СТАТИЧНА РІВНОВАГА ВУЗЛІВ БІОТЕНСЕГРІТІ-МОДЕЛІ ОПОРНО-РУХОВОГО АПАРАТУ ЛЮДИНИ

The study is devoted to the investigation of the mathematical conditions of static equilibrium of nodes in a discretely represented interpretive biotensegrity model of the human musculoskeletal system (MSS). The relevance of this topic is determined by the need for a formalized mathematical description of the joint mechanical behavior of bones, muscles, and tendons forming the lower part of the human body, considered as a mechanical system subjected to prescribed gravitational loads. Such a description makes it possible to construct a model that, in turn, enables the determination of internal forces in all its elements through discrete geometric modeling. The model is based on the concept of geometrically invariant mesh structures, in which each element, within a mechanical interpretation, works exclusively in compression or tension, thus preventing the occurrence of bending or torsional moments due to the hinged connections between the corresponding elements. At the same time, the model possesses the properties of spatial tensegrity structures, in which all compressed elements are represented by struts, while all tensioned elements are represented by cables. When applied to biomechanical problems, this approach describes the behavior of so-called biotensegrity models of the musculoskeletal system. The present study is a logical continuation of previous research on the principles of forming geometrically stable mesh structures through their step-by-step kinematic analysis. Based on the concept of self-equilibrated mesh structures, a system of static equilibrium equations has been formulated for the free nodes of spatial biotensegrity models. This system allows for the determination of the interaction between compressive and tensile elements within the limits of their elastic deformation under applied nodal loads. The specific features of constructing the corresponding equations for discrete systems with prestressed elements are also considered. It is demonstrated that the application of methods of applied geometry, combined with the principles governing classical mechanical systems, ensures a correct mathematical interpretation of the functioning of the human musculoskeletal system. The obtained results provide a foundation for further numerical studies, including the modeling and analysis of stress–strain state components of the interpretive model elements, their step-by-step optimization, and their application in problems of biomechanics, physical therapy, and rehabilitation.