SPLINE FINITE ELEMENT ANALYSIS OF AXISYMMETRIC SHELLS

Abstract

The analysis of shell structures has long been an important area of study in the field of structural engineering. Many methods of analysis are available but in recent years, the finite element method has become the most popular method used by the researchers and practising engineers. Much research of the method has been carried out over the past few decades and the current trend in the development of finite elements appears to be directed towards the improvement of solution accuracy and computational efficiency. In an attempt to obtain an element with better performance, a spline finite element suitable for the analysis of axisymmetric shells is developed in this thesis. The distinctive feature of this development lies in the numerical modelling of the element in which a new set of B-spline shape functions for the interpolation of geometry as well as displacements is adopted. These shape functions are derived from 83-spline functions and have inherited the efficiency and accuracy of spline interpolation. The spline finite element developed is therefore, superior to the conventional finite elements. In the present analysis, the classical thin shell theory based on Kirchhoff-Love hypotheses is assumed. Only linear analysis is considered and the displacement approach of finite element formulation is used. The element developed is doubly curved and axisymmetric. However, the loading on the element may be either axisymmetric or non-axisymmetric. For the non-axisymmetric case, the analysis is carried out by decomposing the loading on the element by Fourier series in the circumferential direction. Each harmonic may be solved independently and the total response of the structure is obtained by superimposing the results of all the harmonic terms considered. The element has been applied to static as well as free vibration analysis of various axisymmetric shells. For the static analysis, eight examples are presented. These include standard test cases as well as problems of practical interest. The types of loadings considered are body forces, surface pressures and nodal ring loads. In all the examples analysed, highly accurate results have been obtained with relatively few number of elements. For the free vibration analysis, consistent mass matrix is used and a number of examples, including hyperboloidal shell, spherical shell, conical shells and circular plates etc. are also given. The accuracy and efficiency of the element is again demonstrated. In this thesis, the merits of spline interpolation have been successfully incorporated into the finite element method. The spline finite element developed has been adequately tested for its validity and is proven to be a powerful numerical tool for the static and free vibration analysis of various shells of revolution.