Elastic Equilibrium of Semi-Infinite Solid. 



^ + /^ 



^ + /^ 



-fiC„-2fukD,„ = Z, 



G,„+fxMB„, + ï),„) = 0, 



An = 0. 



From these equations, combining (13) and (l-")), we have 



B,„ = 



Z 

 Z 



c, = 



'^ + ,n 



^ ^ _ U + 2; .)^ 



A,„ = 0, 



B... = 



Z 



J) = _ (A + '2iJ.)Z 



'2//Ät;.+//.) 



A,„ = 0, 



Putting these vahies in the formuhe (12) and (14) and adding them 

 together, we have an exact solution of the form 



= (^ ^ 1 {zco^md + Zün\md\j'Jh-)e-'\ 



We 



= U \ )( 



= -{ 



2// 2(>Ï + //)A; 

 z _^ X + 2/ J. 



Zcosmd —Zäinmd 



]{ 



Zcosmd + Zsin^nd 



kr 



(20) 



2/^ 2iJi[X + [i)h 



corresponding to tlie l»omidary conditions (19). Tlie formuho for 

 stress are 



Tz = (1 + kz){z coii md + Z sin /// o\j,„iJir)<'^'', 



zr = —kz I Z coamd + Z sin md\j',„(kr)e~''^ 



7d = -kz Izcoümt^ -Zs'mitid] ^"'-- J„ß.r)e"', 

 I ) kr 



etc. 



(21) 



