Stress Field of Orthotropic Cylinder Subjected to Axial Compression
-
摘要: 基于材料体积不可压假设,对轴向压缩作用下圆柱试件在加载面内的环向和径向应力分布进行理论分析,计算结果表明:当试件材料本构为正交各向异性时,环向和径向应力分布为半径的幂函数形式;试件材料为横观各向同性时,环向和径向应力为半径的二次函数.在圆柱试件轴线上环向和径向应力相等,且均具有最大值;试件圆周边界上径向应力为0,环向应力具有极小值.通过最大拉伸应变破坏理论对试件环向应变进行分析,获得了产生环向拉伸破坏时的临界轴向载荷;并采用Hill-蔡强度理论对试件圆周边界上计算得到的应力参量进行描述,得到了轴压作用下圆柱试件的Hill-蔡强度理论表达式,其不仅取决于轴向应力和试件材料的基本力学性能,还与试件轴向变形的应变率及应变率随时间的变化率相关.Abstract: Based on the material volume cons tancy hypothesis, circum ference and radial stresses of cylinder specmien were analyzed when the cylinder is loaded along the axial direction. Circum ference and radial stress distribution is radius parameter power function when specimen material constitutive relation is orthotropic. The stress distribution is radius parameter quadratic function for transverse isotropy material. A long the cylinder axial line, circum ference and radial stresses were maxmium and equal to each other. In the circum ference boundary surface, radial stress is zero and circum ference stress value is the minmium. The maxtensile circumference strain failure theory is applied to calculate critical axial loading. Circum ference boundary layer failure criterion of orthotropic material cylinder is described by HillTsai strength theory. The obtained strength theory is not only related to axial stress and specmien materialm echanical properties, but a lso to specmienaxial de formation strain rate and change rate of strain rate.
-
Key words:
- ortho tropic /
- axial compression /
- axial symmetry /
- stress distribution /
- strain rate
-
[1] Cazacu O, Plunkett B, Barlat F. Orthotropic yield criterion for hexagonal closed packed metals[J]. International Journal of Plasticity, 2006, 22(7): 1171-1194. doi: 10.1016/j.ijplas.2005.06.001 [2] Plunkett B, Cazacu O, Barlat F. Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals[J]. International Journal of Plasticity, 2008, 24(5): 847-866. doi: 10.1016/j.ijplas.2007.07.013 [3] 曾纪杰, 傅衣铭. 正交各向异性圆柱壳的弹塑性屈曲分析[J]. 工程力学, 2006, 23(10): 25-29. [4] Abd-Alla A M, Farhan A M. Effect of the non-homogenity on the composite infinite cylinder of orthotropic material[J]. Physics Letters A, 2008, 372(6): 756-760. doi: 10.1016/j.physleta.2007.08.029 [5] 田燕萍, 傅衣铭. 考虑损伤效应的正交各向异性板的弹塑性后屈曲分析[J]. 应用数学和力学, 2008, 29(7): 764-774. [6] Jeffrey E B, Ellen M A, Karl G. Finite element simulations of orthotropic hyperelasticity[J]. Finite Elements in Analysis and Design, 2002, 38(10): 983-998. doi: 10.1016/S0168-874X(02)00089-6 [7] Romashchenko V A, Tarasovskaya S A. Numerical studies on the dynamic behavior of multilayer thick-walled cylinders with helical orthotropy[J]. Strength of Materials, 2004, 36(6): 621-629. doi: 10.1007/s11223-005-0008-z [8] Redekop D. Buckling analysis of an orthotropic thin shell of revolution using differential quadrature[J]. International Journal of Pressure Vessels and Piping, 2005, 82(8): 618-624. doi: 10.1016/j.ijpvp.2005.02.003 [9] Grigorenko Y M, Rozhok L S. Influence of orthotropy parameters on the stress state of hollow cylinders with elliptic cross-section[J]. International Applied Mechanics, 2007, 43(12): 1372-1379. doi: 10.1007/s10778-008-0008-3 [10] Xu H M, Yao X F, Feng X Q, et al. Fundamental solution of a power-law orthotropic and half-space functionally graded material under line loads[J]. Composites Science and Technology, 2008, 68(1): 27-34. doi: 10.1016/j.compscitech.2007.05.041 [11] Emery T R, Dulieu-Barton J M, Earl J S, et al. A generalised approach to the calibration of orthotropic materials for thermoelastic stress analysis[J]. Composites Science and Technology, 2008, 68(3/4): 743-752. doi: 10.1016/j.compscitech.2007.09.002 [12] Capsoni A, Corradi L, Vena P. Limit analysis of orthotropic structures based on Hill’s yield condition[J]. International Journal of Solids and Structures, 2001, 38(22/23): 3945-3963. doi: 10.1016/S0020-7683(00)00241-9 [13] Valot E, Vannucci P. Some exact solutions for fully orthotropic laminates[J]. Composite Structures, 2005, 69(2): 157-166. doi: 10.1016/j.compstruct.2004.06.007 [14] Ma G W, Gama B A, Gillespie J W, Jr. Plastic limit analysis of cylindrically orthotropic circular plates[J]. Composite Structures, 2002, 55(4): 455-466. doi: 10.1016/S0263-8223(01)00174-X [15] Shipsha A, Berglund L A. Shear coupling effects on stress and strain distributions in wood subjected to transverse compression[J]. Composites Science and Technology, 2007, 67(7/8): 1362-1369. doi: 10.1016/j.compscitech.2006.09.013 [16] Mackenzie-Helnwein P, Mullner H W, Eberhardsteiner J, et al. Analysis of layered wooden shells using an orthotropic elasto-plastic model for multi-axial loading of clear spruce wood[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(21/24): 2661-2685. doi: 10.1016/j.cma.2004.07.051 [17] Lyons C K. Stress functions for a heterogeneous section of a tree[J]. International Journal of Solids and Structures, 2002, 39(18): 4615-4625. doi: 10.1016/S0020-7683(02)00381-5 [18] Lyons C K, Guenther R B, Pyles M R. Elastic equations for a cylindrical section of a tree[J]. International Journal of Solids and Structures, 2002, 39(18): 4773-4786. doi: 10.1016/S0020-7683(02)00373-6 [19] Galicki J, Czech M. Tensile strength of softwood in LR orthotropy plane[J]. Mechanics of Materials, 2005, 37(6): 677-686. doi: 10.1016/j.mechmat.2004.07.001 [20] 徐卫亚, 张贵科. 节理岩体正交各向异性等效强度参数研究[J]. 岩土工程学报, 2007, 29(6): 806-810. [21] 徐芝纶. 弹性力学[M]. 北京: 高等教育出版社, 1990,93-97.
点击查看大图
计量
- 文章访问数: 1581
- HTML全文浏览量: 113
- PDF下载量: 991
- 被引次数: 0