Aims of research. This paper deals with the problem of determining the radius of the neutral surface of the bending strip at the same time the action of tensile stresses. Methods. In the development of technological processes of sheet bending and the calculation of the initial billet (sweep), most often considered a flat stress state and preference is given to the theory of pure bending, providing uniform curvature of the individual layers of metal under the action of the bending moment and neglecting the action of transverse tensile forces. However, in reality, bending is always accompanied by sliding of the metal along the deforming tool, causing the appearance of friction forces and creating a complex loading in the form of plastic bending with stretching in the metal, which will additionally displace the neutral surface, forcing the experienced one to adjust the technology of manufacturing bent parts. Provides an overview and analysis of the most famous works dedicated to the topic, specifying the distribution of the contact stresses from the inner surface to the center of curvature and developed the theory of complex bending, which allows to specify the radius of the neutral surface in conditions of stretching of the flexible strip of the additional tangential stresses. Results. The results obtained will allow to simulate the stress state of the metal in the development of technological processes of sheet stamping and, in particular, to assess the specific braking force during the bending (straightening) of the strip in the process of pulling through the thresholds and brake edges of the die tooling to eliminate possible defects in the elongated parts and to clarify the dimensions of the workpiece and the finished profile.

Relevance. As part of the implementation of the Federal Law No. 117-FZ “On the Safety of Hydraulic Structures”, it is necessary to continuously monitor the state of hydraulic structures and related facilities by equipping with control and measuring instruments. The development of modern computer complexes allows us to carry out and predict the state of objects by combining computational research and field observations. The work is aimed at organizing a comprehensive assessment of the state of the HPS and ensuring the safety of existing and projected mutually influential complexes. Aims of research. Improving the safety of the operated (under construction) complex of interfering hydraulic structures. Assessment of sufficient and highquality engineering and repair work carried out on the HPS. Development of recommendations for improving the efficiency of construction of new and modernization of operated hydropower facilities. HPS on the example of the Zagorsk HPS. Methods. Representation of the interaction ideology of various software systems of mathematical modeling, using control and measuring instruments data for calibration and verification of mathematical models. Results. The structure of the HSC calculation module was updated, systematization of the calculation models was carried out, interaction and transfer of the initial data to the calculation module of the software and hardware complex was revealed. The implementation of scientific research is aimed at improving the safety of the complex hydraulic structures.

Aims of research. Studying the possibility of forming Monge carved surfaces, defined by the method of their formation, creating an algorithm and program in the AutoLISP language to demonstrate the formation of surfaces in the AutoCAD environment in a dynamic mode. Methods. Monge carved surfaces are formed by a flat curve, located in the tangent plane to the fixed guide of the developable surface, when the plane and the curve roll along the guide surface without sliding. The described method of formation of these surfaces allows to perform their formation by the kinematic method in the AutoCAD environment using AutoLISP software. The article describes the construction of the Monge surfaces using cylindrical and conical surfaces as guides. A straight line and a sine wave are used as the forming lines. Results. An algorithm and a program in the AutoLISP language were created to form sets of compartments of several Monge surfaces and to visualize the formation of these surfaces in a dynamic mode by sequentially displaying the compartments on the monitor screen. The mini-film about formation of Monge surface by rolling a plane with a straight line along a circular cone is created. In the mini-film the drawings received by transformation of drawings of the AutoCAD environment are used.

Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

Aims of research. Derivation of consistent equations of the theory of thin elastic shells without hypotheses and stress averaging over the shell thickness. Methods. Using the iterative method of Saint-Venant - Picard - Banach, the three-dimensional problem of the theory of elasticity is solved without any hypotheses. By the principle of compressed mappings, the solution converges asymptotically, regardless of the choice of the values of the initial approximation. Results. A method has been developed for integrating the spatial equations of the theory of elasticity in curvilinear coordinates for a thin shell. The presence of a small parameter allows the integration of the system of equations in such a way that the output data of the first operator is input to the next operator, etc., dividing the original complex operator into a sequence of simple integrable Picard type operators. Each equation contains terms of only one asymptotic order.

Aims of research. Expert validation of all proposed design solutions, development of necessary design solutions for the heightening of the Limon dam according to the ICOLD recommendations. Methods. The detailed static and seismic (dynamic) analyses of stressstrain state and seepage of concrete face rockfill dam Limon (Peru) were performed using the advanced software FLAC-3D (USA) and PLAXIS 2D (Holland), respectively. The elasto-plastic model with Mohr - Coulomb criterion with variable shear angles of gravel and pebble zones of dam materials and its foundation soils was used in the static and seismic (dynamic) analyses of the dam. The dynamic nonlinear analyses of stress-strain state of two variants of Limon dam with full reservoir under Maximum Credible Earthquake (MCE) action of the Mar-Chile Earthquake accelerogram. Results. On the base of these analyses the recommendations were developed for the project of the dam heightening from 43 up to 82 m before the initial filling of the reservoir. Expert validation of all proposed design solutions, necessary design solutions for the heightening of the Limon dam were developed according to the ICOLD recommendations.