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非线性弹性大变形问题的率型解法

梁非 张善元

梁非, 张善元. 非线性弹性大变形问题的率型解法[J]. 应用数学和力学, 1994, 15(2): 121-128.
引用本文: 梁非, 张善元. 非线性弹性大变形问题的率型解法[J]. 应用数学和力学, 1994, 15(2): 121-128.
Liang Fei, Zhang Shan-yuan. A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity[J]. Applied Mathematics and Mechanics, 1994, 15(2): 121-128.
Citation: Liang Fei, Zhang Shan-yuan. A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity[J]. Applied Mathematics and Mechanics, 1994, 15(2): 121-128.

非线性弹性大变形问题的率型解法

A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity

  • 摘要: 本文分别采用Jaumann应力率、Truesdell应力率和Green-Naghdi应力率导出了非线性各向同性弹性体的率型本构表达形式,通过对Mooney-Rivlin材料的简单剪切大变形分析表明,三种率型的本构关系均与全量本构关系相等价。文中还给出了相应的率型变分原理,并采应Ritz法,数值求解了受单轴拉伸的矩形橡皮薄膜的大变形问题。
  • [1] Truesdall, C., Hypo-elasticity, J. Rational Mech, Anal., 4(1955), 83-133.
    [2] Truesdell, C. and W. Noll, Hunduch der Physik, Ⅲ/3, Springer-Verlag(1965)
    [3] Dienes, J. K., On the analysis of rotation and stress rate in deforming bodies, Acta Mech., 32, 2(1979), 217-232
    [4] 李松年、黄执中.《非线性连续统力学》,北京航空学院出版社(1987), 390-401
    [5] Oden, J. T. and D. R. Bhandri. Variational principle in nonlinear viscoelasticity, Int. J. Solids Struct., 8(1972), 1017-1026.
    [6] Hill, R., Some basic principle in the mechanics of solids without a nature time, J. Mech.Phys. Solids, 7(1959), 209-225.
    [7] 张善元.率型的广义变分原理.因体力学学报.(4) (1991), 117-126
    [8] Oden, J. T. and T. Sato, Finite strains and displacement of elastic membranes by the finite element method, Int. J. Solids Structures, 3(1967), 471-488.
    [9] Feng, W. W. and J. T. Tielking, Large plane deformations of rectangular elastic sheets, ZAMP, 27(1976),781-789.
    [10] Tielking, J. T. and W. W. Feng, The application of the minimum potential energy principle to nonlinear axisymmetric membrane problems, J. Appl. Mech., 41(1976),491-497.
    [11] Szabó, Lãszlo and Mihãly Balla, Comparison of some stress rates, Int. J. Solids Struct., 25(1989), 279-297.
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出版历程
  • 收稿日期:  1992-09-09
  • 刊出日期:  1994-02-15

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