Boundary conditions in the vlasov theory of cylindrical shells: PMM vol. 43, no.1, 1979, pp. 178–181

Abstract

Semi-membrane theory of thin shells of Vlasov [1] reduces the number of the boundary conditions which have to be fulfilled at the curvilinear edges of the shell, to two. The remaining two conditions hold by virtue of the arbitrariness of the simple edge effect. In analogy with the membrane theory, when the shell is computed using the Vlasov theory, the tangential conditions are usually made to hold at the curvilinear edges and the discrepancies appearing in the nontangential conditions are removed with help of the simple edge effect. In the present paper the boundary conditions at the curvilinear edges were obtained for the Vlasov system of equations using the asymptotic method. As a result, it was found that for certain types of clamping of the shell edges the boundary conditions sought must contain the non-tangential terms. The results obtained were confirmed by a numerical example. Gol'denviezer generalized the Vlasov theory to embrace arbitary shells of zero curvature. The stress-strain state under consideration is called in [2], the generalized edge effect. The terminology and notation used below are those of [2].