臺灣博碩士論文加值系統

本論文主要探討對於複合圓錐殼以及多層旋轉空心圓柱受到不同的邊界條件情況下，其二維軸對稱虛靜偶合的熱彈性暫態反應。利用混合拉式轉換以及有限差分法來處理此類問題。首先，將推導完成的控制微分方程式以及邊界條件利用有限差分法來處理；然後，經過離散化之後的方程式，使用拉式轉換來解決時間項的問題。再利用矩陣相似轉換以及逆拉式轉換來獲得數值解。為了證明此混合方法的效用，本論文分別針對以下三類關於熱彈性暫態反應的問題來進行分析：（1）複合圓錐殼建立在曲線圓錐座標下的熱彈性問題。（2）複合圓錐殼當底部固定的情況下，而且內部受到爆炸性壓力以及外部受到冷卻效應的熱彈性問題。（3）多層旋轉空心圓柱受到內壓力以及外冷卻效應的熱彈性問題。同時所得到結果將顯示其收斂性是很快速的。這種目前使用的混合方法也可以在特定時間能獲得穩定解，更進一步可以斷定這種方法對於處理熱彈性問題是一種強有力和有效率的計算的過程。 利用此混合方法，對於溫度、位移以及熱應力的分佈可以獲得暫態以及穩態下的數值解。 而且，在這些數值結果下，不同的旋轉速度對於其造成的影響也可以被探討出來。

The problem of the two-dimensional axisymmetric quasi-static coupled thermoelastic transient response for the laminated circular conical shells and rotating annular multilayered cylinder subjected to arbitrary boundary conditions is presented. The analysis is carried out using a hybrid Laplace transformation and finite difference method. The present method divides the governing differential equations and boundary conditions into the finite difference method and then removes the time dependences from the discretized equations with the Laplace transform. The solutions were obtained by using the matrix similarity transformation and inverse Laplace transform. To demonstrate the proposed method’s validity, a series of problems of the thermoelastic transient response are evaluated as three categories: (1) the problems of laminated circular conical shells based on the curvilinear circular conical coordinates; (2) the problems of the laminated circular conical shells with clamped surface subjected to an internal blasting pressure and the external cooling process; (3) the problems of a rotating annular multilayered cylinder with inner and outer surfaces subjected to internal pressure in the inner surface and external cooling process in the outer surface. It was shown that the solutions are rapidly convergent. When applied to many nodes it takes an excessive amount of computer time. The present hybrid method can obtain stable solutions at a specific time; thus it is a further concluded that the method and the computing process of the generalized coupled transient thermoelastic problems are powerful and efficient. Solutions for the temperature, displacement and thermal stress distributions in both transient and steady state are obtained. Moreover, the effects of the different rotational speeds on these numerical results with the rotating annular multilayered cylinder were also discussed.

中文摘要.......................................................i
Abstract......................................................ii
致謝.........................................................iii
Contents......................................................iv
Tables........................................................vi
Figures......................................................vii
Chapter 1. Introduction and Background Survey..................1
Chapter 2. A Generalized Thermoelasticity Problem of Multilayered Conical Shells....................................9
2.1. Formulation...............................................9
2.2. Computational Procedures.................................14
2.3. Numerical Results and Dscussions.........................20
Chapter 3. Thermoelasticity Problems of Multilayered Conical Shells Sbjected to Internal Pressure and External Cooling.....33
3.1. Formulation..............................................33
3.2. Computational Procedures.................................34
3.3. Numerical Results and Discussions........................37
Chapter 4. Thermoelastic Transient Response of a Rotating Annular Multilayered Cylinder Subjected to Internal Pressure and
External Cooling.............................................41 Formulation...................................................50
4.2. Computational Procedures.................................53
4.3. Numerical Results and Discussions........................59
Chapter 5. Conclusions........................................77
References....................................................78
Appendix A. Derivation of the governing equation in chapter 2.............................................................81
Appendix B. The matrices in chapter 2.........................85
Appendix C. The matrices in chapter 3.........................94
Appendix D. The matrices in chapter 4........................104
Appendix E. Computer Programs................................114
自述.........................................................161

1. Timoshenko, S., Woinowsky-Krieger, S., 1959. Theory of plates and shells. McGraw-Hill, New York, N.Y.
2. Flügge, W., 1960. Stresses in shells. Springer-Verlag, Berlin, W. Germany.
3. Jianpong, P. and Harik, I. E., 1990. Iterative FD solution to bending of axi- symmetric conical shells. Journal of Structural Engineering 116, 2433-2446.
4. Wu, C. P., Hung, Y. C., 1999. Asymptotic theory of laminated circular conical shells. International Journal of Engineering Science 37, 977-1005.
5. Wu, C. P., Hung, Y. C., Lo, J. Y., 2002. A refined asymptotic theory of laminated circular conical shells. European Journal of Mechanics A/Solids 21, 281-330.
6. Wu, C. P., Chiu, S. J., 2001. Thermoelastic buckling of laminated composite conical shells. Journal of Thermal Stresses 24, 881-901.
7. Wu, C. P., Chiu, S. J., 2002. Thermally induced dynamic instability of laminated composite conical shells. International Journal of Solids and Structures 39, 3001-3021.
8. Wu, C. P., Tarn, J. Q., Yang, K. L., 1996. Thermoelastic analysis of doubly curved laminated shells. Journal of Thermal Stresses 19, 531-563.
9. Lu, C. H., Mao, R., Winfield, D. C., 1995. Stress analysis of thick laminated conical tubes with variable thickness. Composites Engineering 5, 471-484.
10. Tavares, S. A., 1996. Thin conical shells with constant thickness and under axisymmetric load. Computer and Structures 60 (6), 895-921.
11. Sofiyev, A. H., 2003. The buckling of an orthotropic composite truncated conical shell with continuously varying thickness subject to a time dependent external pressure. Composites: Parts B 34, 227-233.
12. Kardomateas, G. A., 1989. Transient thermal stresses in cylindrically orthotropic composite tubes. Journal of Applied Mechanics 56, 411-417.
13. Kardomateas, G. A., 1990. The initial phase of transient thermal stresses due to general boundary thermal loads in orthotropic hollow cylinders. Journal of Applied Mechanics 57, 719-724.
14. Ootao, Y., Tanigawa, Y., 2002. Transient thermal stresses of angle-ply laminated cylindrical panel due to nonuniform heat supply in the circumferential direction. Composite Structures 55, 95-103.
15. Khdeir, A. A., 1996. Thermoelastic analysis of cross-ply laminated circular cylindrical shells. International Journal of Solids and Structures 33 (27), 4007-4017.
16. Jane, K. C., Lee, Z. Y., 1999. Thermoelastic transient response of an infinitely long multilayered cylinder. Mechanics Research Communications 26, 709-718.
17. Jane, K. C. and Lee, Z. Y., 1999. Thermoelasticity of multilayered cylinder. Journal of Thermal Stresses 22, 57-74.
18. Pagano, N. J., 1972. The stress field in a cylindrically anisotropic body under two-dimensional surface tractions. Journal of Applied Mechanics 39, 791-796.
19. Wang, J. T. S., Hsu, T. M., 1970. A theory of laminated cylindrical shells consisting of layers of orthotropic laminate. AIAA Journal 8 (12), 2141-2146.
20. Ahmed, S. M., Zeiden, N. A., 2002. Thermal stresses problem in non-homogeneous transversely isotropic infinite circular cylinder. Applied Mathematics and Computation 133, 337-350.
21. Chaudhuri, R. A., 1986. Arbitrarily laminated, anisotropic cylindrical shell under internal pressure. AIAA Journal 24 (11), 1851-1858.
22. Bhimaraddi, A., Chandraskhehara, K., 1992. Three-dimensional elasticity solution for static response of simply supported orthotropic cylindrical shells. Composite Structures 20, 227-235.
23. Eduljee, R. F., Gillespie, J. W., 1996. Elastic response of post- and in situ consolidated laminated cylinders. Composites 27A, 437-446.
24. Jing, H. S., Tzeng, K. G., 1993. Approximate elasticity solution for laminated anisotropic finite cylinders. AIAA Journal 31 (11), 2121-2129.
25. Wang, J. T. S., Lin, C. C., 1994. Stresses in composite cylinders. Composites Engineering 4 (11), 1129-1141.
26. Türkmen, H. S., 2002. Structural response of laminated composite shells subjected to blast loading: comparison of experimential and theoretical methods. Journal of Sound and Vibration 249 (4), 663-678.
27. Wang, X., Zhang, K., Zhang, W., Chen, J. B., 2000. Theoretical solution and finite element solution for an orthotropic thick cylinderical shell under impact load. Journal of Sound and Vibration 236 (1), 129-140.
28. Abd-Alla, A. M., Adb-alla A. N., Zeidan, N. A., 2001. Transient thermal stresses in a transversely isotropic infinite circular cylinder. Applied Mathematics and Computation 121, 93-122.
29. Drozdov, A. D., 1997. The non-isothermal behavior of polymers. 2. Numerical simulation. European Journal of Mechanics A/Solids 16, 937-991.
30. Hyer, M. W., Cooper, D. E., 1986. Stresses and deformations in composite tubes due to a circumferential temperature gradient. Journal of Applied Mechanics 53, 757-764.
31. Wang, X., Li, S. J., 1992. Analytic solution for interlaminar stresses in a multilaminated cylindrical shell under thermal and mechanical loads. International Journal of Solids Structures 29 (10), 1293-1302.
32. El-Naggar, A. M., Abd-Alla, A. M., Ahmed, S. M., 1995. On the rotation of non-homogeneous composite infinite cylinder of orthotropic material. Applied Mathematics and Computation 69, 147-157.
33. Abd-All, A. M., Abd-Alla, A. N., Zeidan, N. A., 1999. Transient thermal stresses in a rotation non-homogeneous cylindrically orthotropic composite tubes. Applied Mathematics and Computation 105, 253-269.
34. Chen, C. K., Chen, H. T., Chen, T. M., 1987. Hybrid Laplace Transform/Finite Element Method for One-Dimensional Transient Heat Conduction Problems. Computer Methods in Applied Mechanics and Engineering 63, 83-95.
35. Chen, C. K., Chen, H. T., 1988. Application of Hybrid Laplace Transform/Finite Different Method to Transient Heat Conduction Problem. Numerical Heat Transfer 14, 343-356.
36. Boresi, P., Chong, K. P., 1987. Elasticity in Engineering Mechanics. Elsevier, New York.