Hierarchical plate and shell element incorporating symbolic computations

Subbarayalu, Sethuramalingam (1999) Hierarchical plate and shell element incorporating symbolic computations. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (11MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

A hierarchical nine node p-version curved shell finite element is developed incorporating symbolic computations. The element has five nodal degrees of freedom, three translations and two rotations. The displacement approximation functions which are hierarchical in nature are derived from the Lagrangian functions. The hierarchical finite elements have a distinct advantage of saving computational effort in comparison with h-version elements. However, as the order of the displacement polynomial increases, the number of gaussian points required for integration have to be increased to obtain element matrices. This increases the computational effort required for element generation. The nature of hierarchical formulation offers certain avenues for the usage of symbolic computations which substantially reduces the computational effort involved in the element generation. A number of locations where the usage of symbolic computations offers significant reduction in computational effort are identified and are incorporated. The problems associated with the development of finite element codes can be successfully addressed by the usage of Object Oriented Programming(OOP) techniques. A Finite element program for the shell element is developed using this OOP technique. The performance of the present element is demonstrated using various numerical examples.

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