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Mozzi–Chasles' theorem says that every Euclidean motion is a screw displacement along some screw axis. In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a screw displacement. A direct Euclidean isometry in three dimensions involves a translation and a rotation ...
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference ...
Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love [2] using assumptions proposed by Kirchhoff. It is assumed that a mid-surface plane can be ...
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 ...
Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
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 ...