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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク bending of plates ： ウィキペディア英語版 bending of plates Bending of plates or plate bending refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments. The amount of deflection can be determined by solving the differential equations of an appropriate plate theory. The stresses in the plate can be calculated from these deflections. Once the stresses are known, failure theories can be used to determine whether a plate will fail under a given load. == Bending of Kirchhoff-Love plates == In the Kirchhoff–Love plate theory for plates the governing equations are〔Reddy, J. N., 2007, Theory and analysis of elastic plates and shells, CRC Press, Taylor and Francis.〕 :$$ N_ = 0 and :$$ M_ - q = 0 In expanded form, :$$ \cfrac + \cfrac = 0 ~;~~ \cfrac + \cfrac = 0 and :$$ \cfrac + 2\cfrac + \cfrac = q where $q(x)$ is an applied transverse load per unit area, the thickness of the plate is $H=2h$, the stresses are $\backslash sigma\_$, and :$$ N_ := \int_^h \sigma_~dx_3 ~;~~ M_ := \int_^h x_3~\sigma_~dx_3~. The quantity $N$ has units of force per unit length. The quantity $M$ has units of moment per unit length. For isotropic, homogeneous, plates with Young's modulus $E$ and Poisson's ratio $\backslash nu$ these equations reduce to〔Timoshenko, S. and Woinowsky-Krieger, S., (1959), Theory of plates and shells, McGraw-Hill New York.〕 :$$ \nabla^2\nabla^2 w = -\cfrac ~;~~ D := \cfrac = \cfrac where $w(x\_1,x\_2)$ is the deflection of the mid-surface of the plate. In rectangular Cartesian coordinates, :$$ \cfrac + 2\cfrac + \cfrac = -\cfrac \,. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「bending of plates」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.