Axisymmetric Indentation of Circular Rigid Plate on Layered Elastic Halfspace with Transverse Isotropy

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2024-10-09 DOI:10.1007/s10659-024-10090-9

Sha Xiao, Zhongqi Quentin Yue

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Abstract

This paper investigates the contact problem of a layered elastic halfspace with transverse isotropy under the axisymmetric indentation of a circular rigid plate. Fourier integral transforms and a backward transfer matrix method are used to obtain the analytical solution of the contact problem. The interaction between the rigid plate and the layered halfspace can be expressed with the standard Fredholm integral equations of the second kind. The induced elastic field in the layered halfspace can be expressed as the semi-infinite integrals of four known kernel functions. The convergence and singularity of the semi-infinite integrals near or at the surface of the layered halfspace are resolved using an isolating technique. The efficient numerical algorithms are used and developed for accurately calculating the Fredholm integral equations and the semi-infinite integrals. Numerical results show the correctness of the proposed method and the effect of layering non-homogeneity on the elastic fields in layered transversely isotropic halfspace induced by the axisymmetric indentation of a circular rigid plate.

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具有横向各向同性的层状弹性半空间上的圆形刚性板轴对称压痕

本文研究了具有横向各向同性的层状弹性半空间在圆形刚性板的轴对称压痕作用下的接触问题。本文采用傅里叶积分变换和后向传递矩阵法求得接触问题的解析解。刚性板与层状半空间之间的相互作用可以用标准的第二类弗雷德霍姆积分方程来表示。层状半空间中的诱导弹性场可表示为四个已知核函数的半无限积分。利用隔离技术解决了半无限积分在层状半空间附近或表面的收敛性和奇异性问题。使用并开发了高效的数值算法，用于精确计算弗雷德霍姆积分方程和半无限积分。数值结果表明了所提方法的正确性，以及分层非均质性对圆形刚性板轴对称压痕诱导的分层横向各向同性半空间弹性场的影响。

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来源期刊

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.