AN INVESTIGATION OF NONLINEAR DEFORMATION AND BUCKLING OF NONCIRCULAR CYLINDRICAL SHELLS SUBJECT TO TORSION

摘要

The buckling of noncircular shells has not been studied as fully as is the case for circular shells. There are thousands of publications on circular shells, but only dozens on noncircular ones. This astonishing disparity can be explained, on the one hand, by the less frequent occurrence of noncircular shells and, on the other hand, by the difficulties associated with solving the corresponding problems. These difficulties are due to the fact that the radius of curvature of noncircular shells is not constant, which leads to the appearance of variable coefficients in the buckling equations. The familiar solutions of the buckling problems were obtained by analytical methods, as a rule, in the linear approximation, i.e., in the classical statement. This statement does not takes into account couple stresses and nonlinearities in the pre-critical state of the shell. Modern computers make it possible to solve such problems stated in more adequate terms. The present paper is aimed at the finite element approach to the formulation and solution of such problems. By integrating the equations obtained by equating the linear strain components to zero, we find explicit expressions for the displacements of elements of noncircular cylindrical shells, these elements being regarded as rigid bodies. These expressions are used for the construction of the shape functions of a quadrangular finite element. On the basis of this element, we develop an algorithm for the investigation of nonlinear deformation and buckling of shells. The buckling stability of a cylindrical shell with elliptic cross-section subjected to torsion is investigated. We analyze the influence of the elliptic cross-sectional shape and the nonlinear character of the deformation at the pre-critical state.