Abstract

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)

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