Scientia Sinica

No. 1 HU: EQUILIBRIUM & VIBRATION OF TRANSVERSELY ISOTROPIC ELASTIC BODY 9

7. 4 iy U dz, (43) Bo

the first two equations of (42) can be written in the forms

oO? Ou oo 07 oO? Bu gar + Besa + Bugz + Biscay plate -% (44) 3? Oru O*u oO? Cees + Bee aaa + Bua + By SS + Bis 55 = (VW) 0. In order to satisfy these two equations, we may put __ OF __ OF “~~ 8x Oz” ~~ 8y Oz ° (45) w=W +52 Sa By3 Oz? The stress function F in this case satisfies the equation (vit a Ihe 33 Bre 3 oY By Bas ew Wan oe B33 Oz? J Pre eo)

This equation has the same form as (10). Therefore its special solution may be obtained by the same method.

V. THERMAL STRESSES

The temperature distribution T may depend on the time ¢. But we shall assume as usual that the inertial terms may be neglected. Under this assumption, the problem becomes a quasi-static problem, and system (4) is simplified to the form

Oru Oru Ow | Ow Oia Easeer ae oon oy 2 + Bas En OO Pere oo ke

Ou ov Oy 8? 6T : Buzia, + Be oa +B So + Ba So + Bis eeaD

a? ev & a2w 2 T Ba geag + Be yay + Ba gar + Bape + Bs Ga — GZ = 0

By letting