Solutions of the Plane-Strain Problems in a Power Hardening and Incompressible Material

Lin Bai-song

Volume 5 Issue 5

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1984 > 5(5): 723-730

Lin Bai-song. Solutions of the Plane-Strain Problems in a Power Hardening and Incompressible Material[J]. Applied Mathematics and Mechanics, 1984, 5(5): 723-730.

Citation:

Lin Bai-song. Solutions of the Plane-Strain Problems in a Power Hardening and Incompressible Material[J]. Applied Mathematics and Mechanics, 1984, 5(5): 723-730.

Citation:

Lin Bai-song. Solutions of the Plane-Strain Problems in a Power Hardening and Incompressible Material[J]. Applied Mathematics and Mechanics, 1984, 5(5): 723-730.

PDF( 415 KB)

Solutions of the Plane-Strain Problems in a Power Hardening and Incompressible Material

Lin Bai-song

Central-South Institute of Mining and Metallurgy, Changsha

Received Date: 1983-09-09
Publish Date: 1984-10-15

Abstract

Abstract

According to Iliushin's small elastic-plastic deformation theory,in this paper,we derive the basic equations of plane-strain problems in a power hardening and incompressible material.In addition,this paper presents two methods to solvethese basic equations,i.e. the displacement function_stress method and the stress function_strain method. Twoexamples have been calculated to illustrate the application of these two methods.

FullText(HTML)

References(4)

References

[1]	Соколовский В.В.,Теорця Плсмцчкосмц,Москва,(1950).
[2]	Rice,J.R.,et al.,Plane strain deformation near a crack tip in a power-law hardening material,J.Mech.Phys.Solids 16,1(1968),1-12.
[3]	Hutchinson,J.W.,Singularbehaviour at the end of a tensile crack in a hardening material,J.Mech.Phys.Solids,16,1(1968),13-31.
[4]	Hutchinson,J.W.,Plastic stress and strain fields at a crack tip,J.Mech.Phys.Solids,16,5(1968),337-347．

Relative Articles

[1]	WANG Bin, ZHOU Yanping, BIE Qunyi. Energy Conservation of the 4 D Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2023, 44(8): 999-1006. doi: 10.21656/1000-0887.430370
[2]	QIU Zhouhua, ZENG Zhong, LIU Hao. A P_N×P_N-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289
[3]	CHEN Yafei, ZHENG Yunying. A Discontinuous Galerkin FEM for 2D Navier-Stokes Equations of Incompressible Viscous Fluids[J]. Applied Mathematics and Mechanics, 2020, 41(8): 844-852. doi: 10.21656/1000-0887.400379
[4]	WU Feng, SUN Yan, ZHONG Wan-xie. Inter-Belt Finite Element for the Analysis of Incompressible Material Problems[J]. Applied Mathematics and Mechanics, 2013, 34(1): 1-9. doi: 10.3879/j.issn.1000-0887.2013.01.001
[5]	S.Tariverdilo, J.Mirzapour, M.Shahmardani, Gh.Rezazadeh. Free Vibration of Membrane/Bounded Incompressible Fluid[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1091-1101. doi: 10.3879/j.issn.1000-0887.2012.09.006
[6]	YUAN Xue-gang, ZHANG Wen-zheng, ZHANG Hong-wu, ZHU Zheng-you. Stability Analysis of Radial Inflation of Incompressible Composite Rubber Tubes[J]. Applied Mathematics and Mechanics, 2011, 32(3): 286-292. doi: 10.3879/j.issn.1000-0887.2011.03.005
[7]	YUAN Xue-gang, ZHANG Hong-wu, REN Jiu-sheng, ZHU Zheng-you. Some Qualitative Properties of Incompressible Hyperelastic Spherical Membranes Under Dynamic Loads[J]. Applied Mathematics and Mechanics, 2010, 31(7): 860-867. doi: 10.3879/j.issn.1000-0887.2010.07.011
[8]	ZHANG Yong-ming, ZHOU Heng. PSE as Applied to Problems of Transition in Compressible Boundary Layers[J]. Applied Mathematics and Mechanics, 2008, 29(7): 757-763.
[9]	YUAN Xue-gang, ZHU Zheng-you, CHENG Chang-jun. Qualitative Analysis of Dynamical Behavior for an Imperfect Incompressible Neo-Hookean Spherical Shell[J]. Applied Mathematics and Mechanics, 2005, 26(8): 892-898.
[10]	WEN Gong-bi, CHEN Zuo-bin. Unsteady/Steady Numerical Simulation of Three-Dimensional Incompressible Navier-Stokes Equations on Artificial Compressibility[J]. Applied Mathematics and Mechanics, 2004, 25(1): 53-66.
[11]	MENG Qing-guo. Analytic Solutions of Incompressible Laminar Flow in the Inlet Region of a Pipe[J]. Applied Mathematics and Mechanics, 2004, 25(8): 815-818.
[12]	Sun Jian'an, Zhu Zhengyou. A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1259-1266.
[13]	Wang Zhenqing, Shi Shouxia. Stress-Strain Field near the Crack-Tip of an Incompress Rubber-Like Material[J]. Applied Mathematics and Mechanics, 1996, 17(8): 721-727.
[14]	Huang Dun, Yang Chun. Numerical Modeling of the lnitial Stage of the Generation of Unsteady Vortices from Sharp Corner in Plane Compressible Flow[J]. Applied Mathematics and Mechanics, 1994, 15(8): 665-670.
[15]	Shi Zhi-fei, Gao Yu-chen. The Plane Stress Crack-Tip field for an Incompressible Rubber Material[J]. Applied Mathematics and Mechanics, 1994, 15(5): 471-477.
[16]	Guo Ben-yu, Cao Wei-ming. Spectral-Finite Element Method for Compressible Fluid Flow[J]. Applied Mathematics and Mechanics, 1992, 13(8): 677-692.
[17]	Wang Zi-kun, Wei Xue-xia, Gao Xin-liu. Solution of the Plane Stress Problems of Strain-Hardening Materials Described by Power-Law Using the Complex Pseudo-Stress Function[J]. Applied Mathematics and Mechanics, 1991, 12(5): 455-464.
[18]	Tang Zhi-jing, T. C. T. Ting, Li Yong-chi. Two Dimensional Stress Wave Analysis in Incompressible Elastic Solids[J]. Applied Mathematics and Mechanics, 1989, 10(8): 669-678.
[19]	Yuan Yi-wu. A New Approximate Analytical Solution of the ideal Potential Flow around a Circular Cylinder between Two Parallel Flat Plates[J]. Applied Mathematics and Mechanics, 1988, 9(1): 63-71.
[20]	Lia Tong-ji, Pu Qun. An Exact Solution for Incompressible Flow Through a Two-Dimensional Laval Nozzle[J]. Applied Mathematics and Mechanics, 1986, 7(6): 487-495.