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A. Arnold, L. Neumann, W. Hochhauser:
"Stability of glued and embedded Glass Panes: Dunkerley straight Line as a conservative Estimate of superimposed buckling Coefficients";
in: "ASC Report 01/2012", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2012, ISBN: 978-3-902627-05-6, 1 - 6.

We consider a rectangular glass pane as part of a stiffening and force-transmitting timber-glass
composite building element. The glass pane is assumed to be both glued circumferentially and
embedded into a timber substructure via block setting which enables a load transfer of horizontal
forces via vitreous shear areas and compression diagonals within the glass. To verify the stability
of the glass pane, the buckling coefficient has to be determined.
In this note we first present a PDE model (based on linear elasticity) for the stress tensor within
the glass pane and the eigenvalue problem for buckling of the pane. These two equations (in weak
formulation) are then solved subsequently with the software COMSOL, i.e. the computed stress
field is an input coefficient for the eigenvalue problem of the plate equation. We are interested
in the critical load that implies buckling. It is determined by zero becoming an eigenvalue of the
plate equation. Numerical results are presented for pane geometries between 1:1 and 4:1. We
also find that an additional transversal surface pressure does not influence the critical buckling
loads (at linear order).
The maximum load is a non-linear function of the compression and shear forces applied at
the boundary of the pane. To provide a simplified analysis for the practitioner, we prove
that the Dunkerley straight line represents a conservative estimate for superimposed buckling
coefficients and therefore for the critical buckling load. This mathematically rigorous proof is
based on an application of the generalized Dunkerley theorem for eigenvalue problems.

plate buckling, stability analysis, von K´arm´an plate equations, eigenvalue problem,

http://www.asc.tuwien.ac.at/preprint/2012/asc01x2012.pdf