STABILITY OF A DOUBLE-CONNECTED CONICAL SHELL OF MINIMAL SURFACE UNDER THERMAL AND POWER LOADING WITH CONSIDERATION OF GEOMETRIC NONLINEARITY

In the practice of designing thin-walled spatial structures (shells of minimal surfaces) in the form of complex surfaces, the task of determining the coordinates of the discrete majority of points on the surface of the coating often arises. Minimal surfaces consisting of points defined by three coordinates are most naturally modulated in modern computational complexes such as Femap with Nastran. An important task in the design of minimal surfaces of thin-walled coatings is to include lines of a given shape and position (most often second-order curves or higher-order curves) in the surface frame. The shells created in most cases are monotonous and geometrically primitive, in this scientific article we consider shells of minimal surface, which in fact, due to the coordinate method of setting the point frame, are optimized in shape. In fact, the optimal shape of the shell of the minimum surface is due to the fact that the internal forces, namely, bending moment, transverse force, and longitudinal force, are of small values and are compensated by its shape. An interesting point is that these shells can be specified on any shape in terms of plan: round, square, rectangular, trapezoidal, conical, and others. The stability of this type of shells of minimal surfaces is an interesting applied problem and numerical modeling for structural and applied mechanics. Problems of geometric nonlinearity are an important issue in structural and applied mechanics. The nonlinearity of differential equations does not help to apply analytical approaches, which necessitates the use of numerical methods such as the finite element method (FEM). For these problems, the finite element method has been studied in the problems of isotropic bodies. In this scientific work, a numerical study of the stability of a double-connected cone shell of minimal surface was performed, and new applied results were obtained. The eigenvalue of the safety factor is 0.9999, which means that there is no safety margin in the shell, and we can further use these results for multicriteria parametric optimization, and the results of the study are confirmed by the authors' methodology for objects where optimization of the shell geometry is taken into account.