A shell problem 'highly sensitive' to thickness changes

P.S. Lee (1) , Klaus-Jürgen Bathe (1) , Dominique Chapelle (2)

1 MIT - Massachusetts Institute of Technology
2 MACS - Modeling, analysis and control in computational structural dynamics

In general, shell structural problems can be identified 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-defined 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 significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution using finite element analysis.

Mots clés: shells; asymptotic analysis; finite element solution

Domaines: Analyse numérique [math.NA]

P.S. Lee, Klaus-Jürgen Bathe, Dominique Chapelle. A shell problem 'highly sensitive' to thickness changes. International Journal for Numerical Methods in Engineering, 2003, 57 (8), pp.1039-1052. ⟨10.1002/nme.708⟩. ⟨hal-00839250⟩