By Ian Naismith Sneddon (auth.), S. Flügge (eds.)

ISBN-10: 3662428016

ISBN-13: 9783662428016

ISBN-10: 3662430819

ISBN-13: 9783662430811

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1) 2(an + i-rns) =ax+ ay + e- 2 i"(ax- ay + 2i-rxy)' and it follows that 2 (Pxn while + i Pyn) = dz Ts ei" (ax+ ay) . 6) . 7) e Then, from Eqs. 7) i (X+ i Y) = J[q/(z) + ip'(z)] ~~ + J[zip"(z) + 1p'(z)] ~~ J:s [cp(z) + 1p\z) + zip'(z)] ds AB ds AB ds, = AB and hence X+ i Y = - i [cp (z) + 1p(z) + zip'(z)U. 8) The moment M is given by M = J(xPyn- YPxn) ds = Re {- :£z(Pxn + ipyn) ds} AB =- Re{ I z [cp'(z) + ip'(z)] ~; ds AB +I z [zip"(z) + 1p'(z)] ~~ ds} AB in a similar fashion, where x'(z) and we have = 1p(z), M=Re[x(z) -z1p(z) -zzcp'(z)U.

I 34. Transformation to orthogonal curvilinear systems. In many applications of this theory it will be necessaryto have expressions for the stress and displacement components in an orthogonal curvilinear coordinate system (~, 'YJ) which we take to be defined _by the conformal transformation z = w (C) where C= ~ + i'Yj. l5. to the curve 'YJ = const at the point P(x, y) and the normal, s, to the curve ~=constat the same point, taken in the directions ~ increasing, 'YJ increasing, respectively. Since the stress components form a tensor it follows that if n makes an angle a.

3). Putting T(z) =To(,), VJ(z) = VJo(') we have from Eqs. 5) 2f1 (u; w'(C) [ (~") + z. , T' (z) =

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