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a is the distance between the two plates; The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of ħ shows that the Casimir force per unit area F c / A is very small, and that furthermore, the force is inherently of quantum-mechanical origin.
The potential profile between two plates is normally obtained by solving this equation numerically. Once the potential profile is known, the force per unit area between the plates expressed as the disjoining pressure Π can be obtained as follows. The starting point is the Gibbs–Duhem relation for a two component system at constant ...
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.
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
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 ...
Derjaguin approximation related the force between two spheres (top) and the interaction energy between two plates (bottom). The Derjaguin approximation (or sometimes also referred to as the proximity approximation), named after the Russian scientist Boris Derjaguin, expresses the force profile acting between finite size bodies in terms of the force profile between two planar semi-infinite ...
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In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field.