A function f(x,y) is defined as subharmonic in a region R if 2 f 0

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A function f(x,y) is defined as subharmonic in a region R if ∇2f ≥ 0 at all points in R. It can be proved that the maximum value of a subharmonic function occurs only on the boundary S of region R. For the torsion problem, show that the square of the resultant shear stress τ,2 = τ,2xz + τ,2yz is a subharmonic function, and thus the maximum shear stress will always occur on the section boundary.

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