Stability Analysis Of Elliptic Cylindrical Shells

With the rapid development of modern science and technology, non-circular cylindrical shell is more widely used in engineering practice, the stability analysis of non-circular cylindrical shell has become a hot spot and has gained a great amount of research results. These main results of these studies are mainly based on the equations for the thin shell with small deflection. But the deformation of non-circular cylindrical shell can not be determined, whether the simplified shell theory is suitable for the non-circular cylindrical shell,it deserves to be studied. Non-circular cylindrical shells have a wide range of applications in the pressure vessel, automotive, civil engineering and aerospace industries. These are primarily designed based on the previous experiences, the research of the mechanical properties is not very mature. It is essential to give them a further discussion.The present study is focus on research of elliptical cylindrical shell on behalf of non-circular cylindrical shell. The basic stability differential equations governing the buckling problem of elliptical cylindrical shell are derived, the stability of elliptic cylindrical shells subjected to axial compression and uniform external pressure is discussed respectively.(1) The derivation of basic equations.Based on the Kirchhoff-Love assumption, the geometric equations of elliptical cylindrical shell are obtained, then giving the physical equations. Based on the shell internal forces balance of infinitesimal body, the vector forms of equilibrium equations are derived. Based on the characteristic of the stability of thin shell, the balance equations are simplified. The appropriate orthogonal curvilinear coordinates of elliptic cylindrical shells is established, and the appropriate expression of the radius of curvature is selected.(2) The stability problem of cylindrical shell with an elliptic section under axial compressionFirstly, the "basic governing equations are derived in the form of displacement under uniform axial compression. Based on Galerkin method, assuming the displacement function, the linear equations of the differential equations governing the buckling problem of axially compressed simply supported shells on both ends is achieved, so that the critical conditions for the stability of the shell are obtained. Then the results are discussed. In order to verify the correctness, the results are firstly degenerated into a circular cylindrical shell, and compared with the results of cylindrical shell which are relatively mature. Then the ratio curve between elliptic section and circular section cylindrical shells with the same perimeter are drawn with the changes of eccentricity. The curves of different eccentricity elliptical cylindrical shells under the critical loads with wavelength are given. And also calculations of different geometric parameters are obtained.(3) The stability problem of cylindrical shell with an elliptic section under uniform external pressureFirstly, the basic governing equations are derived in the form of displacement under uniform external pressure. Similarly, based on Galerkin method, assuming the displacement function, the linear equations of the differential equations governing the buckling problem of uniform external pressure simply supported shells on both ends is achieved, so that the critical conditions for the stability of the shell are obtained. Then the results are discussed. In order to verify the correctness, the results are firstly degenerated into a circular cylindrical shell with the same perimeter, and compared with the results of cylindrical shell which are relatively mature. Then the changing trend of buckling loads with eccentricity is given. Also, the curves of shell buckling loads with different eccentricity are drawn. Finally, calculations of different geometric parameters are obtained.