基于粘弹性材料标准固体模型的接触问题数值方法研究

Study on the Numerical Method of the Contact Problem Based on the Standard Solid Model of Viscoelastic Material

基于粘弹性材料标准固体模型给出了一种求解刚性滚筒以给定速度滚过粘弹性体问题的数值解法。在这一方法中,问题的解被展开成付立叶级数的形式,以标准固体模型描述粘弹性材料的力学性能,借助标准固体模型三维微分形式的本构方程来建立付立叶级数各阶系数之间的函数关系,从而在粘弹性体的边界上建立边界元方程实现问题的求解。最后,以一个移动载荷作用在粘弹性半空间上的算例验证了方法的正确性。

The numerical method based on the standard solid model is developed to solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic body. In the present method,the solution is expanded into a set of Fourier series,a so-called standard solid model is used to characterize the viscoelastic properties for the viscoelastic foundation,the three-dimensional differential constitutive equations of the viscoelastic material is used to relate Fourier coefficients,and a special boundary element is developed to handle the rolling contact boundary condition. Finally,a verification example of moving pressure on the viscoelastic half space is given to validate the methodology.