辛求解体系下功能梯度材料平面梁的完整解析解

赵莉; 陈伟球; 吕朝锋

doi:10.3879/j.issn.1000-0887.2012.10.001

辛求解体系下功能梯度材料平面梁的完整解析解

doi: 10.3879/j.issn.1000-0887.2012.10.001

1.
宁波工程学院建筑工程学院,浙江宁波 315016;
浙江大学工程力学系,杭州 310027;
浙江大学土木系,杭州 310058

基金项目: 国家自然科学基金资助项目（11202111; 11090333; 10972193）;宁波市自然科学基金资助项目（2011A610077）

详细信息

通讯作者:
赵莉(1982-),女,山东人,讲师,博士 (Tel:+86-574-87080435; E-mail: zhaoli06@zju.edu.cn);吕朝锋(1978-),浙江人, 副教授,博士生导师(联系人.Tel: +86-571-88208473; E-mail: lucf@zju.edu.cn).

中图分类号: O343.1;O343.7
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- 文章访问数: 1699
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出版历程
- 收稿日期: 2012-01-18
- 修回日期: 2012-03-21
- 刊出日期: 2012-10-15

Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework

1.
¹Department of Civil Engineering, Ningbo University of Technology, Ningbo, Zhejiang 315016, P.R.China;²Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, P.R.China;³Department of Civil Engineering, Zhejiang University, Hangzhou 310058, P.R.China

摘要

摘要: 采用辛弹性力学解法，求取弹性模量沿轴向指数变化，而Poisson比保持不变的功能梯度材料平面梁的完整解析解．通过求解被Saint-Venant原理覆盖的一般本征解，建立起完整的解析分析过程，进而给出平面梁位移和应力的精确分布规律．传统的弹性力学分析方法常常忽略被Saint-Venant原理覆盖的解，但这些衰减的本征解对材料的局部效应起着较大的影响作用，可能导致材料或结构的突然失效．采用辛求解方法，充分利用本征向量之间的辛共轭正交关系，得到了功能梯度材料梁的完整解析解．两个数值算例分别将功能梯度材料平面梁的位移和应力分布与相应均匀材料情形的结果进行比较，研究了材料非均匀性对位移和应力解的影响．
- 功能梯度材料 /
- 精确解 /
- 本征展开 /
- 辛弹性力学
Abstract: Exact solutions for generally supported functionally graded plane beams were given within the framework of symplectic elasticity. The Young’s modulus was assumed to vary exponentially along the longitudinal direction while Poisson’s ratio remained constant. The state equation with a shiftHamiltonian operator matrix had been established in our previous work, but limited to the SaintVenant solution. Here it was presented that a complete rational analysis of the displacement and stress distributions in the beam by exploring the eigensolutions which were usually covered up by the SaintVenant principle. These solutions played a significant role on local behavior of materials that was usually ignored by the conventional elasticity methods but may be crucial to the failure of the materials/structures. The analysis made full use of symplectic orthogonality of the eigensolutions. Two illustrative examples were presented to compare the displacement and stress results with those for homogenous materials, and to demonstrate the effect of material inhomogeneity.
- functionally graded materials /
- exact solutions /
- expansion of eigenfunctions /
- symplectic elasticity

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参考文献(27)

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辛求解体系下功能梯度材料平面梁的完整解析解

doi: 10.3879/j.issn.1000-0887.2012.10.001

通讯作者:
赵莉(1982-),女,山东人,讲师,博士 (Tel:+86-574-87080435; E-mail: zhaoli06@zju.edu.cn);吕朝锋(1978-),浙江人, 副教授,博士生导师(联系人.Tel: +86-571-88208473; E-mail: lucf@zju.edu.cn).

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Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework

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目录

留言板

辛求解体系下功能梯度材料平面梁的完整解析解

doi: 10.3879/j.issn.1000-0887.2012.10.001

通讯作者: 赵莉(1982-),女,山东人,讲师,博士 (Tel:+86-574-87080435; E-mail: zhaoli06@zju.edu.cn);吕朝锋(1978-),浙江人, 副教授,博士生导师(联系人.Tel: +86-571-88208473; E-mail: lucf@zju.edu.cn).

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出版历程

Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework

计量

出版历程

目录

通讯作者:
赵莉(1982-),女,山东人,讲师,博士 (Tel:+86-574-87080435; E-mail: zhaoli06@zju.edu.cn);吕朝锋(1978-),浙江人, 副教授,博士生导师(联系人.Tel: +86-571-88208473; E-mail: lucf@zju.edu.cn).