ДОСЛІДЖЕННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ НИЖНЬОЇ ЩЕЛЕПИ МЕТОДОМ ГРАНИЧНИХ ЕЛЕМЕНТІВ

Abstract

The work considers the movable part of the human skeleton - the lower jaw. The article takes into account that a person chews food many times a day. Determination of internal force factors, stresses and deformations is one of the main tasks of scientific research in orthopedics and maxillofacial surgery. The study examined the methodology for the formation of the design scheme of the lower jaw as a spatial frame structure. For the frame, such types of resistance as bending, torsion, shear, and tension-compression are taken into account. It should be noted that the latter types of resistance are usually neglected. The work shows schematically the chewing load and the contact of the upper and lower jaw in the form of a pivotally movable support. To determine the parameters of internal force factors, stresses, and deformations of the tender jaw as a spatial frame, a numerical-analytical version of the boundary element method was used for the first time, as well as the well-known dependences of the mechanics of a deformable solid. The article takes into account the linear dimensions of the lower jaw, the places of applying an external load are schematically reflected, and the boundary conditions are taken into account. When applying the numerical calculation method, the model takes into account the overall dimensions of the cross-sections of the jaw and the mechanical characteristics of the bone. To apply the numerical-analytical version of the boundary element method (CA MBE), the equation of compatibility of linear and angular displacements, the equilibrium equation of the nodes for the transverse forces, bending and torques are compiled. The state vector of the skin area of the spatial frame is compiled according to the algorithm of the CA MBE. As a result of the calculation, the values of the deflections, bending moments and rotation angles are obtained. The CAE program implementing the CA MBE is designed so that it is possible to display on a computer monitor diagrams both for the entire frame and for individual nodes selected by the user.