Numerical implementation of multicriteria parametric optimization of minimum surface shell on a square contour under thermforce loading

Abstract

The article considers the numerical study of the multicriteria parametric optimization of the minimum surface shell on the square contour under thermoforce loading. The mathematical algorithm for solving the problem of multicriteria parametric optimization of minimal surfaces shellsis described: the necessary output data are given, which target functions can be used, design variables and constraints are described. The influence of initial data on the numerical study of multicriteria parametric optimization was shown. The calculation of necessary components and matrices for multicriteria parametric optimization of minimal surfaces shells, as well as methods of its simplification, depending on the initial data was made. Was shown in which cases the algorithm is executed successfully, and where it was necessary to return to change the initial parameters.
 The sensitivity analysis of multi-criteria parametric optimization of minimal surfaces shells is presented. In article reveals the inner essence of the structure's work while the optimization calculation was done. Work with internal forces and stresses, the connection with the finite element method and its stiffness matrix were made.
 The process and methodology of setting ofthermoforce loadare revealed.All initial parameters, as well as how the load works with multicriteria parametric optimization are shown.
 The numerical experiment made it possible to reduce the weight of minimum surface shell on the square contour by 5%, and the movement along the coordinate axes by 38%, which are the target functions of multicriteria parametric optimization. Redistribution of the thickness of the minimum surface shell on the square contour from 1 mm to 31 mm was realized. The interaction of the objective functions is shown - they conflict, as well as the graphs of changes in Mises stresses, shear stresses and strain energy, which makes it possible to reveal the internal processes of multi-criteria parametric optimization of the minimum surface shell on a square contour.
 Subject of this study is an interesting applied problem for construction mechanics, as it is the first time to display the application of two types of optimization on one research object.