用独立接触边界技术求解接触问题的拉格朗日乘子函数逼近方法的比较

Q3 Mathematics
M. Galanin, V. Lukin, P. V. Solomentseva
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引用次数: 0

摘要

本文在不考虑摩擦的静态空间二维公式中考虑弹性理论中的接触问题。针对弹性理论方程的离散化问题,采用三角形非结构化网格和线性二次基函数进行有限元分析。为了考虑接触边界条件,提出了一种具有独立接触边界的拉格朗日乘子修正方法。该方法可以构造具有求解精度所需的光滑度的接触边界,并可以独立于接触体内部的网格执行拉格朗日乘子函数的逼近。研究了不同类型的拉格朗日乘子函数逼近,包括分段常数、连续分段线性函数和不同单元边界处不连续的分段线性函数。给出了具有直线和曲线接触边界的问题的试验计算实例。在这两种情况下,使用拉格朗日乘子函数的不连续近似可以在网格细化时获得较少的人工振荡和较高的收敛率的数值解。结果表明,在不改变接触体内部网格的情况下,对接触边界进行更细致的离散化可以提高数值解的精度
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparison of the Lagrange Multipliers Function Approximation Methods in Solving Contact Problems by the Independent Contact Boundary Technique
The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
40
期刊介绍: The journal is aimed at publishing most significant results of fundamental and applied studies and developments performed at research and industrial institutions in the following trends (ASJC code): 2600 Mathematics 2200 Engineering 3100 Physics and Astronomy 1600 Chemistry 1700 Computer Science.
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