Plate theory

<p>In <a href="/facts/Continuum_mechanics/vI7LpFDk">continuum mechanics</a>, plate theories are mathematical descriptions of the <a href="/facts/Mechanics/A3yHLQA5">mechanics</a> of flat <a href="/facts/Plate_(structure)/jLhVvh0T">plates</a> that draw on the <a href="/facts/Bending/gxA8Pks1">theory of beams</a>.  Plates are defined as plane <a href="/facts/List_of_structural_elements/BdYjdKrq">structural elements</a> with a small thickness compared to the planar dimensions.  The typical thickness to width ratio of a plate structure is less than 0.1.  A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem.  The aim of plate theory is to calculate the <a href="/facts/Deformation_(mechanics)/xK7R59oI">deformation</a> and <a href="/facts/Stress_(mechanics)/ErAXDbbd">stresses</a> in a plate subjected to <a href="/facts/Structural_load/MAxjDyhc">loads</a>.
</p><p>Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering. These are
</p>
<ul><li>the <a href="/facts/Gustav_Kirchhoff/Ygfzlywy">Kirchhoff</a>–<a href="/facts/Augustus_Edward_Hough_Love/Gr5jqu7v">Love</a> theory of plates (classical plate theory)</li>
<li>The <a href="/facts/Reissner-Mindlin_plate_theory/agdX3CrS">Reissner-Mindlin</a> theory of plates (first-order shear plate theory)</li></ul>

Plate theory open-in-new

Plate theory