| 弹性力学Hamilton体系下的稳定问题 |
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| 引用本文： | 李俊永,吕和祥.弹性力学Hamilton体系下的稳定问题[J].工程力学,2007,24(8):81-85. |
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| 作者姓名： | 李俊永 吕和祥 |
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| 作者单位： | 大连理工大学工程力学系,工业装备结构分析国家重点试验室,大连,116023;大连理工大学工程力学系,工业装备结构分析国家重点试验室,大连,116023 |
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| 摘 要： | 通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的屈曲基本方程。并运用弹性力学方程组一般解的统一理论给出其一般解。最后作为例子,给出了两端简支的梁、组合梁和四边简支板、组合板的临界载荷,并与经典解做了比较。结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解。为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。
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| 关 键 词： | Hamilton体系 屈曲基本方程 一般解 临界载荷 精确解 |
| 文章编号： | 1000-4750（2007）08-0081-05 |
| 修稿时间： | 2006-01-062006-06-26 |
STABILITY PROBLEMS OF THEORY OF ELASTICITY IN HAMILTON SYSTEM |
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| LI Jun-yong,LU He-xiang.STABILITY PROBLEMS OF THEORY OF ELASTICITY IN HAMILTON SYSTEM[J].Engineering Mechanics,2007,24(8):81-85. |
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| Authors: | LI Jun-yong LU He-xiang |
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| Affiliation: | State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R. China |
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| Abstract: | By considering the nonlinear term in Hellinger-Reissner variation principle, the buckling formulation in Hamilton system is derived. Its general solution is obtained according to the united theory on general solutions of systems of elasticity equations. As examples, a beam and a composite beam with two ends simply supported were studied. A plate and a composite plate with four edges simply supported were also investigated as instances. The results were compared with the classical ones. The results obtained are the exact solutions based on the exact elasticity theory (without any geometrical hypothesis). This paper provides a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation. |
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| Keywords: | Hamilton system buckling formulation general solution critical load exact solutions |
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