This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. Most of the theories and finite elements that have been proposed over the last thirty years are in fact based on these types of approaches. The paper has been divided into three parts. Part I, has been devoted to the description of possible approaches to plate and shell structures: 3D approaches, continuum based methods, axiomatic and asymptotic two-dimensional theories, classical and mixed formulations, equivalent single layer and layer wise variable descriptions are considered (the number of the unknown variables is considered to be independent of the number of the constitutive layers in the equivalent single layer case). Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformability, zig-zag effects and interlaminar continuity, have been discussed and summarized by the acronimC
 -Requirements. Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymtotic and continuum based approaches have been overviewed. Classical theories and their refinements are first considered. Both case of equivalent single-layer and layer-wise variables descriptions are discussed. The so-called zig-zag theories are then discussed. A complete and detailed overview has been conducted for this type of theory which relies on an approach that is entirely originated and devoted to layered constructions. Formulas and contributions related to the three possible zig-zag approaches, i.e. Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera ones have been presented and overviewed, taking into account the findings of a recent historical note provided by the author. Finite Element FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are first outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist of a specific application of finite element techniques, such as hybrid methods and so-called global/local techniques. The extension of finite elements that were originally developed for isotropic one layered structures to multilayerd plates and shells are first discussed. Works based on classical and refined theories as well as on equivalent single layer and layer-wise descriptions have been overviewed. Development of available zig-zag finite elements has been considered for the three cases of zig-zag theories. Finite elements based on other approches are also discussed. Among these, FEs based on asymtotic theories, degenerate continuum approaches, stress resultant methods, asymtotic methods, hierarchy-p,_-s global/local techniques as well as mixed and hybrid formulations have been overviewed.

Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells

In this paper, a review of the shear deformation plate and shell theories is presented and a consistent third-order theory for composite shells is proposed. The discussion of plate and shell theories from Stavsky to the present is largely a review of various theories for modeling laminated shells, including shear effects and some analytical studies. Following this discussion, a finite element formulation of the proposed theory is developed. The formulation has seven displacement functions satisfying the tangential traction-free conditions on the inner and outer surfaces of the shell. Exact computations of stress resultants are carried out through numerical integration of material stiffness coefficients of the laminate. Numerical examples are presented for typical benchmark problems involving isotropic and composite plates, and cylindrical and spherical shells.

Shear Deformation Plate and Shell Theories: From Stavsky to Present

The present paper is devoted to a state-of-the-art review on the computational treatment of laminated composite and sandwich panels. Over two hundred texts have been included in the survey with the focus put on theoretical models for multilayered plates and shells, and FEM implementation of various computational concepts. As a result of the review, one could notice a lack of a single numerical model capable for a universal representation of all layered composite and sandwich panels. Usually, with the increase of the range of rotations considered in the particular model, one can observe the decrease of the degree of complexity of the through-the-thickness representation of deformation profiles.

https://www.degruyter.com/downloadpdf/j/eng.2011.1.issue-1/s13531-011-0005-x/s13531-011-0005-x.xml

A literature review on computational models for laminated composite and sandwich panels

W artykule przedstawiono przegląd modeli obliczeniowych stosowanych w analizie laminowanych powlok kompozytowych i sandwiczowych. W przeglądzie uwzgledniono ponad 200 pozycji literatury traktujących o modelach teoretycznych dla plyt i powlok wielo-warstowych oraz/lub o implementacjach numerycznych roznych modeli obliczeniowych. Jako podstawową konkluzje z dokonanego przeglądu, nalezy uznac, ze nie istnieje jeden uniwersalny model matematyczny zdolny do efektywnego reprezentowania ogolu konstrukcji warstwowych. Praktyczna przydatnośc roznych sformulowan teoretycznych zalezy istotnie od specyfiki analizowanego problemu. Przy oczywistych ograniczeniach zdolności obliczeniowych, glownie natury sprzetowej i ekonomicznej, calkiem naturalnym zjawiskiem jest zauwazalna tendencja do zmniejszania rzedu dokladności opisu deformacji profilu poprzecznego wraz ze wzrostem stopnia nieliniowości analizowanych zagadnien.

Refined shear-deformation models for composite laminates with finite rotations

A moderate rotation theory of laminated anisotropic shells, proposed by Schmidt and Reddy [ J. appl. Mech . 55 , 611–617.1988], is developed and its application is presented. All aspects of the derivations are explicitly developed and specific forms of the equations are derived in this part. The finite-element formulation and its applications are presented in Part 2 of the paper.

On a moderate rotation theory of laminated anisotropic shells—Part 1. Theory☆

The finite element model of the moderate rotation theory (MRT) is developed and its application to composite plates and shells is presented. Comparison of results obtained by the moderate rotation theory with the von Karman non-linear theory and continuum 2D theory is made.

A.F. Palmerio

Papers

On a moderate rotation theory of laminated anisotropic shells—Part 1. Theory☆

On a moderate rotation theory of laminated anisotropic shells—Part 2. Finite-element analysis