New Ways of Representing Finite Element Results of Shell Structures

Abstract

The Finite Element Method is used in many computer programs to analyse the mechanical behaviour of shell structures. Although this method provides good quantitative insight into the mechanical behaviour of shell structures, it provides little qualitative insight. This master graduation thesis is aimed at expanding Finite Element Analysis (FEA) programs in order to obtain better insight in the qualitative aspect of the mechanical behaviour of shell structures. A FEA-program can compute and display forces, stresses, strains and displacements in a structure due to a prescribed load or displacement. Based on these quantities (i.e. forces, stresses, strains and displacements), five new quantities have been computed and researched during this thesis. These new quantities are aimed at increasing the insight in the qualitative aspect of the mechanical behaviour of shell structures. Four shell structures have been modelled in the 3D modelling software package Rhinoceros. The FEAprogram TNO DIANA has then been used to obtain the required quantities for computing the five new quantities. This computation of the new quantities has been done with the aid of a self-made post processing tool. This tool has been developed in the Rhinoceros plug-in Grasshopper so that Rhinoceros is also used for displaying the analysis results. As it turned out, two quantities in particular produced good results. These are the strain energy and the buckling load factor. Strain energy is the energy that is stored in a structure when it deforms due to a load. The buckling load factor is the ratio between the occurring normal forces in a shell structure and the normal force that will cause the shell to fail by buckling. With the aid of strain energy it turned out to be possible to show whether a shell structure is displaying shell or plate behaviour. Furthermore, strain energy combines forces and deformations in all directions, resulting in a single display of analysis results with which a shell structure can be assessed. The buckling load factor shows where and to what extend a shell structure is most likely to buckle. With the self-made post processing tool it is also possible to display the steepest descends in every part of a shell structure. This provides the tool with opportunities for implementation of the Rain Flow Analogy. The Rain Flow analogy is an alternative method that shows how forces are transferred throughout a shell structure. Based on the results above it is proposed to implement the strain energy and the buckling load factor in existing FEA-programs. These quantities allow for the design and development of better shell structures by increasing the insight in the mechanical behaviour of these structures.