| 非线性弹性大变形问题的率型解法 |
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| 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. |
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| 作者姓名： | 梁非 张善元 |
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| 作者单位： | 太原工业大学 |
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| 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．
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| 关 键 词： | 非线性弹性，次弹性，大变形，应力率张量 |
A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity |
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| 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. |
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| Authors: | Liang Fei Zhang Shan-yuan |
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| Abstract: | In this paper,we obtain the rate-type constitutive expressions of the nonlinear isotropic elasticity by using the Jaumann,Trucsdell and Green-Naghdi stress rate respectively.Through an alysing the simple shear deformation for Mooney-Rivlin material,three kinds of rate-type constitutive equations are verified to be equivalent to the original equation,Rate-type variational principles are also presented.and the Ritz method is used to obtain the numerical solution of a rec-tangular rubber membrane under uniaxial stretch. |
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| Keywords: | nonlinear elasticity hypoelasticity large deformation stress rate tensor |
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