An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus
Abstract
:1. Introduction
2. Mathematical Model for Mandible Body
3. Equations of a Plane Spring Loaded Perpendicular to Its Plane [1]
- .
- (-Mr)on—radial moment;
- (-Mt)on—tangential moment.
- A resultant with module .
- (-Mr + dMr) on ;
- (-Mt + dMt) on .
- γt (s) after tangent;
- γn (s) after normal;
- γt (s) ds;
- γn (s) ds;
- Projection on :dMt + Mr dψ + γt ds = 0,
- Projection on :dMr + Mt dψ + γn ds − Tds = 0,
- Projection on :d T = − p (s) ds.ds = R dψ.
- E—Longitudinal modulus of elasticity (Young’s modulus);
- G—Transverse modulus of elasticity;
- I—Moment of inertia around the horizontal axis;
- J—Torsional stiffness inertia.
4. Transfer Matrix of Spring Model Loaded Perpendicular to Its Plane
4.1. General Expression of the Transfer Matrix
4.2. Calculus of Elements for the Vector Corresponding to an External Vertical Concentrate Load in Section at Angle θ = θ0
5. Application to a Model as a Quarter Circle for Mandible Body by TMM: Results
6. Discussion
Funding
Data Availability Statement
Conflicts of Interest
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Suciu, M. An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus. Mathematics 2023, 11, 450. https://doi.org/10.3390/math11020450
Suciu M. An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus. Mathematics. 2023; 11(2):450. https://doi.org/10.3390/math11020450
Chicago/Turabian StyleSuciu, Mihaela. 2023. "An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus" Mathematics 11, no. 2: 450. https://doi.org/10.3390/math11020450
APA StyleSuciu, M. (2023). An Approach Using the Transfer Matrix Method (TMM) for Mandible Body Bone Calculus. Mathematics, 11(2), 450. https://doi.org/10.3390/math11020450