Parametric optimization of frequency oscillation minimum surface shell on a rectangular contour under thermal load

Abstract

Providing all parameters according to two groups of limit states at the design stage is a multi–criteria task. Optimal design helps to perform such tasks. When the phenomenon of resonance occurs, it is necessary to change the frequency of forced oscillations of the load–bearing structures of various tanks and coatings in order to ensure sufficient strength and stability of the structure and the building in general. For this purpose, there is a separate type of problem in optimal design that allows us to change the forced frequencies of oscillations using the example of the shell of the minimum surface on a rectangular contour.
 In mathematical point of view, optimal design tasks are optimization tasks, finding the extremum of the target function (maximum or minimum). Methods of solving optimal design problems can be conditionally divided into two groups. One of them will include methods that are based on using necessary conditions for the extremum of the objective function. The second group includes methods: linear, convex and dynamic programming, random search methods. The application of modern methods of mathematical optimization requires powerful PCs with a large RAM, therefore, when choosing optimization, it is necessary to take into account the capabilities of computer equipment.
 The optimization algorithm for single–criteria parametric optimization is performed as follows: the objective function is the weight of the shell of the minimum surface on a rectangular contour, the design variables are the shell thickness from 1 to 50 mm, the constraints are presented with first forced oscillation frequency is 0,15 Hz.
 Using software complex Femap with Nastran and our own software, a single–criterion parametric optimization was made. The results of changing the objective function are reducing the weight of the shell by 2300 kg of C240 steel, which is equivalent to 10,3% without losing the strength and stability of the minimum surface shell on a rectangular contour. Using author's methodology and own software, it is possible to perform an effective optimization calculation for the minimum surface shell on a rectangular contour.