Recent General Solutions in Linear Elasticity and Their Applications
Recent General Solutions in Linear Elasticity and Their Applications
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DOI：
10.1115/1.2909607
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发表时间：
2008-05
影响因子：
14.3
通讯作者：
Min-zhong Wang;Bai-Xiang Xu;C. Gao
中科院分区：
文献类型：
--
作者：
Min-zhong Wang;Bai-Xiang Xu;C. Gao
本文综述了自1972年以来弹性力学通解及其应用的研究进展。除了对文献中通解方法的发展进行总结和评述外，本文旨在为读者提供一个系统的、建设性的方案，从给定的控制微分方程出发，发展通解，然后证明其完备性，并研究其非唯一性特征。构造性格式的有效性表现在几乎所有的经典解，不仅包括经典位移势，而且包括经典应力函数，都可以通过使用该格式重新推导。此外，由于该格式的系统性，它产生了一个建设性的方法来研究的完整性和非唯一性的通解，并具有更大的灵活性，这有利于扩展弹性通解方法更一般的椭圆型微分方程组。在此框架下，综述了通解在各向同性和各向异性材料问题，热弹性、磁弹性、压电弹性、多孔弹性、准晶弹性等耦合问题，以及不同工程结构问题中的广泛应用，梁和板的精确理论本文共引用参考文献213篇。DOI：10.1115/1.2909607
A review is given on the progress in the study of general solutions of elasticity and their applications since 1972. Apart from summarizing and remarking the development of the general solution method in literature, this review aims to present the readers with a systematic and constructive scheme to develop general solutions from given governing differential equations and then to prove their completeness and investigate their nonuniqueness features. The effectiveness of the constructive scheme manifests itself in the fact that almost all the classic solutions, including not just classic displacement potentials but also classic stress functions, can be rederived by using this scheme. Furthermore, thanks to the systematic features of the scheme, it produces a constructive approach to study the completeness and nonuniqueness of general solutions and possesses more flexibility, which facilitates the extension of elastic general solution methods to more general systems governed by elliptic differential equations. Under the framework of this scheme, a comprehensive review is presented on wide application of general solutions in a variety of research areas, ranging from problems with different materials, isotropic or anisotropic, to various coupling problems, such as thermoelasticity, magnetoelasticity, piezoelectric elasticity, porous elasticity, and quasicrystal elasticity, and to problems of different engineering structures, for instance, the refined theories for beams and plates. There are 213 references cited in this review article. DOI: 10.1115/1.2909607