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Optymalizacja kształtu kolumn realizujących wybrane przypadki obciążenia Eule-ra za pomocą zmodyfikowanego algorytmu symulowanego wyżarzania

Szmidla J., Wawszczak A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2008

z. 74 [258]

333-344

In this paper, we present the shape optimization method applied to slender's systems (columns) subjected to Euler's loads. The method used to describe the problem, consist in dividing column into elements. These elements are described by their length (the same for every element) and variable diameter. Total potential energy is determined for two systems varying in loading method. Equation of motion and boundary conditions are determined by taking into account energetic method (the minimum of potential energy). Solution of boundary value problem leads to setting transcendental equation for the value of critical load. It is assumed that volume and total length of column are constant. Basing on this assumption, the shape's optimization comes down to matching diameters of particular system's elements. The maximum value of critical load is obtained for each set of diameters. The modified simulated annealing algorithm is used to finding maximum of critical force, which is described by function of several variables. Applied in the algorithm neighbourhood generator changes its behaviour with temperature function. Taking into account the method of column's mounting, the results of numeric calculations for chosen values of structures mounting's elasticity coefficient are presented.