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Mechanics of Solids and Materials by Vlado Lubarda, Robert Asaro

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2 Basic Integral Theorems

2.1 Gauss and Stokes’s Theorems

The divergence theorem of Gauss may be expressed as follows:

THEOREM 2.1: If V is a volume bounded by the closed surface S and A is a vector field that possesses continuous derivatives (and is singled valued in V), then

(2.1)

where n is the outward pointing unit normal vector to S. Note that we may extend this result to the case where A is a tensor field with the same proviso’s. The basic theorem is proven below.

Stokes’s theorem takes the following form:

THEOREM 2.2: If is an open, ...

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