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The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads. Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering. These are the Kirchhoff–Love theory of plates (classical plate theory)
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 plate theory is a model of volcanism that attributes all volcanic activity on Earth, even that which appears superficially to be anomalous, to the operation of plate tectonics. According to the plate theory, the principal cause of volcanism is extension of the lithosphere .
Deformation of a plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Reissner–Mindlin theory of plates is an extension of Kirchhoff–Love plate theory that takes into account shear deformations through-the-thickness of a plate. The theory was proposed in 1951 by Raymond Mindlin. [1]
Plate tectonics (from Latin tectonicus, from Ancient Greek τεκτονικός (tektonikós) 'pertaining to building') [1] is the scientific theory that Earth's lithosphere comprises a number of large tectonic plates, which have been slowly moving since 3–4 billion years ago.
Bending of plates, or plate bending, refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments. The amount of deflection can be determined by solving the differential equations of an appropriate plate theory .
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. This permits a two-dimensional plate theory to give an excellent approximation to the actual three-dimensional motion of a plate-like object.
Their mechanics are the main subject of the plate theory. Thin plates are initially flat structural members bounded by two parallel planes, called faces, and a cylindrical surface, called an edge or boundary. The generators of the cylindrical surface are perpendicular to the plane faces. The distance between the plane faces is called the ...