Parametric Stability Analysis of Open Circular-Cylindrical Grid Shell

Abstract

Grid shells show properties of discrete structures as well as properties of the continuous shell due to its topology. For single layered grid shells, the major failure mode is buckling. The major factors that affect the load-carrying capacity of grid shells are grid element properties, connection property, shell geometry and imperfections. Determination of buckling load of grid shell before the design process is very necessary. This is achieved by establishing equivalency between a grid shell and a continuous shell and applying the analytical equation of a continuous shell. Different equivalent models (volume, area, moment of inertia, split rigidity & orthotropic equivalency) are used to determine equivalent properties and an analytical equation for the continuous shell is modified to accommodate those properties to calculate the buckling load of the grid shell. The geometry is an open circular-cylindrical grid shell subjected to normal load with simply supported boundary conditions. The analysis parameters are grid shape, grid size and span to depth ratio. The analytical solution is achieved by solving the buckling equation of the continuous shell for different equivalent models. A 2D Arch analysis is prepared to establish the accuracy of modelling techniques and the accuracy of FEM. A program in MATLAB is written for the analytical method. Geometries are generated in Rhino6 using the Grasshopper plugin. A numerical solution is achieved by modelling geometry and grid element properties in ANSYS and performing a linear buckling analysis. The result from the analytical and numerical methods is compared. From parametric analysis, it is concluded that a denser grid shows bending dominated characteristics whereas a coarser grid shows membrane dominated characteristics. For the denser grid, the orthotropic equivalence model for the quadrilateral grid and equivalent split rigidity for the triangular grid, and coarser grid equivalent volume model can be used to calculate the load-carrying capacity of the grid shell