence of the finite structure size on its critical force

    图  6  单胞a与单胞b在条带截面的法向合力

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  6.  Normal resultant forces of unit cell a and unit cell b at the strip section

    图  7  后屈曲变形的数值结果

    Figure  7.  Numerical results of post-buckling deformation

    图  8  后屈曲变形的理论模型

    Figure  8.  Theoretical models for post-buckling deformation

    图  9  周期性多孔高弹体

    Figure  9.  The periodic porous elastomer

    图  10  理论临界压力与数值模拟结果的比较

    Figure  10.  Comparison of theoretical critical pressures and numerical simulation results

    图  11  椭圆孔周期结构的单胞屈曲模式相图

    Figure  11.  The phase diagram of unit cell buckling modes in the periodic structure with elliptical holes

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  • 被引次数: 0
出版历程
  • 收稿日期:  2021-04-16
  • 录用日期:  2021-04-16
  • 修回日期:  2021-05-10
  • 网络出版日期:  2021-12-31
  • 刊出日期:  2021-12-01

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