Mechanics of Composite Materials by Richard M. Christensen

Author:Richard M. Christensen [Christensen, Richard M.]
Language: eng
Format: epub
ISBN: 9780486136660
Publisher: Dover Publications
Published: 2012-10-22T21:00:00+00:00

(4.3)

There are 11 generalized displacement functions in (4.2). The governing 11 equations of equilibrium are given by

(4.4)

where the resultants appearing in (4.4) are defined by

(4.5)

and

where, for brevity, the notation σx = σxx, and so on, is employed. The effective load terms in (4.4) are given by

(4.6)

Along the edge of the plate, one member of each of the following 11 products must be prescribed:

(4.7)

where n and t are the directions normal and tangential to the edge of the plate.

The equations and boundary conditions given in (4.4)—(4.7) are independent of the properties of the materials of the plate and hence hold true for homogeneous isotropic as well as laminated plates.

In the laminated plate context the combination of relations (4.3)—(4.5) can be used to state the 11 governing equilibrium equations in terms of the 11 unknown displacement functions. These 11 equations, in matrix notation, are given by

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