Theory of Elasticity for Scientists and Engineers pp 297-315 | Cite as

# Elementary Theory of Plates

## Abstract

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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