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Theoretical and numerical studies of nonlinear shell equations. (English) Zbl 0951.74021
Summary: We study the solution field \({\mathcal M}\) of a parameter-dependent nonlinear two-point bondary value problem which models the buckling of a thin-walled spherical shell under a uniform external static pressure. The boundary value problem is formulated as an abstract operator equation \(T(x,\lambda)=0\) in Banach spaces. By exploiting the equivariance of \(T\), we obtain detailed information about the structure of \({\mathcal M}\). These theoretical results are used to compute efficiently interesting parts of \({\mathcal M}\) with numerical standard techniques. Bifurcation diagrams, a stability diagram and pictures of deformed shells are presented.

MSC:
74G60 Bifurcation and buckling
74K25 Shells
Software:
RWPKV; RWPM
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References:
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