TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (5): 451-460.

TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

胡元太, 赵兴华

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

收稿日期:1994-01-15 修回日期:1994-10-05 出版日期:1995-05-18 发布日期:1995-05-18

TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

Hu Yian-tai, Zhao Xing-hua

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

Received:1994-01-15 Revised:1994-10-05 Online:1995-05-18 Published:1995-05-18

摘要/Abstract

摘要： The general and shnplified formula for anisotropic medium with a hyperbolic boundary subjected to pure bending M₀ is provided in this paper. The stress and strain fields in medium are obtained. Based upon the above results, we analyse the hoop stress along the hyperbolic curve and the stress distributions on the plane x₂=0 for aluminium (cubic crystal). When the boundary curve degenerates into an external crack three kinds of stress intensity factors (k₁, k₂, k₃) are obtained, and it is easily found that the first stress intensio, factor k₁ is independent of the material constants.

关键词: orthotropic rectangular thin plate with variable thickness, nonlinear unsymmetrical bending, equilibrium equation, compatibility equation, basic equation, dimensionless equation

Abstract: The general and shnplified formula for anisotropic medium with a hyperbolic boundary subjected to pure bending M₀ is provided in this paper. The stress and strain fields in medium are obtained. Based upon the above results, we analyse the hoop stress along the hyperbolic curve and the stress distributions on the plane x₂=0 for aluminium (cubic crystal). When the boundary curve degenerates into an external crack three kinds of stress intensity factors (k₁, k₂, k₃) are obtained, and it is easily found that the first stress intensio, factor k₁ is independent of the material constants.

Key words: orthotropic rectangular thin plate with variable thickness, nonlinear unsymmetrical bending, equilibrium equation, compatibility equation, basic equation, dimensionless equation

胡元太;赵兴华. TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(5): 451-460.

Hu Yian-tai;Zhao Xing-hua. TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(5): 451-460.

参考文献

[1] Chien Wei-zang and Yih Kai-yuan,Theroy of Elasticity,Science Press(1980).(in Chinese)
[2] G.P.Cherepanov,Mechanics of Brittle Fracture,McGraw-Hill Inc.(1979).
[3] S.G.Lekhnitskii,Theroy of Elasticity of an Anisotropic Body,MIR Moscow(1981).
[4] S.S.Wang and I.Choi,Boundary layer thermal stress in angle-ply composite laminates, Modern Developments in Composite Materials and Structures,ASME(Edited by J.R. Vinstor)(1979),315-341.
[5] J.D.Eshelby,W.T.Read and W.Shockley,Anisotropic elasticity with applications to dislocations theory,Acta Metallurgica,1(1953),251-259.
[6] A.N.Stroh,Dislocations and cracks in anisotropic elasticity,Phil.Mag,3(1958),625-646.
[7] A.N.Stroh,Steady state problems in anisotropic elasticity,J.Math.Phys.,41(1962), 7 7-103.
[8] D.M.Barnett,and J.Lothe,An image force theorem for dislocation in anisotropic bicrystals,J.Phys,F.,4(1974),1618-1635.
[9] D.M.Barnett,J.Lothe,K.Nishioka and R.J.Asaro,Elastic surface waves in anisotropic crystals:a simplified method for calculating Rayleigh velocities using dislocation theory,J,Phys.F.,3(1973),1083-1096.
[10] R.J.Asaro,J.P.Hirth,D.M.Barnett and J.Lothe,The elastic energy of a straight dislocation in an infinite anisotropic elastic medium,Phys.State.Sol.B.,60(1973),261-271.
[11] J.Lothe,and D.M.Barnett,On the existence of surface-wave solutions for anisotropic elastic half-space with free surface,J.Appl.Phys.,47(1976),428-433.
[12] P.Chadwick,and T.C.T.Ting,On the structure and invariance of the Barnett-Lothe tensors,Q.Appl.Math.,45(1987),419-427.
[13] T.C.T.Ting,Some identities and the structure of Ni in the Stroh formalism of anisotropic elasticity,Q.Appl.Math.,46(1988),109-120.
[14] T.C.T.Ting,The Stroh formalism and some invariable quantities in two-dimensional anisotropic elasticity,Advance in Mechanics,29.(1992),145-160.
[15] T.C.T.Ting,Line forces and dislocations in angularly inhomogeneous anisotropic elastic wedges and spaces,Q.Appl.Math.,47(1988),123-128.
[16] T.C.T.Ting,The critical angle of the anisotropic elastic wedge asubjected to uniform tractions,J.Elast.,20(1988),113-130.
[17] B.A.Auld,Acoustic Fields and Waves in Solhts,John Wiley(1973).
[18] G.C.Sih a.nd H.Liebowitz,Mathematical theory of Brittle fracture,An Advance Treatise on Fracture,2,ed.H.Leibowitz,Academic Press(1968),67-190.
[19] T.C.T.Ting,Barnett-Lothe tensors,and their associated tensors for monoclinic materials with the symmetryplane at x₃=0,J.Elast.,27(1992),143-165.

TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

编辑推荐

Metrics

本文评价

[1]	武秀根;郑百林;贺鹏飞;刘曙光. Equilibrium equations for 3D critical buckling of helical springs[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(8): 1049-1058.
[2]	施惟慧;沈春;王曰朋. Analytical solution of basic equations set of atmospheric motion[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(3): 385-385 .
[3]	黄家寅. UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 817-826.
[4]	黄家寅. BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 812-816.
[5]	汤昕燕. NEW SCALAR-TYPE EQUILIBRIUM EQUATIONS OF THE GENERAL SPACE FORCE SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(10): 1169-1176.
[6]	郑永刚;方铎;李桂芬. BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(9): 883-890.
[7]	吕恩琳. A NEW SOLUTION TO STRUCTURAL FUZZY FINITE ELEMENT EQUILIBRIUM EQUATIONS (SFFEEE)[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(4): 385-391.
[8]	黄民丰. COORDINATES OF PRINCIPAL STRESSES FOR ELASTIC PLANE PROBLEM[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(2): 157-162.
[9]	施惟慧. A STABILITY STUDY OF NAVIER-STOKES EQUATIONS (Ⅲ)[J]. Applied Mathematics and Mechanics (English Edition), 1994, 15(12): 1125-1130.