物质点方法与有限元方法在二维接触问题中的对比

Comparision Between Finite Element Method and Material Point Method Over 2D Contact Problem

针对非线性力学问题,特别是接触类问题时,有限元法经常暴露出时间成本高,计算结果不容易收敛等先天性缺陷。相比之下,物质点法具有更好的性质,接触应力由物质点之间的动量守恒直接计算得到,理论上计算开销更小,同时具备更高的计算精度和准确度。本文采用物质点方法、有限元法和解析方法对赫兹接触问题进行求解,并将三种方法计算得到的最大接触应力进行比较。计算分析后发现,相比有限元法,物质点法的计算结果的精确度与准确度略高。本文的分析研究为计算接触问题提供了新的思路,具备一定工程应用价值。

For nonlinear mechanical problems,especially the contact problems,the finite element method often exposes the high time cost,and the calculation results are not easy to converge and other congenital defects.In contrast,the material point method has better properties.The contact stress is directly calculated from the momentum conservation between material points,which has less computational cost and higher accuracy.In this paper,the material point method,finite element method and analytical method are used to solve the Hertz contact problem,and the maximum contact stress calculated by the three methods is compared.The calculation results show that compared with the finite element method,the accuracy of the material point method is slightly higher.The analysis and study of this paper provides a new way of thinking for the calculation of contact problems,and has a certain value of engineering application.