TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (8): 701-712.

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

唐之景¹, 丁启财², 李永池¹

1. University of Science and Technology of China, Hefei;
2. University of Illiaois at Chicage, U.S.A

收稿日期:1988-03-30 出版日期:1989-08-18 发布日期:1989-08-18

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

Tang Zhi-jing¹, T.C.T. Ting², Li Yong-chi¹

1. University of Science and Technology of China, Hefei;
2. University of Illiaois at Chicage, U.S.A

Received:1988-03-30 Online:1989-08-18 Published:1989-08-18

摘要/Abstract

摘要： Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.

Abstract: Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.

唐之景;丁启财;李永池. TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS[J]. Applied Mathematics and Mechanics (English Edition), 1989, 10(8): 701-712.

Tang Zhi-jing;T.C.T. Ting;Li Yong-chi. TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS[J]. Applied Mathematics and Mechanics (English Edition), 1989, 10(8): 701-712.

参考文献

[1] Chu,B.-T.,Finite amplitude waves in incompressible perfectly elastic materials,J.Mech.Phys.Solids,12(1964),45-57.
[2] Bland,D.R.,On shock waves in hyperelastic media,IUTAM Symp.on Second-Order Effects in Elasticity,Plasticity and Fluid Dynamics(1964),93-108.
[3] Bland,D.R.,Dilatalional waves and shock waves in large displacement isentropic dynamic elasticity,J.Mech.Phys.Solids,12(1964),245-267.
[4] Bland,D.R.,Plane isentropic large displacement simple waves in a compressible elastic solid,Z.Angew.Math.Phys.,16(1965),752-769.
[5] Davison,L.,Propagation of plane waves of finite amplitude in elastic solids,J.Mech.Phys.Solids,14(1966),247-270.
[6] Collins,W.D.,One-dimensional non-linear wave propagation in incompressible elastic materials,Q.J.Mech.Appl.Math.,19(1966),259-328.
[7] Howard,J.C.,Finite simple waves in a compressible transversely isotropic elastic solid,Q.J.Mech.Appl.Math.,19(1966),329-341.
[8] LI,Y.and T.C.T.Ting,Plane waves in simple elastic solids and discontinuous dependence of solution on boundary conditions.Inf.J.Solids Structures,19(1983),989-1008.
[9] Tang,Z.and T.C.T.Ting,Wave curves for the Riemann problem of plane waves in isotropic elastic solids,Int.J.Engngng.Sci.,25(1987),1343-1381.
[10] Li Y.and T.C.T.Ting,Simple waver,and shock waves generated by an incident shock wave in two-dimensional hyperelastic materials,J.Appl.Mech.,51(1984),586-594.
[11] Whilworth,A.W.,Simple waves in constrained elastic materials,Q.J.Mech.Appl.Math.,35(1982),461-484.
[12] Duszcyk,B.,S.Kosinski and Z.Wesolowski,Shock reflection patterns in a rubber-like material,Arch.Mech.,36(1984),587-602.
[13] Duszczyk,B.,S.Kosinski and Z.Wesolowski,Reflection of oblique shock waves in incompressible elastic solids,J.Austral Math.Soc.,B 27(1985),31-47.
[14] Wright,T.W.,Nonlinear waves in a rod:Results for incompressible elastic materials,Stud.Appl.Math..72(1985),149-160.
[15] Varley,E.,Simple waves in general elastic materials,Arch.Rat.Mech.Anal.,20(1965),309-328.
[16] Truesdell,C.and W.Noll,The non-linear field theory of mechanics,Handbuch der Pitysik,Vol 111/3,Springer-Verlag,Berlin(1965).
[17] Daformos,C.M.,Quasilinear hyperbolic systems that result from conservation laws,Nonlinear Waves.Ed.S.Leibovich and A.R.SeeBass,Cornell Univ.Press(1974),82-102.
[18] Lax,P.O.,Hyperbolic systems of conservation lawsⅡ,Commun.On Pure an d Appl.Math..10(1957),537-566.
[19] Tang,Z.,Wave curves for the Riemann problem of plane waves in simple isotropic elastic solids,Ph.D.Thesis,Univ.of Illinois at Chicago(1985).

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价