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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.
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 ...
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 .
In fluid dynamics a shear mapping depicts fluid flow between parallel plates in relative motion. In plane geometry , a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction. [ 1 ]
where is the number of theoretical plates (also called the "plate count"), H is the total bed height and HETP is the height equivalent to a theoretical plate. The material in packed beds can either be random dumped packing (1-3" wide) such as Raschig rings or structured sheet metal.
A simple displacement diagram illustrates the follower motion at a constant velocity rise followed by a similar return with a dwell in between as depicted in figure 2. [4] The rise is the motion of the follower away from the cam center, dwell is the motion where the follower is at rest, and return is the motion of the follower toward the cam ...
Where the plates meet, their relative motion determines the type of plate boundary (or fault): convergent, divergent, or transform. The relative movement of the plates typically ranges from zero to 10 cm annually. Faults tend to be geologically active, experiencing earthquakes, volcanic activity, mountain-building, and oceanic trench formation.