| Abstract [eng] |
The ability to design the rational structure in short terms is obvious economical demand hence the engineer must have at his disposal the methodology of optimization of such structures. Grillage structures are widely used in engineering practice, e. g. in construction of so-called grillage-type foundations (further grillages). Nowadays the good-performing optimization algorithms for topology optimization of grillages – separately investigating each beam in the grillage – are elaborated therefore the main attention of this work is devoted to the simultaneous topology and size optimization of grillages, which is obviously insufficiently explored so far. The optimal grillage should meet twofold criteria: the number of piles should be minimal, and the connecting beams should receive minimal feasible bending moments what leads to minimal consumption of concrete for beams. Obviously two separate optimization problems are considered here: determination of minimal number of piles and determination of minimal volume of beams. Whereas the carrying capacity of a single pile is known, the first optimization problem can be rendered as minimization of the maximal reactive force in piles among all set of piles. Analogously, the second problem corresponds to the minimization of the maximal bending moments in connecting beams. The bending moments depend also on stiffness of beams hence the cross-sectional dimensions of beams must be identified simultaneously. Both problems can be incorporated into one applying a compromise objective function. The results of optimization are the number of required piles and their placement scheme, and the cross-sectional dimensions of connecting beams. The minimal possible number of piles is determined by dividing all active forces (applied on a grillage) by carrying capacity of a single pile. An even distribution of reactive forces among all set of piles and even distribution of bending moments in connecting beams indicates an ideal grillage. Practically it is hardly possible, especially in case when a designer introduces the so-called “immovable supports” (usually at the corners of grillages) which cannot change their position and are not involved into optimization process. Such supports could hinder to achieve global solution hence the immovable supports are not considered in the present work and piles are allowed to take whatever position in the grillage. Therefore the objective functions are very sensitive to the placement of piles: even a small shift of one pile could lead to a significant change of value of the objective function. In mathematical terms, it is a highly non-convex, global optimization problem. |
