A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems

DING Hao-jiang; WANG Hui-ming; CHEN Wei-qiu

Volume 23 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(2): 128-134

DING Hao-jiang, WANG Hui-ming, CHEN Wei-qiu. A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 128-134.

Citation:

PDF( 1889 KB)

A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems

1.
Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P R China;
2.
Department of Mechanics, Zhejiang University, Hangzhou 310027, P R China

Received Date: 2000-02-08
Rev Recd Date: 2001-09-18
Publish Date: 2002-02-15

Abstract

Abstract

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.
- axisymmetric plain strain problem,
- special function,
- integral transform,
- cylindrically isotropic

FullText(HTML)

References(10)

References

[1]	Huth J H,Cole J D.Elastic-stress waves produced by pressure loads on a spherical shell[J].Journal of Applied Mechanics,1955,22(4):473-478.
[2]	Mcivor I K.The elastic cylindrical shell under radial impulse[J].Journal of Applied Mechanics,1966,33(4):831-837.
[3]	Baker W E,Hu W C L,Jackson T R.Elastic response of thin spherical shells to axisymmetric blast loading[J].Journal of Applied Mechanics,1966,33(4):800-806.
[4]	Chou P C,Koenig H A.A unified approach to cylindrical and spherical elastic waves by method of characters[J].Journal of Applied Mechanics,1966,33(1):159-167.
[5]	Rose J L,Chou S C,Chou P C.Vibration analysis of thick-walled spheres and cylinders[J].Journal of the Acoustical Society of America,1973,53(3):771-776.
[6]	Cinelli G.Dynamic vibrations and stresses in elastic cylinders and spheres[J].Journal of Applied Mechanics,1966,33(4):825-830.
[7]	WANG Xi,GONG Yu-ning.A theoretical solution for axially symmetric problem in elastodynamics[J].Acta Mechanica Sinica,1991,7(3):275-282.
[8]	王熙.各向异性轴对称问题的弹性动力学解[J].力学学报,1997,29(5):606-610.
[9]	王熙.有界圆柱体的动应力和动应力集中现象[J].振动与冲击,1995,14(1):23-29.
[10]	丁皓江,陈伟球,邹道勤,等.横观各向同性弹性力学[M].杭州:浙江大学出版社,1997.

Relative Articles

[1]	YANG Yonglin, WANG Xu, LI Xing. Effects of Proplet on the Deformation of Elastic Gradient Thin Substrate[J]. Applied Mathematics and Mechanics, 2021, 42(1): 58-70. doi: 10.21656/1000-0887.410175
[2]	WANG Zhi-qiao, DUI Guan-suo. Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1115-1122.
[3]	BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.
[4]	M. K. Ghosh, M. Kanoria. Displacements and Stresses in a Composite Mult-Layered Media Due to Varying Temperature and Concentrated Load[J]. Applied Mathematics and Mechanics, 2007, 28(6): 724-734.
[5]	CAO Xu-long, TONG Deng-ke, WANG Rui-he. Exact Solutions for Nonlinear Transient Flow Model Including a Quadratic Gradient Term[J]. Applied Mathematics and Mechanics, 2004, 25(1): 93-99.
[6]	FENG Wen-jie, LI Xiang-guo, WANG Shou-dong. Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1278-1284.
[7]	BIAN Wen-feng, WANG Biao, JIA Bao-xian. Mathematical Problems in the Integral-Transformation Method of Dynamic Crack[J]. Applied Mathematics and Mechanics, 2004, 25(3): 228-232.
[8]	WANG Li-min, XU Shi-lang. Analysis on the Cohesive Stress at Half Infinite Crack Tip[J]. Applied Mathematics and Mechanics, 2003, 24(8): 812-820.
[9]	Tong Dengke, Chen Qinlei. Generalized Flow Analysis of Non-Newtonian Visco-Elastic Fluids Flow Through Fractal Reservoir[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1267-1274.
[10]	Sun Lu, Deng Xuejun. Dynamic Analysis to Infinite Beam under a Moving Line Load with Uniform Velocity[J]. Applied Mathematics and Mechanics, 1998, 19(4): 341-347.
[11]	Liu Youwen, Guo Jianlin. The Illustration Calculations of Second Order Effects in Elastic Half-Space Acted upon By A Non-Uniform Shear Load[J]. Applied Mathematics and Mechanics, 1997, 18(6): 523-530.
[12]	Liu Youwen, Gou Jianlin. The General Solution of Second order Effects in Elastic Half-Space Acted upon by a Non-Uniform Shear Load[J]. Applied Mathematics and Mechanics, 1997, 18(4): 341-355.
[13]	He Guangyu, Huang Junqi, Liu Ciqun. General Second Order Fluid Flow in a Pipe[J]. Applied Mathematics and Mechanics, 1995, 16(9): 767-773.
[14]	Huang Jun-qi, Liu Ci-qun. Unsteady Rotative Flow of Non-Newtonian Fluid In an Annular Pipe[J]. Applied Mathematics and Mechanics, 1995, 16(4): 323-328.
[16]	Zhu Wen-hui, Liu Ci-qun. Analytical Solution of Flow of Second-Order Non-Newtonian Fluid through Annular Pipes[J]. Applied Mathematics and Mechanics, 1993, 14(3): 195-201.
[17]	Ding Hao-jiang, Xu Bo-hou. General Solutions of Axisymmetric Problems in Transversely Isotropic Body[J]. Applied Mathematics and Mechanics, 1988, 9(2): 135-142.
[18]	Cheng Yuan-sheng. A Theorem on Potential of Isotropic Symmetric Second-Order Tensor Function[J]. Applied Mathematics and Mechanics, 1983, 4(1): 89-92.
[19]	Guo Zhong-heng. Representation Theorem for Linear, lsotropic Tensor Functions of a Skew Argument[J]. Applied Mathematics and Mechanics, 1983, 4(3): 297-301.
[20]	Guo Zhong-heng. Representations of Linear, Isotropic Tensor Functions of an Asymmetric Argument[J]. Applied Mathematics and Mechanics, 1981, 2(6): 613-620.