两对边固支另两对边自由弹性矩形薄板理论解

钟阳; 殷建华

doi:10.11835/j.issn.1674-4764.2005.06.007

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两对边固支另两对边自由弹性矩形薄板理论解

更新时间：2023-11-28

- 两对边固支另两对边自由弹性矩形薄板理论解
- Theoretical Solution of Elastic Rectangular Thin Plate with Opposite Boundary Completely Clamped Support and Others Free
- 土木与环境工程学报（中英文） 2005年27卷第6期页码：29-32
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  科学技术部重大基础研究项目资助(2004CCA03300)
- DOI：10.11835/j.issn.1674-4764.2005.06.007
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- 纸质出版：2005
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钟阳, 殷建华. 两对边固支另两对边自由弹性矩形薄板理论解[J]. 土木与环境工程学报（中英文）, 2005,27(6):29-32.

ZHONG Yang~1, YIN Jian-Hua~2. Theoretical Solution of Elastic Rectangular Thin Plate with Opposite Boundary Completely Clamped Support and Others Free[J]. Journal of Civil and Environmental Engineering, 2005, 27(6): 29-32.
钟阳, 殷建华. 两对边固支另两对边自由弹性矩形薄板理论解[J]. 土木与环境工程学报（中英文）, 2005,27(6):29-32. DOI： 10.11835/j.issn.1674-4764.2005.06.007.

ZHONG Yang~1, YIN Jian-Hua~2. Theoretical Solution of Elastic Rectangular Thin Plate with Opposite Boundary Completely Clamped Support and Others Free[J]. Journal of Civil and Environmental Engineering, 2005, 27(6): 29-32. DOI： 10.11835/j.issn.1674-4764.2005.06.007.

摘要

利用辛几何的方法推导出了两对边固支另两对边自由支承条件情况下，弹性矩形薄板问题的理论解。在推导过程中并不需要事先人为的假定挠度函数，而是直接从弹性矩形薄板问题的控制方程出发，利用纯数学的手段推导出问题的解析解，使得求解过程更加理论化，从而为进一步解决了这类问题（例如动力问题）奠定了理论基础。文中还给出了算例来验证方法的正确性。

Abstract

In this paper

the analytical solutions for an elastic rectangular thin plate with opposite boundary completely clamped support and others free were derived by a Symplectic geometry method.Due to the fact that the basic elasticity equations of the thin plate were only used

it was not necessary to select the deformation function arbitrarily.Therefore

the solutions in this paper are much more general mathematically.In order to prove the validity of the formulations

numericam results were presented to be compared with those derived by other references.

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