Elementary Theory of Plates
As we stated earlier the plane problems of elasticity theory describe, approximately, the behavior of a thin elastic body (see Chapter 6.1). The plate theory is also an approximation to the three-dimensional problems of elasticity theory. The plate represents approximation of an elastic body when one dimension of the body is much smaller than other two. A plane dividing the thickness of the plate in half is called the middle plane. The stress tensor and displacement vector in plate theory are expressed as functions of points in the middle plane. As a matter of fact, this can be taken as a definition: a plate is an elastic body (no matter how thick) for which the stress tensor and displacement vector are functions of points on a single plane (called the middle plane) of a body.
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