Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue
Abstract
:1. Introduction
2. Materials and Methods
2.1. Formulation of the Problem of the Mechanics of a Four Implant-Supported Overdenture
2.2. Mathematical Model of the Interaction of a Four-Implant Overdenture with Bone Tissue Research Methodology
2.2.1. Basic Assumptions of the Model
- (1)
- The metal structure, including 4 implants, a unifying polygonal bar, and an arched base of the dentition, is a solid and absolutely rigid spatial frame;
- (2)
- (3)
- The mechanical contact between the components is considered perfect.
2.2.2. Coordinate Systems and Some Vector Operations
2.2.3. Key Equations of the Model
Kinematics
Statics
Physical Relations
Equation of Statics in Displacement
Stress Calculation Scheme
Strength Conditions
3. Results and Analysis
3.1. Analytical Solution
3.2. Examples of Calculation
3.2.1. Example 1
3.2.2. Example 2
4. Discussion
- −
- A computed tomography (CT) analysis of the state of the jaw and dentition;
- −
- The identification of the mechanical properties of bone tissue and teeth according to the established CT density distribution;
- −
- The development of a solution to the problem of jaw interaction with an overdenture variant based on finite element analysis using ANSYS, SolidWorks, or ABACUS software systems;
- −
- Overdenture design based on the results of the numerical analysis.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Implant No. | 1 | 2 | 3 | 4 |
---|---|---|---|---|
−21 | −12 | 12 | 21 | |
17 | 6 | 6 | 17 | |
−21 | −12 | 12 | 21 | |
5.5 | −5.5 | −5.5 | 5.5 |
Tooth No. | |||||||
---|---|---|---|---|---|---|---|
3 | 9 | 15 | 19 | 23 | 25 | 28 | |
1 | 3 | 7 | 13 | 20 | 29 | 40 | |
3 | 9 | 15 | 19 | 23 | 25 | 28 | |
−10.5 | −8.5 | −4.5 | 1.5 | 8.5 | 17.5 | 28.5 |
No. of Implant | 1 | 2 | 3 | 4 |
---|---|---|---|---|
−16 | −6 | 6 | 16 | |
11 | 4 | 4 | 11 | |
−16 | −6 | 6 | 16 | |
3.5 | −3.5 | –3.5 | 3.5 |
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Pelekhan, B.; Dutkiewicz, M.; Shatskyi, I.; Velychkovych, A.; Rozhko, M.; Pelekhan, L. Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue. Materials 2022, 15, 2398. https://doi.org/10.3390/ma15072398
Pelekhan B, Dutkiewicz M, Shatskyi I, Velychkovych A, Rozhko M, Pelekhan L. Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue. Materials. 2022; 15(7):2398. https://doi.org/10.3390/ma15072398
Chicago/Turabian StylePelekhan, Bohdan, Maciej Dutkiewicz, Ivan Shatskyi, Andrii Velychkovych, Mykola Rozhko, and Liubomyr Pelekhan. 2022. "Analytical Modeling of the Interaction of a Four Implant-Supported Overdenture with Bone Tissue" Materials 15, no. 7: 2398. https://doi.org/10.3390/ma15072398