4

(10 + v - v2)( 1 + - 2(7v - 1)-2 + 2((1 + 5v)^ -(6 + v - v2) ) x

+ 2( (1 + 5v)-(6 + v - v2) a2+ (2 + v - v2)^ - 6(1 + v)^

The details of the mathematical treatment may be found in Lee and Ballesteros (1960).

2.5.7 Orthotropic Plates

Plates of anisotropic materials have important applications owing to their exceptionally high bending stiffness. A nonisotropic or anisotropic material displays direction-dependent properties. Simplest among them are those in which the material properties differ in two mutually perpendicular directions. A material so described is orthotropic, for example, wood. A number of manufactured materials are approximated as orthotropic. Examples include corrugated and rolled metal sheets, fillers in sandwich plate construction, plywood, fiber reinforced composites, reinforced concrete, and gridwork. The last example consists of two systems of equally spaced parallel ribs (beams), mutually perpendicular, and attached rigidly at the points of intersection.

The governing equation for orthotropic plate similar to that of isotropic plate (Equation 2.87) takes the form d4w d4w x dx4 ^ dx2dy2

where

0 0

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