有限变形下理想刚-塑性体动力学中的两个间断定理
Two Theorems Concerning Discontinuities in Dynamics of Rigid-Perfectly Plastic Continua under Finite Deformation
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摘要: 本文推广了文献[1]中的结论,在有限变形下证明了理想刚-塑性动力学中的两个间断定理,即证明了刚-塑性交界面上面力的连续性以及当刚-塑性交界面的运动方向是由塑性区向刚性区扩展时界面上变形率的连续性.此结论也适用于不忽略剪切变形和转动惯量的梁、板、壳结构.Abstract: In this paper the results of ref [1] are gentralized. Two theorems concerning discontimsities in dynemics of rigid-perfectly plastic continua under finite deformation are proved, namely: i) the traction on the interface between the rigid and the plastic regions is contineous and ii) when the interface moves from the plastic region into the rigid region, the rate of deformation is continuous too. These conclusions can also be applied to structures such as beams, pletes and shells in which the shear deformation and rotatory inertia are considered.
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[1] 黄筑平,理想刚-塑性动力分析中的间断性质,力学学报.5 (1983), 500-508. [2] Thomas,T.Y.,The general theory of compatibility conditions.Int.J.Engng.Sci.4.3(1966).207-233. [3] Hill,R.,Discontinuity relations in mechanics of solids,Progress in Solid Mechanics.2(1961).247-276. [4] Thomas.T.Y.,Plastic Flow and Fractures in Solids.Academic Press.New York(1961). [5] 金泉林.理想刚-塑性Timoshenko梁动力响应的分析解,力学学报,16, 5(1984),504-511. [6] Jones.N.and J.G.de Oliveira.The influence of rotatory inertia and transverse shear on the dynamic plastic behavior of beams J.Appl.Mech.46(1979).303-310. [7] Jones.N.and J.G.de Oliveira.Dynamic plastic response of circular plates with transverse shear and rotatory inertia.J.Appl.Mech.47(1980).27-34. [8] Jones.N.and J.G.de Oliveira,Impulsive loading of a cylindrical shell with transverse shear and rotatory inertia,Int.J.Solids Structures 19.3(1983) 263-279． -
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