Cauchys Reciprocal Theorem

21 If we consider t1 as the traction vector on a plane with normal n1, and t2 the stress vector at the same point on a plane with normal n2, then or in matrix form as t1 = n1 and t2 = n2a {ti} = L«1JM and {¿2} = L«-2JH

If we postmultiply the first equation by n2 and the second one by n1, by virtue of the symmetry of [0] we have

Figure 2.4: Cauchy's Reciprocal Theorem r

Figure 2.4: Cauchy's Reciprocal Theorem

22 In the special case of two opposite faces, this reduces to

23 We should note that this theorem is analogous to Newton's famous third law of motion To every action there is an equal and opposite reaction.

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