Abstract Southwell showed the relation between the stress functions-Maxwell's and Morera's-and the so-called“equations of compatibility”. His treatment of the surface integral, however, does not appear to the author to be very clear. Moreover, the consideration of the “dislocation”in an elastic body occupying a multiply-connected region, is lacking. These deficiencies are corrected in this paper.
Maxwell's and Morera's stress functions are united to form a “stress functions tensor”(3). Then the “incompatibility tensor”is derived as the variational coefficient of the “stress energy” with respect to the “stress functions tensor.” Incidently, the surface-inregral appears, and is transformed into the sum of the porducts of line-ire egrals and the remaining surface-integral. The variation of the “stress-energy” can be written, finally in the form 28) from which the conditions of compatibilit y-both in the small and in the large-are derived, the latter being coincident with Volterra's theory.(9)

抄録全体を表示

Abstract 1. The reattachment of the separated laminar boundary layer occurs in a manner that was thought by Doenhoff, but the process is a transient one and in the stationary state, the vortex that lies leeward of the separation point attracts the separated layer to the surface.
2. The stability of the separated laminar boundary layer breaks down at the Reynolds Number 25, 000, and this value is independent of the turbulence in the stream. But if the Reyonlds munber of the boundary layer thickness at the point of separation is less than 1200, the instability does not occur.
3. After the bieak down of the stability, the disturbance spreads under the angle which depends on the turbulence in the stream.
4. If the point of the reattachment is too far from the laminar reparation point, the reattachment is imperfect and the separation and the reattachment are repeated.
5. The length of the separated region affects the bonndary layer thereafter greatly. Therefore, the study of the turbulent boumdary layer is meaningless if the condition of the transition region is not clear.

抄録全体を表示

Abstract To overcome the difficulty of determining the critical buckling load of thin rectangular plates in compression, a new method is proposed, which is based upon the load-deflection characteristics of plates having small initial deformation. at the post-buckling negion. This new method is applied to the determiation of the buckling loads of thin rectangular plates in compression which are freely supported at four edges and was ascertained that the new method is very satifactory compared with the methods originated by Cox, Southwell and Donnell.

抄録全体を表示