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首页> 外文期刊>International Journal of Solids and Structures >Contact problem for magneto-electro-elastic half-plane materials indented by a moving punch. Part I: Closed-form solutions
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Contact problem for magneto-electro-elastic half-plane materials indented by a moving punch. Part I: Closed-form solutions

机译:移动冲头压入的磁电弹性半平面材料的接触问题。第一部分:封闭式解决方案

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A theoretical model is developed for the exact contact analysis of magneto-electro-elastic half-plane materials indented by a moving rigid punch in this paper, which is Part I of a series of papers. A numerical analysis based on this theoretical model will be presented in Part II. The Galilean transformation and the Fourier sine and cosine transforms are applied to make the transient problem tractable. Detailed analyses of the eigenvalue distributions of the double-biquadrate order characteristic equation related to the magneto-electro-elastic governing equations are performed. Real fundamental solutions are derived for each eigenvalue distribution. The punch may have a flat or cylindrical profile and may be electrically and magnetically conducting, electrically conducting and magnetically insulating, electrically insulating and magnetically conducting, or electrically and magnetically insulating. For each type of punch, the singular integral equations are derived with the surface contact stress, surface electric charge, and/or surface magnetic induction inside the contact region as the unknown functions. Exact solutions to the system of integral equations are obtained. In particular, closed-form expressions for the stresses, electric displacements, and magnetic inductions in terms of fundamental functions are derived, which provide a scientific basis for the interpretation of the contact behaviors of multiferroic materials as will be shown in Part II of this series of papers.
机译:本文开发了一个理论模型,用于精确地分析运动的刚性冲头压入的磁电弹性半平面材料,这是该系列论文的第一部分。第二部分将介绍基于该理论模型的数值分析。伽利略变换以及傅立叶正弦和余弦变换可用于使瞬态问题变得易于处理。对与磁电弹性控制方程有关的双二阶阶特征方程的特征值分布进行了详细分析。为每个特征值分布导出实际的基本解。冲头可以具有平坦的或圆柱形的轮廓,并且可以是导电的和磁的,导电的并且是磁绝缘的,电绝缘的并且是磁导电的或者电绝缘的是磁绝缘的。对于每种类型的冲头,在接触区域内部的表面接触应力,表面电荷和/或表面磁感应为未知函数的情况下,导出了奇异积分方程。获得了积分方程系统的精确解。特别是,得出了基本功能方面的应力,电位移和磁感应强度的闭式表达式,这为解释多铁性材料的接触行为提供了科学依据,这将在本系列的第二部分中进行展示。的论文。

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