Classical Plate Problems
Bending of plates refers to internal states of stress such that the membrane stress resultants vanish. From the kinematic point of view, it means that the in-plane displacements of the material points of the plate are null. In other words, the degrees of freedom of plates in bending are the out-of-plane displacement (thick and thin plates), together with the two material rotations (thick plates only) – see article “Direct Derivation of Plate Theories”.
The out-of-plane displacement is usually called deflection of the plate.
This article discusses a few classical, closed-form solutions of plate problems. It is restricted to bending problems of isotropic, homogeneous, linearly elastic plates subjected to distributed forces only (no distributed couples).
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