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非线性本构关系下两端固定多孔梁的大挠度弯曲变形
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Abstract:
本文以经典梁理论和非线性本构关系为基础，研究了两端固定多孔梁在不同的孔隙分布类型下受到外部均匀荷载作用的大挠度弯曲问题。首先设多孔梁的弹性模量与应变是线性函数关系，对非线性本构关系下多孔梁弯曲问题的基本方程进行了推导。采用打靶法计算出该边界条件下的多孔梁弯曲问题的数值解，分析非线性本构参数、载荷、孔隙率、孔隙分布类型对弯曲变形行为的影响。
Based on classical beam theory and nonlinear constitutive relationships, the large deflection bending problem of a fixed porous beam under different pore distribution types under external uniform loads was studied. Firstly, the elastic modulus and strain of porous beams are assumed to be a linear function relationship, and the basic equations for the bending problem of porous beams under nonlinear constitutive relationships are derived. The numerical solution of the bending problem of porous beam under this boundary condition is calculated by shooting method, and the effects of nonlinear constitutive parameters, load, porosity and pore distribution type on bending deformation behavior are analyzed.
| [1] | 滕兆春, 马铃权. 热环境中多孔功能梯度材料转动Timoshenko梁的自由振动特性分析[J]. 兰州理工大学学报, 2022, 48(6): 164-171. |
| [2] | 杨静宁, 王永祥, 唐健. 热机载荷下形状记忆合金梁超静定问题分析[J]. 兰州理工大学学报, 2021, 47(1): 158-163. |
| [3] | Ambartsumyan, S.A. 不同弹性模量理论[M]. 邬瑞锋, 张允真, 译. 北京: 中国铁道出版社, 1986. |
| [4] | 张鹏, 范存新. 四边固支的双模量矩形板的弯曲计算[J]. 常州工学院学报, 2015, 28(6): 1-6. |
| [5] | 王康建, 赵永刚, 王铭慧, 等. 拉压弹性模量不等材料杆的过屈曲分析[J]. 甘肃科学学报, 2014, 26(6): 19-22. |
| [6] | Fraternali, F., Spadea, S. and Ascione, L. (2013) Buckling Behavior of Curved Composite Beams with Dif-ferent Elastic Response in Tension and Compression. Composite Structures, 100, 280-289.
https://doi.org/10.1016/j.compstruct.2012.12.021 |
| [7] | 蔡来生, 俞焕然. 拉压模量不同弹性物质的本构[J]. 西安科技大学学报, 2009, 29(1): 17-21. |
| [8] | 穆琳, 胡宝庆, 凌雷, 等. 拉压弹性模量不等材料简支梁在横向载荷作用下的线性振动问题[J]. 甘肃科学学报, 2013, 25(4): 105-107. |
| [9] | 吴晓, 杨立军. 双模量泡沫铝芯夹层梁的弯曲计算分析[J]. 应用力学学报, 2015, 32(6): 922-927, 1098. |
| [10] | 马连生, 贾金政. 机械载荷作用下功能梯度梁的过屈曲分析[J]. 兰州理工大学学报, 2020, 46(3): 160-164. |
| [11] | 张靖华, 司成龙, 马浩. 石墨烯增强功能梯度梁自由振动的解析解[J]. 兰州理工大学学报, 2023, 49(2): 49-55. |
| [12] | 雷芳明. 四边简支功能梯度石墨烯增强复合材料厚板的自由振动分析[J]. 兰州理工大学学报, 2023, 49(4): 166-172. |
| [13] | 曲昭霞, 赵永刚, 秦慧峰. 非线性本构关系下两端固定梁的弯曲变形[J]. 甘肃科学学报, 2020, 32(1): 1-4. |
| [14] | Lei, Y.-L., Gao, K., Wang, X.W. and Yang, J. (2020) Dynamic Behaviors of Single- and Multi-Span Functionally Graded Porous Beams with Flexible Boundary Constraints. Applied Mathematical Modelling, 83, 754-776.
https://doi.org/10.1016/j.apm.2020.03.017 |
| [15] | Fang, W.H., Yu, T.T., Lich, L.V. and Bui, T.Q. (2019) Analysis of Thick Porous Beams by a Quasi-3D Theory and Isogeometric Analysis. Composite Structures, 221, 110890. https://doi.org/10.1016/j.compstruct.2019.04.062 |
