Mathematical modeling in the development of complex objects in mechanical engineering

   Objectives. This paper considers the role of mathematical modeling in the development of complex assemblies and components in mechanical engineering, especially in terms of predicting the operational behavior of assemblies, as well as that of housing components during machining at the design stage.

   Particular attention is paid to the difficulties arising from the multifactorial nature, uncertainty, and nonlinearity of the objects under study, as well as the high reliability requirements of the products being manufactured.

   The development of a variational approach for assessing the rigidity of assemblies and the stability of components during machining is presented.

   Methods. Among the mathematical modeling approaches used at various stages of development, particular attention is paid to finite element analysis, which allows for a detailed study of the mechanical stresses experienced by structural elements during the manufacture and machining of complex components. Analytical techniques are employed to analyze the specific features of forming mathematical models of complex assemblies. The parametric identification method is used to determine the mechanical characteristics of complex components.

   Results. The need to integrate computer technologies and experimental research to improve the efficiency of mechanical engineering design and manufacturing processes is substantiated. The key stages and approaches to creating mathematical models of complex objects are outlined on examples of the successful implementation of numerical analysis and computational mechanics methods in component manufacturing. Experiments revealed that the current theories for modeling complex objects demonstrate a high level of model adequacy.

   Conclusions. The parametric identification method is shown to be suitable for analyzing critical loads on load-bearing components of complex assemblies and in the design of highly loaded components that require high rigidity and stability during machining.

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