The computer analysis of plate and shell buckling and vibration

Tranberg, W. F. C. (1979). The computer analysis of plate and shell buckling and vibration PhD Thesis, School of Engineering, The University of Queensland. doi:10.14264/uql.2014.452

       
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Author Tranberg, W. F. C.
Thesis Title The computer analysis of plate and shell buckling and vibration
School, Centre or Institute School of Engineering
Institution The University of Queensland
DOI 10.14264/uql.2014.452
Publication date 1979
Thesis type PhD Thesis
Supervisor Unknown
Total pages 437
Language eng
Subjects 01 Mathematical Sciences
08 Information and Computing Sciences
Formatted abstract
The thick shell element of Ahmad, Irons and Zienkiewicz (Ref. 1) has been used in the study of plate and shell buckling and vibration problems.

A concise tensor based theory for finite elements, in general, and the shell element, above, in particular is developed in this study. Using this theory, expressions for the geometric stiffness and mass matrix of the above element are developed.

The computer implementation of the theory centred on two aspects. Firstly, the programming of the geometric stiffness and mass matrix expressions. Secondly a general review has been carried out to establish as efficient a program as possible. This efficiency is both in terms of user data preparation and computational effort within the program. In this regard, it should be noted that the numerical integration procedure used in creation of the element stiffness matrices involves many repetitive operations. Therefore any extraneous operations, for example, multiplication of zero terms, leads to large inefficiencies.

The subspace iteration method of Bathe and Wilson (Ref, 13) has been used for determining buckling loads and natural frequencies of vibration, A modified iteration method is developed, which allows use of the method for certain examples which previously were not solvable using the standard method. These examples are characterized by having as a solution set, pairs of eigenvalues, equal in magnitude, but opposite in sign. This modified method has been incorporated in the program with the basic standard method. Examples in the buckling field which exhibit this behaviour include the shear buckling of flat plates and the lateral buckling of beams. Both these cases have been investigated in this study.
Keyword Plates (Engineering) -- Vibration -- Computer programs
Shells (Engineering) -- Vibration -- Computer programs
Finite element method -- Computer programs

Document type: Thesis
Collection: UQ Theses (RHD) - UQ staff and students only
 
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