Development of a software solution to an applied mechanics problem based on numerical methods

The present work delves into the significance of material selection in the manufacturing of tools for milling operations and determines their suitability through a detailed analysis of strength and behavior during material processing. To enhance longevity and optimize production, the utilization of mathematical models and numerical methods, notably the least squares method and the solution of systems of linear algebraic equations (SLAE) employing the Gaussian elimination method with pivot selection, is proposed. These methods are applied for the approximation of experimental data and the analysis of material characteristics, ensuring precision in the evaluation of its properties. Situations where only partial data is known are investigated, along with simplifications in the computation of known functions. The study encompasses software for numerical computation and visualization of various problem types, effectively addressed through the aforementioned methods. The software algorithm for data approximation involves storing information in a text file, user input of variables, and selection of the quantity and type of basis functions. After the user inputs of parameters, the program formulates a system of equations based on selected functions, determines approximation coefficients, and generates a graph for an objective assessment of results. With a user-friendly interface, users can easily interact with the program, input values, and analyze results through graphical representation, streamlining the workflow and facilitating the comprehension of obtained data. The approximation of functions using numerical methods proves to be efficiently applicable in diverse fields for addressing applied mechanics problems.