Scientia Sinica
SCIENTIA SINICA Vol. -V IV. Eouriertum UNDER Bopy Forces PARALLEL TO PLANES OF IsOTROPY
equilibrium under body forces parallel to planes
£ body forces X and Y may be counted separate-
Consider now the case of Under these restrictions, system (4) 1s
of isotropy. Since the effects o
ly, we assume Y=0 temporarily.
reduced to the form Oru 7 Ofw ~
Bilaroy + Bis aoe +xX=0,
2 oe ++ Big ay
as Bu gaz + Bos ay? ax O7u O*u au O*u Ow Bi Bx Oy + Bes Tage + By Syik Buy az? + By ayee 0, (25) . O74 670 Orw Oew Oew Benoa) Egor Oma Gy) Ori
Ox Oz In order to satisfy the last two equations of system (25), we may put B33 0°H | oH
Oy? Oz’
Buy om lee 2 v2 H = iA BOF
u Boo OF , Bu om i ~\ Biz Ox? ° By Oy Bis Oz? / | Bi3 By Bas 2 By B33 ) Oo? | oH | eee, ie aol ae cee ae? | Ox Oy ” ee) Bes 2 Bay 3? | 07H = — | 2% v2 4 —4% 2 Ce ve By; Oz* | Ox Oz
The stress function H satisfies the equation B? 3__X=0, (27)
gE ENE) (wit ea )tt ag ae JET got) 8 Bs Bas Be where s? and s3 are defined by (11) and B 2 28 50 Bas ( ) of a special solution of
Consequently the problem is reduced to the finding also be a polynomial.
equation (27). When X is a polynomial, a special solution of H may In the case X = A cos ax cos By cos Y2 > (29) (30)
x a 3
H= B; . A cos ax cos By cos ¥ By Bag Bes (a? + B?-+ v9 Y’) (a@?+B?+v; Y’) (a?-+ B?-+v2 Y’)
a special solution may be taken as