Mechanical Behavior of Single-Layer Two-Way Grid Cylindrical Latticed Shell with Out-of-Plane Tension Members
Single layer two-way grid shell with in-plane and out-of-plane tension members is a new type of single-layer latticed shell roof. This study treats the effects of tension member installation on the buckling load and strength of a single layer two-way grid cylindrical shell roof by the numerical method. The tension members are installed to stiffen the rigidity of a single layer two-way grid shell roof and improve its stability behavior. Tension member installation and placement pattern is focused as both diagonal members of two-way grids and out-of-plane stiffened members in a cylindrical surface. The diagonal member and the out-of-plane member are used to increase the in-plane and the out-of- plane rigidity of a single layer two-way grid shell, respectively. The tension member placement pattern, the load distribution patterns, the initial imperfections and the initial axial force are considered for the numerical calculation parameters. It is confirmed by the numerical analysis that the tension members in out-of-plane and diagonals caused the increase in the buckling and strength of two-way grid shell.
Stability of metal cylindrical grid shell structures
Based on the fundamental thin shell theory applied to thin continuous cylindrical shells, a method for calculating the stability of the corresponding grid shell structures is developed. Mathematical modeling is performed and factors of critical state of structures are determined. Critical deformation zones are identified and the patterns of changes in shell geometry under actual loads are established. The dependencies of strength and shape-forming parameters are obtained depending on the material and the number of half-waves of the stability loss shape. The critical load is determined taking into account the possible rigidity of multi-element grids, and the results of numerical studies are presented. A noticeable difference in the values of critical load is shown and the admissible limits of applicability of geometric parameters are found. A significant sensitivity of shells with a rhombic mesh are noted.
Exponential stabilization of an axially moving string with geometrical nonlinearity by linear boundary feedback
This paper addresses the vibration suppression problem of an axially moving string using boundary control. Taking into account large transverse motion of the string via the second-order component of Lagrangian strain, a nonlinear oscillation equation is derived for the problem by employing the Hamilton's Principle. Direct Lyapunov method is then adopted to demonstrate that a linear boundary control of negative speed feedback ensures the vibration response of the moving string exponentially stable. The main contributions are a new stability condition in terms of controller gain parameter, and a detailed demonstration on the equilibrium condition at the boundary where the control is applied.