| 固定边矩形板的弯曲问题 |
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| 引用本文： | 胡海昌.固定边矩形板的弯曲问题[J].物理学报,1955,11(1):19-27. |
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| 作者姓名： | 胡海昌 |
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| 作者单位： | 中国科学院数学研究所 |
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| 摘 要： | The problem of bending of orthotropic rectangular plates with clamped edges on elastic foundation may be reduced to the following differential equation and boundary conditions (?4w)/(?x4)+2λ(?4w)/(?x2?y2)+(?4w)/(?y4)+kw=q/D. w=0, (?w)/(?x)=0 at x=±a, w=0, (?w)/(?y)=0, at y=±b. In the case of isotropic plates, λ = 1. In this paper a perturbation method is proposed for the solution of this problem fay expanding w in power series of λ: w=w0+w1λ+w2λ2+……. It is proved that this series is convergent when -1 ≤λ≤1.
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| 收稿时间： | 9/2/1954 12:00:00 AM |
ON THE BENDING OF RECTANGULAR PLATES WITH CLAMPED EDGES |
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| HU HAI-CHANG.ON THE BENDING OF RECTANGULAR PLATES WITH CLAMPED EDGES[J].Acta Physica Sinica,1955,11(1):19-27. |
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| Authors: | HU HAI-CHANG |
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| Abstract: | The problem of bending of orthotropic rectangular plates with clamped edges on elastic foundation may be reduced to the following differential equation and boundary conditions (?4w)/(?x4)+2λ(?4w)/(?x2?y2)+(?4w)/(?y4)+kw=q/D. w=0, (?w)/(?x)=0 at x=±a, w=0, (?w)/(?y)=0, at y=±b. In the case of isotropic plates, λ = 1. In this paper a perturbation method is proposed for the solution of this problem fay expanding w in power series of λ: w=w0+w1λ+w2λ2+……. It is proved that this series is convergent when -1 ≤λ≤1. |
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