Multicriterial parametric optimization in a pair of target functions: weight and movement of the shell minimum surface on the straight

Abstract

The article considers the numerical study of multicriteria optimization of the minimum surface of a shell on rectangular contour taking into account the thermal load. The authors showed the theoretical formulation of multicriteria parametric optimization. Using of thermal force load is very important for objects that have a large span, especially using the static and temperature load in one place of a shell. This makes it possible to cover a wider range of construction site operation. In structural mechanics, there are three main types of standard shells of minimum surface: shape optimization, parametric optimization, and topological optimization. The article simultaneously combines two studies on the same object: shape optimization and parametric. The method of constructing this minimal surface on a rectangular contour is described. The specifics of the issuance of thermal power load in the optimization calculation, which is in all initial indicators and coefficients. The types of work of target functions are shown, namely: under what conditions they conflict, under what conditions they consolidate, under what conditions they are independent of each other. The numerical study uses the author's software, which allows in automatic mode a multicriteria optimization calculation with target functions - weight and Mises stress, design variables - thickness from 1 to 200 mm, presented as a Mises voltage of 240 MPa. The result showed that the target functions of the conflict change, but the weight decreases by 15%, and move along the coordination axes by 80% of the elements. After determining the displacements and stresses according to Mises, the process of designing and selecting the section of the structure for construction begins. The stage of design makes it possible to save material and redistribute it to the desired zones. From the graph of the change of objective functions according to the optimal height, what is the point for the objective functions - weight and move along the coordination axes is absence. The overall purpose of the study shows the possibility of using authoring software to use two types of optimization: optimization of shapes in the form of these minimum surface parameters on rectangular contour and multicriteria optimization together on the research subject, which is interesting and applied in structural mechanics.