\IK i; v MUTHWI i.i. ON TIM: <;KM:RAL THEORY OF ELASTIC STABILITY. 



The above system of distorting forces must l>e exactly balanced by the restoring 

 system shown in the upper part of the figure. Hence we obtain the following 

 equations of neutral stability : 



; 



R 9z a 80 a 



8^ T, ISP, au,_ 



a 80 a a 30 82 ' 



82* + a 80'" ' ' 



v\Jl m 1 Oil ,. 



~Sz ' l ~ a~SO '' ' 



(91) 



Now R and e,, may be expressed in terms of the displacements of the middle 

 surface, as follows : 



1 8V 



R " 8z> ' : 82 ; 



(92) 



and the restoring system of stress resultants may also be expressed in terms of this 

 system, as follows* : 



p 3DT8M/ , 1 / , a-jAI 



-ti = -j-\ T~ + ~~ ( u + ^77 . 

 r L 82 m\ 80/J 









- 



m a \.8082 82; 



. . (93) 



where D is the quantity 



mr 

 m 2 -! 



(94) 



<Mathc " iatiCa 



f Etatid ^' < 80cond editio ). Chap. XXIV. u', ', W ' have the 



of thu 



