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| Complex Variable Method for Axisymmetric Problem of Linear Viscoelasticity involving Time-dependent Boundary Regions |
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Abstract This paper presents the complex variable method for viscoelastic problem which boundaries are varied with time. Laplace transformation is introduced to complex variable method to solve the axisymmetric problem of viscoelasticity. Stress and displacement fields, and boundary conditions are expressed by two analytical functions in terms of time and space. And coefficients in analytical functions can be determined by the boundary conditions. The equations about the coefficients are generally in integral form, but analytical solutions can be obtained in special cases. For the axisymmetric problems of stress, displacement or mixed boundary, the corresponding coefficients are determined exactly by boundary conditions and analytical solutions of displacement and stresses are given also. As an application example, Boltzmann viscoelastic model is employed. The solutions show that stresses and displacements are correlated with boundary variation process. The method in this paper can be applied to axisymmetric problems with random variation of inner or outer radius. In addition, problems with asymmetric load or non-circular section can be solved similarly.
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Received: 20 October 2011
Published: 28 April 2013
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2013, Vol. 34 
