Thermomechanics in Solids: A Symposium Held at CISM, Udine, by W. Nowacki, I. N. Sneddon (eds.)

By W. Nowacki, I. N. Sneddon (eds.)

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Mag. VI, 23, (1937). p. 1017. I. : Sur Ie probleme trois dimensions de la thermoelasticite des corps transversalement isotropes. Bull. de l'Acad. Polon. Sci. Sere Sci. • 11, 5 (1963), 177-181. : The three-dimensional stress distribution in hexagonal aelotropic crystals. Proc. Cambridge Phil. Soc. 44 (1948). 621-630. I. : Tensions axiallement symetriques, dans les corps transversalement isotropes. An. stiint. Univ. lasi, 8, I, {1962}, 119-126. [22] SINGH Avtar: Axisymmetrical thermal stresses in transversely isotropic bodies.

7) Introducing the Helmholtz free energy F - U - ST and eliminating the quantity q i. i from eqs. 7) we obtain . 3F· 3F· e··IJ + "I:' T oT F - ~ oe ij .. 0 .. IJ • eIJ.. 9) Let us now expand the function F( eIj , T) into a infmite series in the neighbourhood of the natural state (0 , 'fo ) 1 C e F ( e ij , T) - '2 ijU ij e k2 R t'ij e 6 + !! 6 2 + .... 10) W. Nowacki 30 From the expansion F( Eij ,T) we retain only the linear and quadratic terms, confming ourselves to linear relations among stresses 0ij strains Eij and temperature change 8.

Mossakowski [22] applied the complex variable method to derive a number of solutions for the action of a heat source in a semi-infinite disc of isogonal anisotropy. l'c'oc10rl' ,'U [291. Thermal Stresses in Anisotropic Bodies 47 For the orthotropic plate we denote by E I and E2 the Young's moduli in the direction of xI and x 2 axis, respectively, by v -Poisson's ratio and by G the shear modulus. l and ~ denote the coefficients of thermal expansion and ~l ,~2 coefficients of thermal conductivity in the directions of x i and X2 axes, respectively.

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