| Item type |
紀要論文 / Departmental Bulletin Paper(1) |
| 公開日 |
2015-03-26 |
| タイトル |
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タイトル |
Buckling and Failure of Thin Rectangular Plates in Compression. |
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言語 |
en |
| 言語 |
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言語 |
eng |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_6501 |
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資源タイプ |
departmental bulletin paper |
| その他のタイトル |
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その他のタイトル |
壓縮を受ける矩形薄板の挫屈と破壊 |
| 著者 |
山本, 峰雄
近藤, 一夫
YAMAMOTO, Mineo
KONDO, Kazuo
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| 出版者 |
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出版者 |
東京帝國大學航空研究所 |
| 出版者（英） |
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出版者 |
Aeronautical Research Institute, Tokyo Imperial University |
| 書誌情報 |
東京帝國大學航空研究所報告
en : Report of Aeronautical Research Institute, Tokyo Imperial University
巻 10,
号 119,
p. 1-22,
発行日 1935-04
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| 抄録 |
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内容記述タイプ |
Abstract |
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内容記述 |
本論文は矩形平板が其一双の邊に並行な壓縮荷重を受けて挫屈を起した後の状態と其破壊の條件を論じたものである.薄板の平衡條件を與へる6個の偏微分方程式から出發して,挫屈による板の變形wを定めた.但し次の樣な四つの假定を行つて居る.(1)T_1=(∂T_2)/(∂y)=S_1=S_2=0茲にT_1,T_2は斷面の單位長に働くx,y方向の直接應力,S_1,S_2は同じく其單位長に働く剪斷力を表す.但し荷重はy軸に並行に働くものとする.(2)壓縮荷重を受ける邊の變位は一樣である.(3)wの導函數について二次の項は無視し得る.(4)荷重に並行なy方向の波形は正弦波である.斯くして,問題は結局次の常微分方程式を解いて,x方向の波形を與へる函數Φ(x)を求める事に歸せられる,[numerical formula]茲にθ=(nπx)/(2b),2b,2dは夫々板の長さ及幅,n/2はy方向の波數,eは見掛上一樣なy方向の歪,e_0は挫屈の臨界點に於ける四邊を支持された方形板のeを表す.四邊を支持された方形板,又はy方向に無限に長い帶状板の場合については[numerical formula]と置いて此方程式の近似解を求め得る.之から導出される主要な結果は次の如くである.(i)此波形を以て應力の分布と,變形と共に荷重の増加する状態を計算してある.一樣歪の條件(2)を飽く迄固執すれば,板の横斷面の中央部に張力が起る事となる.實際には一樣歪の條件が必ずしも満足されては居ないのであらう.(ii)板の屈曲による表面の屈曲應力は直接壓縮のみによる兩端の應力に匹敵する大きさである.從つて板の破壊は壓縮と屈曲の合成應力が最大の點で始まる.斯かる點は一般に板の兩端に近いが夫より少し内側にある.故に板の破壊を論ずるには,挫屈した板の波形を出來る丈正確に求める必要がある.(iii)第8圖によつて直ちに任意の薄板に對する許容荷重を知る事が出來る.是等の結果は正方形板及び帶状板のみならず縱横比の相當大きな矩形板(b>2d)にも近似的に適用出來る. |
| 抄録（英） |
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内容記述タイプ |
Other |
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内容記述 |
(a) If a rectangular plate were subjected to compression at two of its supported edges, the final solution of the problem will be to solve the ordinary differential equation (6"), although certain restrictions are not entirely absent. (b) The solution of (6") for a rectangular plate simply supported at its four edges is given by (8). The wave form and the distribution of the edge stress anticipated from the present solution (8) show the same tendency as in Cox's approximate assumption. But they are much freer from unsatisfactory assumptions. (c) The condition of uniform overall strain is not always satisfied for the merely supported plate. The edges of the straining rigid body and the plate are no longer in contact throughout their lengths; the middle part of the plate edge having slightly receded (shrunk) forming a gap, when the overall strain of the plate exceeds 4.65 e_0. It therefore seems purposeless to apply the equation (8) for too large a value of e/e_0. (d) In practical problems, however, the parts that are nearer to the side edges play the most important role, whether in determing the plate load or the collapse point of the plate. Therefore, for such practical purposes, we may use equation (8) with a fair degree of certainty. (e) The final collapse of the plate occurs when the combined stress of bending and direct compression attains a certain amount. And since the maximum fibre stress due to bending is as great as the direct compressive stress, the influence of curving of the buckled plate is very marked, in consequence of which the wave form after buckling should be expressed as accurately as possible. From this point of view, the authors' solution here may be regarded as an advance on the old method, since it is deduced from the general equations of equilibrium of plate elements, without previously assuming the wave form. (f) For practical purposes it is advisable to use Fig.8, from which can be read at once the permissible load for any given rectangular plate simply supported at its four edges. The present method is believed to be more reliable than the other methods that have been proposed by various authors so far. |
| 書誌レコードID |
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収録物識別子タイプ |
NCID |
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収録物識別子 |
AA00387631 |
| 資料番号 |
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内容記述タイプ |
Other |
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内容記述 |
資料番号: SA4148275000 |
SA4148275.pdf (791.5 kB)
