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Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) 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.
A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry. It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by atom or group. [1] [2] [3] It can be represented generically as: + +
In general, exact solutions for cantilever plates using plate theory are quite involved and few exact solutions can be found in the literature. Reissner and Stein [7] provide a simplified theory for cantilever plates that is an improvement over older theories such as Saint-Venant plate theory.
Vibration mode of a clamped square plate. The vibration of plates is a special case of the more general problem of mechanical vibrations.The equations governing the motion of plates are simpler than those for general three-dimensional objects because one of the dimensions of a plate is much smaller than the other two.
The Mindlin hypothesis implies that the displacements in the plate have the form = (,) ; =, = (,)where and are the Cartesian coordinates on the mid-surface of the undeformed plate and is the coordinate for the thickness direction, , =, are the in-plane displacements of the mid-surface, is the displacement of the mid-surface in the direction, and designate the angles which the normal to the mid ...
The two reactions are named according tho their rate law, with S N 1 having a first-order rate law, and S N 2 having a second-order. [2] S N 1 reaction mechanism occurring through two steps. The S N 1 mechanism has two steps. In the first step, the leaving group departs, forming a carbocation (C +). In the second step, the nucleophilic reagent ...
In this case we start with an assumed form of the displacement and try to fit the parameters so that the governing equation and the boundary conditions are satisfied. The goal is to find Y m ( y ) {\displaystyle Y_{m}(y)} such that it satisfies the boundary conditions at y = 0 {\displaystyle y=0} and y = b {\displaystyle y=b} and, of course ...
electropositive metals with values between 1.4 and 1.9; and electronegative metals with values between 1.9 and 2.54. From the image, the group 1–2 metals and the lanthanides and actinides are very electropositive to electropositive; the transition metals in groups 3 to 12 are very electropositive to electronegative; and the post-transition ...