zbMATH — the first resource for mathematics

Optimization of plastic stepped plates subjected to impulsive loading. (English) Zbl 0985.74052
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 234-249 (2000).
The author considers circular and annular plates of given external and internal radii. The thickness of the plate is piecewise constant with one step in the thickness, and the material of the plate can be ideally homogeneous or fiber-reinforced. The plate is subjected to an initial impulsive loading which is high enough to cause plastic deformations. The problem is to find a design of the plate, for which residual deflections are as small as possible for a given total material volume of the plate. The problem is formulated as an optimization problem, in which the mean and the maximal deflection are chosen as optimality criteria. Using variational methods from optimal control theory, the author establishes necessary optimality conditions. Numerical results are presented for annular plates clamped at the inner edge and free at the outer edge.
For the entire collection see [Zbl 0935.00054].
74P10 Optimization of other properties in solid mechanics
74K20 Plates
74C99 Plastic materials, materials of stress-rate and internal-variable type
74E30 Composite and mixture properties