弹性力学中Navier和球谐核的直接联系

IF 1.8 3区 数学 Q1 MATHEMATICS
D. Labropoulou, P. Vafeas, G. Dassios
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引用次数: 0

摘要

线性各向同性弹性是连续介质力学的一个有趣的分支,由胡克和牛顿的基本定律描述,它们结合在一起,以构建任何材料内位移的控制广义纳维尔方程。在没有外力的情况下,后者被简化为齐次二阶偏微分方程的相应形式,其解通过Papkovich微分表示给出,该表示以调和函数的形式表示位移场。另一方面,球面几何在实际应用中提供了最广泛使用的框架,涉及弹性的内部和外部问题。目前的工作旨在提供一点进展,通过在球坐标下产生现成的线性各向同性弹性的基本函数。因此,我们计算了由球调和本征函数生成的Papkovich本征解,得到了Navier和球调和核之间的联系。最后以实例的形式给出了一组关于球内外位移场计算的有用结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Direct connection between Navier and spherical harmonic kernels in elasticity
Linear isotropic elasticity is an interesting branch of continuum mechanics, described by the fundamental laws of Hooke and Newton, which are combined in order to construct the governing generalized Navier equation of the displacement within any material. Implying time-independence and in the absence of external body forces, the latter is reduced to the corresponding form of a homogeneous second-order partial differential equation, whose solution is given via the Papkovich differential representation, which expresses the displacement field in terms of harmonic functions. On the other hand, spherical geometry provides the most widely used framework in real-life applications, concerning interior and exterior problems in elasticity. The present work aims to provide a little progress, by producing ready-to-use basic functions for linear isotropic elasticity in spherical coordinates. Hence, we calculate the Papkovich eigensolutions, generated by the spherical harmonic eigenfunctions, obtaining connections between Navier and spherical harmonic kernels. A set of useful results are provided at the end of the paper in the form of examples, regarding the evaluation of displacement field inside and outside a sphere.
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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