The stress state x = y = 0, xy = T = constant corresponds

The stress state σ_x = σ_y = 0, τ _xy = T = constant corresponds to the Airy stress function ∅ =–T_xy. For this case with constant Poisson’s ratio, show that the general equation (14.1.6) greatly reduces and gives the result that the allowable Young’s modulus must be of the form 1/E = f(x) + g(y), where f(x) and g(y) are arbitrary functions.

Equation 14.1.6

Transcribed Image Text:

32 /1 2 E 024 2 02 2 + 22 /1 02 2 2 v 3 +2 02 1+r 2 =0