本文內容使用一階剪切變形理論以及虛功原理推導出適合分析圓錐薄殼之大變形理論，使用移動最小二乘法配合quasi-Hermite type formulation，處理平衡方程式以及本構關係式，以便於數值分析。在進行數值求解時，係將推導出之圓錐薄殼大變形的平衡方程式，使用Newton-Raphson method予以變分處理，將其方程式線性化，並利用迭代計算的方式，去逼近其大變形後的位置，進而可以計算出其薄殼發生變形後的軸力、剪力以及彎矩。本文的數值範例分析了封閉圓錐殼討論其承受壓力的挫屈行為，以及承受內壓力膨脹時之非線性行為，還有開放式圓錐殼之snap through行為。

In this article, the assumption of first-order shear deformation and the principle of virtual work are employed to derive large deformation theory of conical shells. With the quasi-Hermite type formulation in moving least squares method (MLS), it can handle equilibrium equations, constitutive relations, to get the numerical solution. When solving the numerical solution, nonlinear equilibrium equations of the conical shells under large deformation is linearized by using the Newton-Raphson method, and using the iterative process to approximate it, and calculate the resulting force, and bending moments after large deformation.
The numerical examples of the nonlinear behavior of conical shells are discussed, it include the buckling behavior of conical shells, nonlinear behavior of the shell under internal pressure, and the snap through behavior of opened conical shell.

參考文獻
1. Lucy, L.B., Numerical approach to testing of fission hypothesis. Astronomical Journal, 1977. 82(12): p. 1013-1024.
2. Lancaster, P. and K. Salkauskas, Surfaces generated by moving least-squares methods. Mathematics of Computation, 1981. 37(155): p. 141-158.
3. Nayroles, B., G. Touzot, and P. Villon, Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics, 1992. 10(5): p. 307-318.
4. Belytschko, T., Y.Y. Lu, and L. Gu, Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994. 37(2): p. 229-256.
5. Liu, W.K., S. Jun, and Y.F. Zhang, Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 1995. 20(8-9): p. 1081-1106.
6. Chen, J.S. ,Pan, C.H.,Wu, C.T. & Liu, W.K., Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996. 139(1-4): p. 195-227.
7. Onate, E. ,Idelsohn, S.,Zienkiewicz, O.C.,Taylor, R.L.,Sacco, C., A stabilized finite point method for analysis of fluid mechanics problems. Computer Methods in Applied Mechanics and Engineering, 1996. 139(1-4): p. 315-346.
8. Zhu, T., J. Zhang, and S.N. Atluri, A meshless local boundary integral equation (LBIE) method for solving nonlinear problems. Computational Mechanics, 1998. 22(2): p. 174-186.
9. Zhu, T., J.D. Zhang, and S.N. Atluri, A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Computational Mechanics, 1998. 21(3): p. 223-235.
10. Atluri, S.N. and T. Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, 1998. 22(2): p. 117-127.
11. Atluri, S.N., J.Y. Cho, and H.G. Kim, Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Computational Mechanics, 1999. 24(5): p. 334-347.
12. Li, S., W. Hao, and W.K. Liu, Numerical simulations of large deformation of thin shell structures using meshfree methods. Computational Mechanics, 2000. 25(2-3): p. 102-116.
13. Aluru, N.R., A point collocation method based on reproducing kernel approximations. International Journal for Numerical Methods in Engineering, 2000. 47(6): p. 1083-1121.
14. Zhang, X.G. ,Liu, X.H.,Song, K.Z.,Lu, M.W., Least-squares collocation meshless method. International Journal for Numerical Methods in Engineering, 2001. 51(9): p. 1089-1100.
15. Liu, G.R. and Y.T. Gu, A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering, 2001. 50(4): p. 937-951.
16. Liew, K.M., T.Y. Ng, and Y.C. Wu, Meshfree method for large deformation analysis - a reproducing kernel particle approach. Engineering Structures, 2002. 24(5): p. 543-551.
17. Li, H. ,Ng, T.Y.,Cheng, J.Q.,Lam, K.Y., Hermite-Cloud: a novel true meshless method. Computational Mechanics, 2003. 33(1): p. 30-41.
18. Yuan-bo, X. and y. Shu, Local Petrov-Galerkin method for a thin plate. Applied Mathematics and Mechanics(English Edition), 2004. 25(2): p. 210-218.
19. 戴伯璋，圓錐殼大變形理論分析，國立成功大學土木工程研究所碩士論文。2006。
20. 張祐綱, Hermite type之移動最小二乘法在板、梁分析上之應用，國立成功大學土木工程研究所碩士論文。2009。
21. Wang, Y.M., S.M. Chen, and C.P. Wu, A meshless collocation method based on the differential reproducing kernel interpolation. Computational Mechanics, 2010. 45(6): p. 585-606.
22. Yang, S.W. ,Wang, Y.M.,Wu, C.P.,Hu, H.T., A Meshless Collocation Method Based on the Differential Reproducing Kernel Approximation. Cmes-Computer Modeling in Engineering & Sciences, 2010. 60(1): p. 1-39.
23. Chen, S.-M., C.-P. Wu, and Y.-M. Wang, A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli-Euler beams and Kirchhoff-Love plates. Computational Mechanics, 2011. 47(4): p. 425-453.
24. 林均威，受束制之移動最小二乘法在古典板上之應用，國立成功大學土木工程研究所碩士論文。2013。
25. 張延宗，基於狀態變數與Hermite型近似之移動最小二乘法在古典板之應用，國立成功大學土木工程研究所碩士論文。2014。