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The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draw on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. [1] The typical thickness to width ratio of a plate structure is less than 0.1.
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 [ 1 ] using assumptions proposed by Kirchhoff .
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 ...
Periodic table of the chemical elements showing the most or more commonly named sets of elements (in periodic tables), and a traditional dividing line between metals and nonmetals. The f-block actually fits between groups 2 and 3; it is usually shown at the foot of the table to save horizontal space.
A plate is a structural element which is characterized by a three-dimensional solid whose thickness is very small when compared with other dimensions. [ 1 ] The effects of the loads that are expected to be applied on it only generate stresses whose resultants are, in practical terms, exclusively normal to the element's thickness.
For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported. The idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution ...
Like the periodic table, the list below organizes the elements by the number of protons in their atoms; it can also be organized by other properties, such as atomic weight, density, and electronegativity. For more detailed information about the origins of element names, see List of chemical element name etymologies.