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

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

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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.

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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

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References(10)

References

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