Keyword: «numerical method»

The problem of determining the optimal sizes of timber and boards during cutting of saw logs with a brus method is considered, taking into account the Pythagoric and the runaway (parabolic) zones.As a criterion of optimality, the volume of lumber obtained is chosen. The mathematical model is compiled by the classical method and consists of the objective function and the coupling equations. To solve the mathematical model, the method of Lagrange multipliers is used. The numerical method is used to determine the optimal dimensions of the timber and boards. It turned out that with increasing log length, the relative sizes (thickness and width) of boards obtained from the run-off zone increase, and their relative length decreases. When the log length is increased, the relative thickness of the log decreases insignificantly within 0.604 ... 0.584. The total volume of sawn timber obtained from the Pythagoric and the runaway zones decreases with increasing log length.It is more profitable to cut sawlogs according to such a sawing scheme with a shorter log length.

The article considers a method for improving the cooling efficiency of a gas turbine GTE based on a numerical method for calculating the thermal fields of the gas flow, using the Fine/Turbo module of the NUMECA software complex . The proposed approach will improve the understanding of the principle of cooling turbines and directions for further improvement of engines in the training of military personnel in military educational institutions.

The article discusses the construction of a mathematical model for the time-optimal vertical lift of a helicopter. The solution is based on the maximum principle in the presence of restrictions on phase co-ordinates and control. To simplify the algorithm fordetermining optimal control, it is proposed to use a numerical optimization method.