Show that plane stress displacements for the Flamant problem in Section 8.4.7 under only tangential force X

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Show that plane stress displacements for the Flamant problem in Section 8.4.7 under only tangential force X are given by:

My  (1  v) - - -0 sin  (1  v)X, -0 cost +  +A cose - B sin 2X,  20 log r cos + A sin + B cost log r sin + +Cr

Data from section 8.4.7

As another half-space example, consider the case of a concentrated force system acting at the origin, as

X 1 1 3 0 X y

= (a12r logra15r0) cos 0+ (b12r log r + b15 r0) sin 0 The stresses resulting from this stress function are 1

X= Sor(a,0)a cosido = -7b15  - * %, (a,0)a sindo Y = == Or Thus, the constants are determined as a15 = Y/T

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