Local Buckling Analysis of Thin-Wall Shell Structures

This master thesis presents research into buckling of thin hyperboloid shells structures. This type of structure is typically applied as the large cooling towers at coal fired electricity plants. However, modelling cooling towers is not the objective of this research. The objective of this research is to understand the buckling behaviour of shells with negative Gaussian curvature, which cooling towers have. In previous research it was found that negatively curved shells are not very sensitive to imperfections and that the first buckling mode provides the most critical imperfection. This research starts from the assumption that a design formula can be derived for predicting the ultimate load of negatively curved shells. A step in this direction is understanding how hyperboloid shells buckle and determining what parameters influence the ultimate load. A finite element model was developed with suitable properties. The influence of the boundary conditions has been studied. The element size and the aspect ratio have been optimised. Various methods of adding imperfections have been considered. The buckling modes have been studied for a large range of curvatures. The influence of the imperfection amplitude on the load displacement curve has been determined by geometrical nonlinear analysis and the arc length method. A parameter study has been performed of a large range of geometries. Varied are the radii of curvature, the thickness, the height of the hyperboloid. Also varied are Young’s modulus and Poisson’s ratio. In total 700 geometrical nonlinear analysis have been performed. The results have been stored in a large data base in Matlab. This includes the support reactions, membrane forces, moments and stresses at each load step. A series of Matlab scripts were developed to generate various graphs. The graphs were used to form a detailed understanding of the buckling behaviour of negatively curved shells and to identify remarkable features. A two-phased curve fitting method has been used is to obtain a formula for the ultimate buckling load and a formula for the peak membrane force of inward buckles. The main conclusion is that hyperboloid shells of significant curvature carry load in three ways: the outward buckles, the inward buckles and the material in-between. First the outward buckles fail then the inward buckles fail and finally the material between the buckles fails. A design method is proposed based on the local linear elastic stress state.

Subject

shell
buckling
arc length
finite element analysis
geometric nonlinear buckling analysis
koiter
curve fitting
buckling load path

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