Multicriteria parametric optimization of the stability of the minimum surface shell on a circular contour, which consists of two inclined ellipses, taking into account geometricnonlinearity under thermostress loading

Abstract

This scientific publication presents an interesting applied problem of numerical research into the optimal design of a spatial thin-walled structure under thermo-mechanical loading. Optimal design of load-bearing structures can be divided into four main types: parametric, topological, shape optimization, and creation of composite materials for a specific task. There may be combinations of two or more types of optimization on a single object under study. This scientific publication considers two types of optimal design on a single object under study.

A minimal surface shell is a thin-walled spatial structure with a given contour and a certain specified height, which was subsequently constructed using the parameter continuation method. The parameter extension method makes it possible to construct the optimal shape of the future minimal surface shell, which minimizes the internal forces, which in turn reduce the Mises stress, which is decomposed into normal and tangential stresses, leading to a reduction in the thickness of the shell.

Optimal design of load-bearing structures into four main types: parametric, topological, shape optimization, creation of composite materials for a specific task. There may be combinations of two or more types of optimization on a single object under study.

Multi-criteria parametric optimization of the minimum surface shell is performed in an automated mode in the Femap with Nastran software package and connected proprietary software, which was developed for a specific area of scientific and technical activity within the framework of applied research.

A theoretical formulation of the relationship between the loss of stability of the minimum surface shell on a circular plane is presented, taking into account geometric nonlinearity under thermo-mechanical loading.

After optimization calculation based on Figures 2-11, the first form of stability loss is λ=1, which corresponds to the minimum limit before stability loss.

Graph 13 shows the change in target functions. We managed to reduce the weight by 8.8 tons, which is 23%, while the coefficient λ decreased from 5.36 to 1.01, which is actually 6 times less. This calculation allows for the minimum thickness of the shell of the minimum surface before loss of stability.