Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

A review of displacement and stress based refined theories for isotropic and anisotropic laminated plates is presented. Various equivalent single layer and layerwise theories for laminated plates are discussed together with their merits and demerits. Exact elasticity solutions for the plate problems are cited, wherever available. Various critical issues related to plate theories are presented, based on the literature reviewed.

A Review of Refined Shear Deformation Theories for Isotropic and Anisotropic Laminated Beams

Completeness and nonuniqueness ofgeneral solutions of transversely isotropic elasticity

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

Recent General Solutions in Linear Elasticity and Their Applications

In this paper a new thick plate theory is derived by using Papkovich-Neuber solution of three-dimensional elasticity.

Thick plate theory based on general solutions of elasticity

A refined theory for transversely isotropic piezoelectric plates is derived from the general solution of three-dimensional transversely isotropic piezoelasticity by means of Lur’e operator method. As a special case, the governing differential equations for transversely isotropic elastic plates are obtained directly.

A refined theory of transversely isotropic piezoelectric plates

There are two general solutions in clastodynamics, which are the Cauchy-Kovalevski-Somigliana general solution (call it CKS for short) and the Boussinesq-Papkovich-Neuber general solution (BPN). In this paper, by constructing two new kinds of decomposition for any vector, the potential functions in CKS and BPN are constructed. Thus the completeness of the two general solutions gets proved in a pithy style. In addition, we also establish the evident relation between the two general solutions.

Constructivity and completeness of the general solutions in elastodynamics

Departing from the refined theory of transversely isotropic piezoelectric plates, an analytical solution for the bending of an infinite piezoelectric plate with a circular hole is obtained. Expressions of moment, stress and electric displacement concentration factors are presented in closed form. When the piezoelectric coupling is absent, the results reduce to the corresponding solutions for the transversely isotropic elastic plates. Some numerical results for PZT-6B piezoelectric ceramics are obtained and illustrated by figures. These results show that the effect of piezoelectric coupling on the concentration factors is not negligible.

W. Wang

Papers

Thick plate theory based on general solutions of elasticity

A refined theory of transversely isotropic piezoelectric plates

Constructivity and completeness of the general solutions in elastodynamics

Bending of piezoelectric plates with a circular hole