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A simple local a posteriori bending indicator for axisymmetric membrane and bending shell elements. (English) Zbl 0951.74066

Summary: We employ several mechanical models for the analysis of thin-walled structures. A bending indicator is developed for a nonlinear adaptive process and applied to thin-walled axisymmetric shell problems, incorporating membrane and bending elements. If the structural response of the model including bending is available, the error made by the reduced membrane model is easy to evaluate. Thus an indication for the bending can be found from the structural response of the reduced membrane model. This is done by an approximation of rotations of the membrane part of the structure, and by an evaluation of the bending energy leading to the bending indicator with these approximated rotations. Finally, we propose a criterion for the change of models based on the bending indicator, and some examples are discussed.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K15 Membranes
74K25 Shells
Full Text: DOI

References:

[1] DOI: 10.1002/nme.1620362307 · Zbl 0790.73066 · doi:10.1002/nme.1620362307
[2] DOI: 10.1002/nme.1620320608 · Zbl 0825.73823 · doi:10.1002/nme.1620320608
[3] DOI: 10.1002/nme.1620371509 · Zbl 0808.73071 · doi:10.1002/nme.1620371509
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[6] DOI: 10.1108/eb023817 · doi:10.1108/eb023817
[7] DOI: 10.1002/nme.1620240206 · Zbl 0602.73063 · doi:10.1002/nme.1620240206
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