The article presents a methodology for creating a computer program based on a three-dimensional model of the dento-mandibular segment to determine the optimal individual parameters of solid cast-cult structures in the treatment of patients with defects in hard tissue of the teeth during the tooth root action of various loads in the periodontal stress and strain. The stress-strain state depends on various factors, such as the length of the root canal, the thickness of its walls, the size of the pin. The study of the influence of these factors is one of the important tasks of orthopaedic dentistry. To solve problems related to the restoration of damaged teeth, a three-dimensional computer model of the dental-maxillary segment was created using mathematical calculation of finite elements. The first stage is the project task. At the heart of the project is the choice of the type of scheme. We have chosen 5 types of general form systems. Each of the model elements with this system has 6 degrees of freedom (3 angles of rotation, 3 linear deformations behind the coordinate axes). The next step is the description of the tooth geometry, which we expect. According to the schematic image of the tooth we set the nodes of the finite element model. For each calculation, we obtained normal and tangential stresses along all coordinate axes; we also investigated equivalent stresses along four basic strength theories. Thus, the investigated three-dimensional tooth models allowed us to calculate the individual parameters of the future orthopedic design, to display digital data that will maximize individualization of the selection of optimal parameters for the restoration of damaged teeth of each patient. The root of the natural tooth has the shape of an elliptical cone. The periodontal thickness is constant over the entire root surface. The force of the tooth is 10 kg at an angle of 120 ° to the horizontal axis. The force is applied to a section that is 3.2 mm away from the cone axis. The height of the tooth is 15 mm, the angle of the cone is 12°, and the periodontal thickness is 0.25 mm with a modulus of elasticity of 1.07 kg / mm2. After the calculations were made, the coordinate of the center of resistance 9.8 mm at 10.2 mm, for example, was almost completely consistent, and the vertical tooth displacement was 0.0296 mm at 0.0309 mm, for example. But the horizontal displacement of the tooth differed very strongly 0,0289 mm at 0.0111 mm, for example.
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