|
|
精确几何模型下杆的压弯大变形
|
Abstract:
采用精确的几何模型，研究了一端固定一端自由约束的细长弹性杆在外部荷载作用下的压弯变形问题。在大变形过程中的精确几何关系下，建立几何方程和平衡方程，建立机械荷载作用下弹性压弯杆几何精确的大变形基本方程。采用打靶法数值对该边值问题进行求解，获得了在数值意义下问题的精确解。绘出该模型下弹性杆的压弯大变形特性曲线。研究外部载荷对弹性杆弯曲大变形的影响，分析压弯杆的力学特性。
Based on accurate geometric model, the large deformation of a rod with free-fixed edges subjected to compress and bending moment loads was studied. Considering the precise geometric relation-ships across the deformation process, the geometric equations and equilibrium equations were es-tablished, and the basis equations of exact geometry under large deformation with linear constitu-tive relationship were established. Using shooting method to numerically solve the boundary value problem, the exact solution in the numerical sense was obtained, and the characteristic figures of the elastic large deformation with compress and bending moment loads were drawn, the influence of the large deformation elastic rod with external load was studied, and the mechanical characteris-tics of the rod were analyzed.
| [1] | 刘延柱. 弹性杆基因模型的力学问题[J]. 力学与实践, 2003(1): 1-5. |
| [2] | 刘延柱. 超大变形弹性细杆几何形态的拓扑描述[J]. 力学与实践, 2004, 26(5): 68-70. |
| [3] | Euler, L. (1744) Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes. |
| [4] | Love, A.E.H. (1927) A Treatise on the Mathematical Theory of Elasticity. Dover, New York. |
| [5] | Lagrange, J.L. (1970) Oeuvres de Lagrange. Readex Microprint, New York. |
| [6] | Pfluger, A. (1964) Stabilit？ts probleme der Elastostatik. Springer, Berlin. https://doi.org/10.1007/978-3-662-25023-5 |
| [7] | Atanackovic, T.M. (1989) Stability of a Compressible Elastic Rod with Imperfections. Acta Mechania, 76, 203-222.
https://doi.org/10.1007/BF01253580 |
| [8] | Gummadi, L. and Palazotto, A.N. (1998) Large Strain Analysis of Beams and Arches Undergoing Large Rotations. International Journal of Non-Linear Mechanics, 33, 615-645. https://doi.org/10.1016/S0020-7462(97)00033-4 |
| [9] | Filpich, C.P. and Rosales, M.B. (1994) Contribution to the Study of the Static Postbuckling of Elastic Columns. Proceedings of the XVI Jornadas Argentinas de Ingeniería Estruc-tural, Vol. I, 197-212. |
| [10] | Filpich, C.P. and Rosales, M.B. (2000) A Further Study on the Postbuckling of Extensible Elastic Rods. International Journal of Non-Linear Mechanics, 35, 997-1022. https://doi.org/10.1016/S0020-7462(99)00076-1 |
| [11] | Plaut, R.H., Suherman, S., et al. (1999) Deflections and Buckling of a Bent Elastica in Contact with a Flat Surface. International Journal of Solids & Structures, 36, 1209-1229. https://doi.org/10.1016/S0020-7683(97)00348-X |
| [12] | 薛纭, 翁德玮. 轴线存在应变时弹性杆力学的两个概念[J]. 力学与实践, 2011, 33(5): 65-67. |
| [13] | 刘延柱, 薛纭, 等. 关于弹性梁的数学模型[J]. 力学与实践, 2011, 33(1): 74-77. |
| [14] | 李世荣, 李中明. 压杆过屈曲分析中轴线无伸长假设的定量讨论[J]. 兰州大学学报: 自然科学版, 1997, 33(4): 42-46. |
| [15] | 李世荣, 杨静宁. 可伸长变截面杆的弹性过屈曲模型及其数值解[J]. 计算力学学报, 2000, 17(1): 114-118. |
| [16] | Li, S.R. and Batra, R.C. (2007) Thermal Buckling and Postbuckling of Euler Bernoulli Beams Supported on Nonlinear Elastic Foundations. AIAA Journal, 45, 712-720. https://doi.org/10.2514/1.24720 |
| [17] | 郭锐, 李世荣, 张靖华. 点间隙约束下轴向受压弹性梁的过屈曲[J]. 甘肃科学学报, 2010, 22(4): 96-99. |
| [18] | 李银山, 刘波, 潘文波, 等. 弹性压杆的大变形分析[J]. 河北工业大学学报, 2011, 40(5): 31-35. |
| [19] | 薛纭, 王鹏. 弹性细杆弯扭度有突变时的Lagrange方程[J]. 动力学与控制学报, 2019, 17(5): 473-477. |
| [20] | 刘荣刚, 边文凤, 李素超, 刘伟, 金松波. 理想弹性杆临界挠度的确定[J]. 力学与实践, 2020, 42(4): 116-118. |
