Multi-criteria parametric optimization of the strength and weight of a shell of a minimum surface on a square contour under thermal and power loading, taking into account geometric nonlinearity

In applied and structural mechanics, many examples of optimal design with different objective functions are considered, but there is a need to take research in this area to a new level. The object under study with two or three simultaneous types of optimization is an actual applied problem in the field of construction and applied mechanics. One of the main tasks of designing minimal surfaces is to find the optimal shell shapes for given overall dimensions and shape in plan, taking into account parametric optimization - it is necessary to implement a modern optimization algorithm in the calculation of this structure. Its solution should be brought to ready-made formulas, graphs, tables, calculation examples and practical. The system of solving equations of the finite element method is formed using the Lagrange's variational principle, according to which the total potential energy P of a finite element model of a body is in a state of stability and equilibrium has a minimum value. Within the framework of the study, a methodology for obtaining the ratio of the finite element method with regard to geometric nonlinearity is presented that does not depend on the shape and properties of the finite elements, so it can be implemented for a plate finite element of a shell of minimal surface. To study the multicriteria parametric optimization of the minimum surface shell with regard to geometric nonlinearity, a special additional optimizer module created by the authors is used, which is linked to the Femap with Nastran calculation complex [12]. The computational model is built by the finite element method, which makes it possible to perform a qualitative study of optimization taking into account the objective functions: Mises stress and structural weight. This methodology proves to be effective in the study of multi-criteria parametric optimization with consideration of geometric nonlinearity. Such an approach to the calculation of building structures makes it possible to use structural materials efficiently, and modern calculation complexes based on the finite element method (FEM) can be used in further development at the level of building codes of Ukraine.