The review outlines modern trends in theoretical developments, novel designs and modern applications of sandwich structures. The most recent work published at the time of writing of this review is considered, older sources are listed only on as-needed basis. The review begins with the discussion on the analytical models and methods of analysis of sandwich structures as well as representative problems utilizing or comparing these models. Novel designs of sandwich structures is further elucidated concentrating on miscellaneous cores, introduction of nanotubes and smart materials in the elements of a sandwich structure as well as using functionally graded designs. Examples of problems experienced by developers and designers of sandwich structures, including typical damage, response under miscellaneous loads, environmental effects and fire are considered. Sample applications of sandwich structures included in the review concentrate on aerospace, civil and marine engineering, electronics and biomedical areas. Finally, the authors suggest a list of areas where they envision a pressing need in further research.

Review of current trends in research and applications of sandwich structures

By means of Non-Uniform Rational B-Splines (NURBS) curves, it is possible to describe arbitrary shapes with holes and discontinuities. These peculiar shapes can be taken into account to describe the reference domain of several nanoplates, where a nanoplate refers to a flat structure reinforced with Carbon Nanotubes (CNTs). In the present paper, a micromechanical model based on the agglomeration of these nanoparticles is considered. Indeed, when this kind of reinforcing phase is inserted into a polymeric matrix, CNTs tend to increase their density in some regions. Nevertheless, some nanoparticles can be still scattered within the matrix. The proposed model allows to control the agglomeration by means of two parameters. In this way, several parametric studies are presented to show the influence of this agglomeration on the free vibrations. The considered structures are characterized also by a gradual variation of CNTs along the plate thickness. Thus, the term Functionally Graded Carbon Nanotubes (FG-CNTs) is introduced to specify these plates. Some additional parametric studies are also performed to analyze the effect of a mesh distortion, by considering several geometric and mechanical configurations. The validity of the current methodology is proven through a comparative assessment of our results with those available from the literature or obtained with different numerical approaches, such as the Finite Element Method (FEM). The strong form of the equations governing a plate is solved by means of the Generalized Differential Quadrature (GDQ) method.

Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates

An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application

A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation

NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells

A review on plate and shell theories for laminated and sandwich structures highlighting the finite element method

This paper presents a discussion on the through-the-thickness stress profiles of thick laminated plates and sandwich structures calculated with a particular generalized unified formulation. It consists on a finite element Unified Formulation (UF) with C-1 continuity of the transverse displacement field implemented in a four node plate element (CGF- Caliri's Generalized Formulation). The current works on unified formulations attempt to simplify and settle the development, use and choice of plate and shell theories. However, even using unified approaches, no generalizations base on specific problems are possible. For instance, the present work demonstrates that a non-linear plate theory may yield worse results when compared to a linear solution. It was found that, for a selected thick sandwich structure, a cubic layerwise theory provided a set of results 27% less accurate than the linear one. Moreover, when the through-the-thickness stress profiles are closely evaluated, the accuracy of the stress profiles are subjected to the solution method and not only the theory. Particularly, the effects of poor mesh resolution and boundary conditions are demonstrated in this work. Nevertheless, CGF is able to predict point-wise accurate results (less than 1% of deviation) even for the for transverse stresses variables.

Through-the-thickness stress profiles in laminated composite and sandwich structure plates via unified formulation

Summary
The contribution of this work is the implementation of a new elastic solution method for thick laminated composites and sandwich structures based on a generalized unified formulation using finite elements. A quadrilateral four-node element was developed and evaluated using an in-house finite element program. The C-1 continuity requirements are fulfilled for the transversal displacement field variable. This method is tagged as Caliri's generalized formulation. The results employing the proposed solution method yielded coherent results with deviations as low as 0.05% for a static simply supported symmetric laminate and 0.5% for the modal analyses of a soft core sandwich structure. Copyright © 2016 John Wiley & Sons, Ltd.

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

New Generalized Unified Solution Method for Thin Laminated Plates

The performance of an element with C1 continuity in the thickness direction was investigated within the scope of unified plate and shell formulations considering skew elements and the shear locking problem. A remedy for the shear locking pathology was found in the form of an algorithm which applies a penalty factor when the element is thinner than L E ∕ H = 2 . Moreover, the proposed test cases showed the ability of Caliri’s Generalized Formulation - CGF to better control the through-the-thickness behavior of the structure at the boundary conditions. Consistent results were obtained even for skew meshes and laminated shells.

Mauricio F. Caliri

Papers

A review on plate and shell theories for laminated and sandwich structures highlighting the finite element method

Through-the-thickness stress profiles in laminated composite and sandwich structure plates via unified formulation

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

New Generalized Unified Solution Method for Thin Laminated Plates

A new C1 4-node flat laminated shell element based on a generalized plate formulation