[Back]

R. Duy, Y. Vetyukov, S. Eisenträger:
"Fictitious Domain Approach for Optimizing Stability Boundaries of Plates with Cutouts";
Talk: 14th World Congress on Computational Mechanics (WCCM 2020, Paris), Paris; 2021-01-11 - 2021-01-15.

In contrast to massive construction designs, the ultimate load, which a thin plate can withstand, is often bounded by the stability reserve. Interestingly, holes in plates may increase the critical buckling loads. Moreover, Blesa Garcia and Rammerstorfer [1] recently suggested a semi-analytical approach to finding positions for the holes such, that an optimal improvement of the stability behavior is achieved.
While the above study addressed infinitesimally small holes, it is desirable to efficiently find optimal shapes of the finite cutouts using repetitive simulations with a slightly varying geometry of the plate. Conventional finite element analysis implies high computational and (manual) pre-processing costs because of the continuous remeshing of each trial geometrical domain, assembling the matrices of the finite element model and post-processing the results. Moreover, this remeshing may result in a non-smooth dependence of the goal function on the geometry of the cutout, which will influence the performance of the optimization algorithm.
The idea of the proposed contribution is to use a type of fictitious domain method [2,3] for efficient buckling analysis of rectangular plates with holes of arbitrary placement and shape. The same regular mesh of the plate finite elements [4] is used for all configurations. The plane stress problem is solved first, and the plate model is then used for the stability assessment. The cutout is accurately excluded from the integration of the global stiffness matrix in the finite element model using the finite cell method. This strategy is shown to be beneficial for series of computations of critical loads for slightly alternating geometries of the holes since only a subset of the elements needs to be re-computed and the procedure is easily automated.
REFERENCES
[1] Blesa Garcia, J. & Rammerstorfer, F. Increase in buckling loads of plates by introduction of cutouts. Acta Mechanica, 2019, 230, pp. 2873-2889
[2] Düster, A. & Parvizian, J. & Yang, Z. & Rank, E. The finite cell method for three-dimensional problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2008, 197, pp. 3768-3782
[3] Duczek, S. & Gabbert, U. Efficient integration method for fictitious domain approaches. Computational Mechanics, 2015, 56(4), pp. 725-738
[4] Vetyukov, Y. Nonlinear Mechanics of Thin-Walled Structures. Asymptotics, Direct Approach and Numerical Analysis. Springer, 2014, 272 p.

Fictitious Domains, FEM, Plate Theory, Stability, Optimization