- A shell problem ‘highly sensitive’ to thickness changes
- K.J. Bathe ; D. Chapelle ; P.S. Lee
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2003 , Volume: 57 , Series:
- Structural Analysis
- Keywords: shells ; asymptotic analysis ; finite element solution
- In general, shell structural problems can be identied to fall into one of the categories of membrane-dominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-defined load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-dened load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes signicantly and indeed can uctuate with changes in shell thickness. We briefly review the dierent asymptotic behaviours that shell problems can display, and then present the specic problem considered and its numerical solution using nite element analysis.