Kinematics |

Kinematics describes how the plate's displacements and strains relate: where |

Kinematics for Classical Plates | ||||||||

The above equations are too general to be useful. A few assumptions on how a plate's cross section rotates and twists need to be made in order to simplify the problem. For the classical plate, the assumptions were given by Kirchoff and dictate how the 'normals' behave (
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Based on these assumptions, the displacement field can be expressed in terms of the distances by which the plate's middle plane moves from its resting (unloaded) position, v, and _{0}w and the rotations of the plate's middle plane, , , and .
_{0}With the normals straight and unstretched, we can safely assume that the shear strain in the Using the assumption that the normals remain normal to the midplane, we can make the The kinematics equations therefore becomes where the strains of the middle plane are and the curvatures (changes of slope) of the middle plane are Note that if there are no in-plane resultants, all strains at the middle plane are zero. Thus | ||||||||