| 非线性粘弹性梁弯曲问题的新算法 |
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| 引用本文： | 张锋伟,张能辉,占海艺.非线性粘弹性梁弯曲问题的新算法[J].兰州大学学报(自然科学版),2002,38(2):37-41. |
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| 作者姓名： | 张锋伟 张能辉 占海艺 |
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| 作者单位： | 1. 甘肃农业大学,机电工程系,甘肃,兰州,730070
2. 上海大学,力学系,上海,200436 |
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| 基金项目： | 上海市教育发展基金 (99A0 1)，上海市博士后基金 (1999年度 )资助项目 |
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| 摘 要： | 首先从松弛型的非线性 L eaderman本构关系出发 ,利用线性几何假设 ,建立了非线性粘弹性梁弯曲问题的数学模型 ;其次 ,利用 L aplace变换法证明了非线性粘弹性梁问题与非线性弹性梁问题之间存在着某些对应关系 .对应关系为粘弹性梁的求解提供了一种新的思路 ,利用这些关系可直接从相应弹性问题获得粘弹性问题的部分响应 ,与传统的时域有限差分法相比 ,计算时间明显缩短
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| 关 键 词： | 非线性粘弹性 对应关系 积分型本构理论 梁 |
| 文章编号： | 0455-2059(2002)02-0037-05 |
| 修稿时间： | 2001年9月18日 |
A new method for bending problems of nonlinear viscoelastic beam |
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| ZHANG Feng-wei ,ZHANG Neng-hui ,ZHAN Hai-yi.A new method for bending problems of nonlinear viscoelastic beam[J].Journal of Lanzhou University(Natural Science),2002,38(2):37-41. |
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| Authors: | ZHANG Feng-wei ZHANG Neng-hui ZHAN Hai-yi |
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| Institution: | ZHANG Feng-wei 1,ZHANG Neng-hui 2,ZHAN Hai-yi 2 |
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| Abstract: | In this paper, firstly, based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for bending problems of nonlinear viscoelastic beams is set up. Secondly, the Laplace transformation method is used to prove that some relations exist between solutions for bending problems of viscoelastic and elastic beams. The corresponding relations provide a new method for solving viscoelastic problems. Part of responses of viscoelastic problems could be obtained directly from the corresponding elastic ones by these relations. Compared with the traditional finite difference method in the time domain, the computational time is greatly shortened. |
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| Keywords: | nonlinear viscoelasticity corresponding relation integral-type constitutive theory beam |
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