Multi-criteria parametric optimisation of the displacement and weight of the shell of a minimal surface with a rectangular plan consisting of two straight lines and two semicircles under thermal and power loading

Abstract

The solution of multi-criteria parametric optimization, where several objective functions are used simultaneously and automatically, is an interesting task for applied and structural mechanics. Modern parametric optimization is performed, because of calculation complexes with additional modules that are programmed in modern programming languages and provide new opportunities for managing calculation methods for spatial structures.

The envelopes of minimal surfaces are very interesting objects of study for optimal design in general and for research in structural and applied mechanics. A minimal surface is a surface in which the median curvature is zero at all points, and thus a minimal surface is a surface of negative Gaussian curvature.

The optimal design of spatial structures is carried out in the main directions, primarily as the main calculations are performed for two groups of boundary states: strength, stability, vibrations, weight, and volume. These are the main objective functions that make it possible to optimize the main characteristics of the structure under static and dynamic external loads when studying the stress-strain state.

Parametric optimization is understood as the process of achieving an extreme goal under the assumption of stationarity of the extreme characteristic of the optimization object in the plane of the minimum surface envelope, which is limited by its geometry and input and output parameters. In this case, the optimization object can either actually exist or be a mathematical model. Methods and algorithms of parametric optimization play an important role in the general mathematical method of design calculation.

A multi-criteria parametric optimizations was used to reduce the weight of the shell. The Mises stresses meet the limit of 260 MPa. It should be noted that the theoretical optimum of the objective functions at the point of intersection of the two objective functions is 260 MPa, which is a limitation, we can conclude that despite the fact that the two objective functions conflict, at the point of optimum, they work quite effectively in this problem statement.