- 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
- Description
- 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.
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- The mathematical shell model underlying general shell elements
- D. Chapelle ; K.J. Bathe
- Book Title / Journal: International Journal for Numerical Methods in Engineering
- Year: 2000 , Volume: , Series:
- Structural Analysis
- Keywords: shell model ; finite element discretization ; degenerated solid
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- Fundamental Considerations for the Finite Element Analysis of Shell Structures
- D. Chapelle ; K.J. Bathe
- Book Title / Journal: Computers & Structures
- Year: 1998 , Volume: 66 , Series:
- Structural Analysis
- Keywords: shells ; Finite element analysis
- Description
- The objective in this paper is to present fundamental considerations regarding the finite element analysis of shell structures. First, we review some well-known results regarding the asymptotic
behaviour of a shell mathematical model. When the thickness becomes small, the shell behaviour falls
into one of two dramatically different categories; namely, the membrane-dominated and bending-dominated cases. The shell geometry and boundary conditions decide into which category the shell structure falls, and a seemingly small change in these conditions can result into a change of category and hence into a dramatically different shell behaviour.
An effective finite element scheme should be applicable to both categories of shell behaviour and the rate of convergence in either case should be optimal and independent of the shell thickness. Such a finite element scheme is difficult to achieve but it is important that existing procedures be analysed and measured with due regard to these considerations. To this end, we present theoretical considerations and we propose appropriate shell analysis test cases for numerical evaluations.
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