不可压缩弹性固体中的二维应力波分析
Two Dimensional Stress Wave Analysis in Incompressible Elastic Solids
-
摘要: 本文研究不可压缩弹性固体中的二维应力波.首先对一般的应变能函数给出了分析简单波和激波的基本方程,然后求出了波速和相应的本征向量,证明在一般情况下有两组简单波和两组激波,最后举了平面变形和反平面变形两个例子.在平面变形的情况下,平面激波的斜反射问题一般无解.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.
-
[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).
点击查看大图
计量
- 文章访问数: 2190
- HTML全文浏览量: 63
- PDF下载量: 570
- 被引次数: 0