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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 Kirchhoff–Love plate theory ： ウィキペディア英語版 Kirchhoff–Love plate theory The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments. This theory is an extension of Euler-Bernoulli beam theory and was developed in 1888 by Love〔A. E. H. Love, ''On the small free vibrations and deformations of elastic shells'', Philosophical trans. of the Royal Society (London), 1888, Vol. série A, N° 17 p. 491–549.〕 using assumptions proposed by Kirchhoff. The theory assumes that a mid-surface plane can be used to represent a three-dimensional plate in two-dimensional form. The following kinematic assumptions that are made in this theory:〔Reddy, J. N., 2007, Theory and analysis of elastic plates and shells, CRC Press, Taylor and Francis.〕 * straight lines normal to the mid-surface remain straight after deformation * straight lines normal to the mid-surface remain normal to the mid-surface after deformation * the thickness of the plate does not change during a deformation. == Assumed displacement field == Let the position vector of a point in the undeformed plate be $\backslash mathbf$. Then :$$ \mathbf = x_1\boldsymbol_1+x_2\boldsymbol_2+x_3\boldsymbol_3 \equiv x_i\boldsymbol_i\,. The vectors $\backslash boldsymbol\_i$ form a Cartesian basis with origin on the mid-surface of the plate, $x\_1$ and $x\_2$ are the Cartesian coordinates on the mid-surface of the undeformed plate, and $x\_3$ is the coordinate for the thickness direction. Let the displacement of a point in the plate be $\backslash mathbf(\backslash mathbf)$. Then :$$ \mathbf = u_1\boldsymbol_1+u_2\boldsymbol_2+u_3\boldsymbol_3 \equiv u_i\boldsymbol_i This displacement can be decomposed into a vector sum of the mid-surface displacement and an out-of-plane displacement $w^0$ in the $x\_3$ direction. We can write the in-plane displacement of the mid-surface as :$$ \mathbf^0 = u^0_1\boldsymbol_1+u^0_2\boldsymbol_2 \equiv u^0_\alpha\boldsymbol_\alpha Note that the index $\backslash alpha$ takes the values 1 and 2 but not 3. Then the Kirchhoff hypothesis implies that If $\backslash varphi\_\backslash alpha$ are the angles of rotation of the normal to the mid-surface, then in the Kirchhoff-Love theory :$$ \varphi_\alpha = w^0_ Note that we can think of the expression for $u\_\backslash alpha$ as the first order Taylor series expansion of the displacement around the mid-surface. 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「Kirchhoff–Love plate theory」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.