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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Numerical Homogenization of Perforated Plates with Application to Buckling
A. Somolová and J. Zeman
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic
A. Somolová, J. Zeman, "Numerical Homogenization of Perforated Plates with Application to Buckling", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 107, 2007. doi:10.4203/ccp.86.107
Keywords: perforated plates, buckling, homogenization, thick and thin plates.
The majority of materials used in civil engineering show a heterogeneous structure. One of the most common approaches to the modeling of heterogeneous bodies are the homogenization methods, which replace a complex heterogeneous material with a homogeneous equivalent with properties reflecting the characteristics of individual constituents as well as their geometrical configuration. In this article, we discuss the homogenization of perforated plate structures.
It is worth noting that especially in the design of a thin-walled structures, the buckling can substantially reduce the load bearing capacity of a member when compared with its pure compressive strength. From this perspective, the plates perforated with a dense array of openings present an attractive alternative as their critical load is much higher than the one of solid plates with the same weight and the reduced thickness.
In the methodology adopted in this work, the values of bending and twisting stiffnesses are deduced from the behavior of a periodic unit cell under the loading by a macroscopic curvature tensor. The approach builds on the parameterization of the average curvatures by rotations and deflections of selected "controlling" points. The collective effect of the material surrounding the unit cell is accounted for by using the periodicity conditions, prescribed by linear tying relations . Advantages of such a procedure are its simplicity and the ease of implementation to the majority of finite element packages.
The homogenization procedures introduced in this work can be applied to generic heterogeneous plates with a periodic structure. Moreover, the proposed methodology proposed for thick and thin plates was successfully validated against the experimental data as well as verified by the results of the detailed numerical modeling. When compared with the detailed numerical model, the proposed homogenization method provides a time-efficient solution (both from the point of view of geometrical modeling and computational time). It is demonstrated that the accuracy of the buckling load is sufficient even for cases when the dimensions of the unit cell are not negligible with respect to dimensions of the whole structure.
The next step is the application of the method to the design of heterogeneous structures, tailored to specific needs. Moreover, as illustrated by this work, the homogenized parameters can be efficiently used as an independent verification of the measured data enabling pinpointing of experimental inaccuracies.
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