| 研究生: |
張芳瑜 Zhang, Fang-Yu |
|---|---|
| 論文名稱: |
移動最小功法在圓柱殼分析之應用 Analysis of cylindrical shells by the moving least work method |
| 指導教授: |
王永明
Wang, Yung-Ming |
| 學位類別: |
碩士 Master |
| 系所名稱: |
工學院 - 土木工程學系 Department of Civil Engineering |
| 論文出版年: | 2018 |
| 畢業學年度: | 106 |
| 語文別: | 中文 |
| 論文頁數: | 95 |
| 中文關鍵詞: | 薄殼理論 、移動最小功法 |
| 外文關鍵詞: | first-order shear deformation theory, Moving Least Work method |
| 相關次數: | 點閱:60 下載:5 |
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本文依據一階剪切變形理論,由虛功原理推得圓柱殼平衡方程式及其邊界條件的位移與合應力的關係式,並且運用加權殘值的概念引進移動最小功法求得數值解,其特點為加權函數是取其共軛的殘值,使其產生類似做功的概念。移動最小功法的近似即是利用局部的基底函數展開建立全區域連續之近似函數。
文中針對封閉圓柱殼與開放圓柱殼兩種結構型式進行分析討論,並將此數值方法以不同的佈點方式及不同的基底階數與解析解比較,以驗證此方法的可行性,並分析其誤差收斂的情形。
In this thesis, the assumption of first-order shear deformation theory (FSDT) and the principle of virtual work are used to derive the equilibrium equations of cylindrical shells and its boundary condition. We used the concept of weighted residual value to obtain the numerical solution by Moving Least Work method (MLW). In experimental examples, we use different point distribution and different order of base function to validate the applicability of this method. Furthermore, the numerical results are compared with analytical solution to examine the accuracy and the rate of convergence of this method.
[1] Lucy, Leon B. "A numerical approach to the testing of the fission hypothesis." The astronomical journal 82 (1977): 1013-1024.
[2] Nayroles, B., G. Touzot, and P. Villon. "Generalizing the finite element method: diffuse approximation and diffuse elements." Computational mechanics 10.5 (1992): 307-318.
[3] Belytschko, Ted, Lei Gu, and Y. Y. Lu. "Fracture and crack growth by element free Galerkin methods." Modelling and Simulation in Materials Science and Engineering 2.3A (1994): 519.
[4] Liu, Wing Kam, Sukky Jun, and Yi Fei Zhang. "Reproducing kernel particle methods." International journal for numerical methods in fluids 20.8‐9 (1995): 1081-1106.
[5] Onate, E., et al. "A stabilized finite point method for analysis of fluid mechanics problems." Computer Methods in Applied Mechanics and Engineering 139.1 (1996): 315-346.
[6] Krongauz, Y., and T. Belytschko. "A Petrov-Galerkin diffuse element method (PG DEM) and its comparison to EFG." Computational Mechanics 19.4 (1997): 327-333.
[7] Zhu, Tulong, J-D. Zhang, and S. N. Atluri. "A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach." Computational mechanics 21.3 (1998): 223-235.
[8] Atluri, S. N., and T-L. Zhu. "The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics." Computational Mechanics25.2-3 (2000): 169-179.
[9] Zhang, Xiong, et al. "Least‐squares collocation meshless method."International Journal for Numerical Methods in Engineering 51.9 (2001): 1089-1100.
[10] Long, Shuyao, and S. N. Atluri. "A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate." Computer Modeling in Engineering and Sciences 3.1 (2002): 53-64.
[11] Wang, Dongdong, and Jiun-Shyan Chen. "Locking-free stabilized conforming nodal integration for meshfree Mindlin–Reissner plate formulation." Computer Methods in Applied Mechanics and Engineering 193.12 (2004): 1065-1083.
[12] Wang, Yung-Ming, Syuan-Mu Chen, and Chih-Ping Wu. "A meshless collocation method based on the differential reproducing kernel interpolation."Computational mechanics 45.6 (2010): 585-606.
[13] 吳建勳,"受束制之移動最小二乘法在二維彈性力學問題上之應用"成功大學土木工程學系學位論文(2013)
[14] 吳梓瑋,"應用移動最小二乘法於圓柱體薄殼大變形分析" 成功大學土木工程學系學位論文(2015)
[15] Timoshenko & S. Woinowsky-Krieger. "Theory of plates and shells (2nd Edition) ." McGraw-Hill book company(1989)
[16] Maan H Jawad. "Theory and design of plate and shell structures."New York : Chapman & Hall(1994)
[17] Michel Fortin. "Plates and shells. "American Mathematical Society (1999)
[18] Werner Soedel. "Vibrations of shells and plates." CRC Press(2004)
[19] J.N.Reddy. "Theory and analysis of elastic plates and shells(2nd Edition) ."CRC Press(2007)