1. Theory of Elasticity Report at the end of term Student number ： M96520007 Name ： YI-JHOU LIN Life-time Distinguished Professor ： Jeng-Tzong Chen

2. Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft Brief introduction : Inverse Theory ? Simple example: P △ 1.Straight Computation Problem P known △ unknown 2. Inverse Computation Problem P un known △ known

3. Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft The question description: ω 1.Polar coordinate system r θ 2.Constant angular velocity ω 3.Concentric circles rim L and L 1 with the radii R and R 1 4.The tightness function g( θ ) is unknown

4. Boundary conditions: 1. 2. Symbol: 1. 2. 3. i 2 = -1 4. Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft :stresses :displacements :const should be determined upon solution

5. For solution of boundary value problen ( １ )we mentally separate the disk and the shaft. We obtain the following boundary conditions for the disk: the normal and tangential contact stresses are unknown and will be determined upon solution of the problem. Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

6. Without loss of generality, expanded in the Fourier series planar theory of elasticity equations of volumetric forces, Let us represent the stressed state in the rotating circular disk in the fo Similarly, the shaft (these stresses are known [1]) Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

7. According to [2], boundary conditions (1) and (2), taking into account (3), can be represented in the form The complex potentials disk are shaft Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

8. For determination of the unknown coefficients, we use boundary condition for displacements. where γ is the weight of a unit volume of the disk; g is the acceleration of gravity; Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

10. optimal design, is provided by the minimization criterion Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

11. REFERENCES: [1]. Timoshenko, S. P., Soprotivlenie materialov (Mechanics of Materials), Moscow: Nauka, 1965. [2]. Muskhelishvili, N. I., Nekotorye osnovnye zadaci matematicheskoi teorii uprugosti (Some Basic Problems of the Mathematical Elasticity Theory), Moscow, Nauka: 1966. [3]. Mirsalimov, V. M. and Allahyarov, E. A., The Breaking Crack Build-Up in Perforated Planes by Uniform Ring Switching, Int. Journ. of Fracture, 1996, vol. 79. no. 1. pp. 17–21. Inverse Theory of Elasticity Problem of Mounting a Disk on a Rotating Shaft

12. Thanks end