RP Isotropic Plates

Fibrous reinforced plates, flat or curved, is commonly made with mat, fabrics, and parallel filaments, either alone or in combination. Mat is usually used for good strength at minimum cost, fabrics for high strength, and parallel filaments for maximum strength in some particular direction. 

Because the fibers in mat are randomly oriented, mat-reinforced materials have essentially the same strength and elastic properties in all directions in the plane of the plate, that is, they are essentially isotropic in the plane. Consequently, the usual engineering theories and design methods employed for isotropic engineering materials may be applied. It is only necessary to know strength, modulus of elasticity, shearing modulus, and Poisson s ratio of the combined mat and resin. These can be obtained from standard stress-strain measurements made on specimens of the particular combination of fiber and plastic under consideration. 

In the foregoing review the direction perpendicular to the plane of the plate has been neglected because the plate is assumed thin and the stresses are assumed to be applied in the plane of the plate rather than perpendicular to it. This assumption, which considerably simplifies the theory, carries through all of the following review. However, it is true that properties perpendicular to the plane of the plate are undoubtedly different than in the plane, and in thick plates this difference has to be taken into account, particularly when stresses are not planar. This summation is not true if 3-D fabrics are used. For isotropic materials, such as mat RPs, if E is the modulus in any direction, the Ej at any angle to this direction is the same, so the ratio is  

Poisson s ratio v is similarly a constant in all directions and the shearing modulus (G) is  

The following familiar relationships between direct stress o and strain e, and shearing stress t and strain y, hold  

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