| 姚伟岸,杨海天,高强.平面粘弹性问题的辛求解方法[J].计算力学学报,2010,27(1):14~20 |
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| 平面粘弹性问题的辛求解方法 |
| A new approach to solve plane viscoelastic problems in the symplectic space |
| 投稿时间：2007-11-09 |
| DOI：10.7511/jslx20101003 |
| 中文关键词: 粘弹性 Laplace变换 辛空间 分离变量 本征函数 |
| 英文关键词:viscoelasticity Laplace transformation symplectic space separation of variables eigenfunction |
| 基金项目:国家自然科学基金(10772039,10721062,10772035);973项目(2005CB321704);辽宁省中青年学术带头人基金资助项目. |
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| 中文摘要: |
| 将弹性力学辛对偶求解方法与Laplace变换相结合,提出了一个求解粘弹性平面问题的新方法。首先利用Laplace变换,将粘弹性平面问题转化为一个准弹性问题,在辛弹性力学的框架下,利用分离变量和辛本征展开法对其进行求解,然后由逆变换得到原问题的解。为证明方法的有效性,求解分析了矩形域平面粘弹性圣维南问题,得到了令人满意的结果。 |
| 英文摘要: |
| This paper presents a new approach solving the plane viscoelastic problem. The advantages of the symplectic solution are utilized to solve a quasi-elastic problem transformed from a viscoelastic one via the Laplace transformation. An inversion is carried out to convert solutions from elasticity to viscoelasticity. An analytical Saint Venant solution of the plane viscoelastic problem in a rectangular domain is given to illustrate the proposed approach. |
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