旋转环形圆盘的三维弹性分析综述

IF 2.5 3区 工程技术 Q2 MECHANICS
Marko V. Lubarda, Vlado A. Lubarda
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引用次数: 0

摘要

提出了一种新的基于应力的三维弹性应力场和位移场的推导方法,该方法是对文献中其他更复杂的推导方法的补充。一阶推导是基于结合运动方程和相容条件得到的平面内应力和和差的两个偏微分方程的直接积分。在二阶导数中,应力函数的简单形式满足Beltrami-Michell相容方程后的一阶非齐次偏微分方程,该方程易于求解。第三种推导是基于轴对称三维弹性的Love应力函数,将其推广为包含旋转惯性力。所得的非齐次双调和偏微分方程通过构造其特解和补解的两种方法求解。Love函数的衍生表达式在以前的文献中没有报道过。本文还介绍了弹性场的基于位移的推导,包括相应的Papkovich-Neuber势的构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A review of the three-dimensional elasticity analysis of a rotating annular disk

Novel stress-based derivations of three-dimensional elastic stress and displacement fields in an isotropic annular disk of uniform thickness, rotating around its axis of symmetry with constant angular speed, are presented, which complement other more involved derivations available in the literature. The first derivation is based on the direct integration of two partial differential equations for the sum and difference of the in-plane stresses, which are obtained by combining the equation of motion and the compatibility condition. In the second derivation the stresses are obtained by using a simple form of the stress function satisfying a first-order nonhomogeneous partial differential equation following from the Beltrami–Michell compatibility equations, which can be solved readily. The third derivation is based on Love’s stress function of axisymmetric three-dimensional elasticity, generalized to include a rotational inertia force. The resulting nonhomogeneous biharmonic partial differential equation is solved by two alternative methods of constructing its particular and complementary solution. The derived expression for Love’s function has not been reported in the literature before. The displacement-based derivation of elastic fields is also presented, including a construction of the corresponding Papkovich–Neuber potentials.

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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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