A numerical study of the multicriteria parametric optimization of the displacement and weight of a two-connected conical shell of minimal surface under thermal and power loading

Abstract

Various methods and approaches are used to solve the problem of optimal design. Problems of this type are used for the optimal design of spatial coverings, which in modern architecture are progressive structures that are of interest to the whole world. Spatial coatings allow to give the building architectural expressiveness, cover large spans and combine load-bearing and enclosing functions.
 The hulls of minimal surfaces are the hulls of negative Gaussian curvature. In general, the geometry of minimal surfaces cannot be described analytically. To solve this problem, which is associated with solving the differential equation that describes the minimal surface in general, under appropriate boundary conditions, one has to use methods of numerical analysis. This approach allows us to build a point frame of the shell, which is a matrix of discrete solutions of functions that searches for a given minimum surface. In view of this, its geometric characteristics can be obtained only in numerical form.
 The basic relations of the linear theory of thin elastic shells of minimal surface are highlighted in the numerical study of parametric optimization. The mathematical justifications of how the external load is perceived and the process of creating the stress-strain state of the shells of minimal surfaces are highlighted.
 For the numerical implementation of the multicriteria parametric optimization of a double-connected conical shell of minimal surface, a finite element model was built from plate finite elements in the amount of 4824 pieces and 4896 nodes. The perimeter is rigidly clamped to the ground disk. The thermal force load is set, which consists of a combination of static and temperature loads.
 The developed methodology shows quite good results that coincide with the works of other authors and makes it possible to use two types of optimization for one research object simultaneously. The first stage is shape optimization, and the second stage is multicriteria parametric optimization.
 This methodology makes it possible to perform optimization processes in an automated mode, which is an important applied task for construction and applied mechanics.