A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

A Simple Higher-Order Theory for Laminated Composite Plates

Micro-structure in linear elasticity

Part 1 Thin plates: introduction the fundamentals of the small-deflection plate bending theory rectangular plates circular plates bending of plates of various shapes plate bending by approximate and numerical methods advanced topics buckling of plates vibration of plates. Part 2 Thin shells: introduction to the general linear shell theory geometry of the middle surface the general linear theory of thin shells the membrane theory of shells applications of the membrane theory to the analysis of shell structures moment theory of circular cylindrical shells the moment theory of shells of revolution approximate theories of shell analysis and their application advanced topics buckling of shells vibration of shells. Appendices: some reference data Fourier series expansion verification of relations of the theory of surfaces derivation of the strain-displacement relations verification of equilibrium equations.

Thin Plates And Shells: Theory Analysis And Applications

This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1! Lekhnitskii ~1935! was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2! Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian ~1958!, who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner ~1984!, who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3 ! On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, ~LMT!, Ambartsumian Multilayered Theory ~AMT!, and Reissner Multilayered Theory ~RMT!. As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4! LMT although very promising, has almost been ignored in the open literature. 5! Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6! RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references. @DOI: 10.1115/1.1557614#

R D Mindlin

Papers

Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates