翻訳と辞書 Words near each other ・ Plane Mad ・ Plane Martin ・ Plane mirror ・ Plane Nuts ・ Plane of immanence ・ Plane of incidence ・ Plane of reference ・ Plane of rotation ・ Plane of Shadow ・ Plane of the solar system ・ Plane partition ・ Plane sailing ・ Plane Saver Credit Union ・ Plane Space ・ Plane strain compression test ・ Plane stress ・ Plane Stupid ・ Plane symmetry ・ Plane Table ・ Plane table ・ Plane wave ・ Plane wave expansion ・ Plane wave expansion method ・ Plane wave tube ・ Planea ・ Planeat ・ Planebruch ・ Planechase ・ Planed Plant ・ Planegg Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Plane stress ： ウィキペディア英語版 Plane stress In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular surface. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 (representable as a 2 × 2 matrix rather than 3 × 3). 〔 A related notion, plane strain, is often applicable to very thick members. Plane stress typically occurs in thin flat plates that are acted upon only by load forces that are parallel to them. In certain situations, a gently curved thin plate may also be assumed to have plane stress for the purpose of stress analysis. This is the case, for example, of a thin-walled cylinder filled with a fluid under pressure. In such cases, stress components perpendicular to the plate are negligible compared to those parallel to it.〔 In other situations, however, the bending stress of a thin plate cannot be neglected. One can still simplify the analysis by using a two-dimensional domain, but the plane stress tensor at each point must be complemented with bending terms. ==Mathematical definition== Mathematically, the stress at some point in the material is a plane stress if one of the three principal stresses (the eigenvalues of the Cauchy stress tensor) is zero. That is, there is Cartesian coordinate system in which the stress tensor has the form : $\backslash sigma\; =$ \begin \sigma_ & 0 & 0 \\ 0 & \sigma_ & 0 \\ 0 & 0 & 0 \end \equiv \begin \sigma_ & 0 & 0 \\ 0 & \sigma_ & 0 \\ 0 & 0 & 0 \end For example, consider a rectangular block of material measuring 10, 40 and 5 cm along the $x$, $y$, and $z$, that is being stretched in the $x$ direction and compressed in the $y$ direction, by pairs of opposite forces with magnitudes 10 N and 20 N, respectively, uniformly distributed over the corresponding faces. The stress tensor inside the block will be : $\backslash sigma\; =$ \begin 500\mathrm & 0 & 0 \\ 0 & -4000\mathrm & 0 \\ 0 & 0 & 0 \end More generally, if one chooses the first two coordinate axes arbitrarily but perpendicular to the direction of zero stress, the stress tensor will have the form : $\backslash sigma\; =$ \begin \sigma_ & \sigma_ & 0 \\ \sigma_ & \sigma_ & 0 \\ 0 & 0 & 0 \end \equiv \begin \sigma_ & \tau_ & 0 \\ \tau_ & \sigma_ & 0 \\ 0 & 0 & 0 \end and can therefore be represented by a 2 × 2 matrix, : $\backslash sigma\_\; =$ \begin \sigma_ & \sigma_ \\ \sigma_ & \sigma_ \end \equiv \begin \sigma_ & \tau_ \\ \tau_ & \sigma_ \end 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「Plane stress」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.