粘弹性力学的对应原理及其数值反演方法

CORRESPONDENCE PRINCIPLES AND NUMERICAL METHODS OF INVERSE INTEGRAL TRANSFORMATION IN VISCOELASTIC MECHANICS

积分变换是处理粘弹性混合边值问题的重要数学工具,积分变换的应用使粘弹性混合边值问题在象空间与相应弹性混合边值问题对应起来，从而使粘弹性混合边值问题的求解可以继承和借鉴弹性问题的求解方法，再利用积分反演方法就可求得时间域粘弹性边值问题的解．本文结合国内外的研究成果，就粘弹性力学中存在的各种对应原理及数值反演方法进行了归类和总结．结合在求解粘弹性边值问题中的应用，对各类方法的特点进行了评述，并指出存在的问题及发展新的数值方法的研究重点．

Integral transformation method is an important mathematical tool, when dealing with viscoelastic mixed boundary problems. By using integral transformation method, viscoelastic mixed boundary problems can be made to correspond with elastic mixed boundary problems,which is the well-known correspondence principle. Then, the methods used for elastic mixed boundary problems, and the inverse integral transformation method may be employed to solve viscoelastic mixed boundary problems in time domain. This paper gives a comprehensive review on various correspondence principles and inverse integral transformation methods used in practice, and according to the applications of various methods in viscoelastic mixed boundary problems,discusses related problems and prospective for developing new methods.