NUMERICAL STUDY OF THE PARAMETRIC OPTIMIZATION OF THE FORCED FREQUENCY OF OSCILLATIONS OF THE MINIMUM SURFACE SHELL ON THE SQUARE CONTOUR UNDER THERMAL LOAD

Abstract

The optimal design in applied mechanics is used to improve the efficiency of minimal surface shells, this process is carried out until the design can no longer be better given the input data, using a certain optimization method.
 It has several advantages while building structures are designing. One of the passes is the optimization process, which provides a systematization, a logical procedure for the design of shells. With the correct use of the optimization algorithm, it is possible to reduce the probability of a designer's mistake. Modern optimization methods can be applied to problems that have more than a million design variables and constraints.
 Optimization algorithms work effectively when there is some regularity in the objective function, such as a convexity or a depression, so when choosing an optimization algorithm, it is necessary to consider their advantages and disadvantages.
 While minimizing the objective function fmin, the main task is to find the point of the global minimum, the value of fmin (X) will be minimal, taking into account the restrictions.
 Determining the global minimum is quite a difficult task. Much more often, a point has a local minimum, and the task of the designer is to investigate where the point of the local and global minimum is.
 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 the square contour, the design variables are the shell thickness from 1 to 100 mm, the constraints are presented - the first forced oscillation frequency is 0.10 Hz.
 The results of changing the objective function are reduction in the weight of the shell, which is in the percentage equivalent of 9.6% without losing the strength and stability of the minimum surface shell on the square contour. The first forced oscillation frequency after the optimization calculation from the thermoforce load is 0.10187155 Hz, which is actually represented by the limitation.
 Using the author's methodology and software, it is possible to perform an effective optimization calculation of the minimum surface shell on the square contour.