Stability and Nonlinear Deformation of Cylindrical Grids

The general stability of single-layer cylindrical grids is studied in linear and nonlinear formulations. Dependence of the general buckling load on the geometry and stiffness parameters of a grid is established in an analytical form. Such grids are numerically analyzed for stability. It is established that the general buckling load is much less than the local buckling load. Typical general buckling modes are found. It is shown that such grids are weakly sensitive to imperfections     

Stability investigations of shells with imperfections

Kiev Structural Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 4, pp. 49–56, April, 1990.     

Stability of torispherical and toriconical vessel heads under internal pressure

International Applied Mechanics -     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

Mesh Discretization of the Vector Relations of Shell Theory in a Curvilinear Coordinate System

Mesh methods for discretization of the differential vector relations are generalized as applied to problems of shell theory. In the finite-difference method, covariant derivatives are replaced by vector differences, which are then projected on the vectors of a local basis. In the finite-element method, vector functions are approximated by a Taylor series with tensor coefficients. It is shown that such schemes satisfy the condition of rigid displacement for a deformable body, which improves considerably the convergence of the solution. The proposed schemes, which are sensitive to approximation uncertainties, were tested by solving problems on deformation of shells     

Study of adaptation in the dynamics of shells

Scientific-Research Institute of Structural Mechanics, Kiev Institute of Construction Engineering. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 41–45, September, 1994.