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

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

Significance Efficient thermal transport is critical for applications ranging from electronics and energy to advanced manufacturing and transportation; it is essential in emerging domains like wearable computing and soft robotics, which require thermally conductive materials that are also soft and stretchable. However, heat transport within soft materials is limited by the dynamics of phonon transport, which results in a trade-off between thermal conductivity and compliance. We overcome this by engineering an elastomer composite embedded with elongated inclusions of liquid metal (LM) that function as thermally conductive pathways. These composites exhibit an extraordinary combination of low stiffness (<100 kPa), high strain limit (>600%), and metal-like thermal conductivity (up to 9.8 W⋅m−1⋅K−1) that far exceeds any other soft materials. Soft dielectric materials typically exhibit poor heat transfer properties due to the dynamics of phonon transport, which constrain thermal conductivity (k) to decrease monotonically with decreasing elastic modulus (E). This thermal−mechanical trade-off is limiting for wearable computing, soft robotics, and other emerging applications that require materials with both high thermal conductivity and low mechanical stiffness. Here, we overcome this constraint with an electrically insulating composite that exhibits an unprecedented combination of metal-like thermal conductivity, an elastic compliance similar to soft biological tissue (Young’s modulus < 100 kPa), and the capability to undergo extreme deformations (>600% strain). By incorporating liquid metal (LM) microdroplets into a soft elastomer, we achieve a ∼25× increase in thermal conductivity (4.7 ± 0.2 W⋅m−1⋅K−1) over the base polymer (0.20 ± 0.01 W⋅m−1·K−1) under stress-free conditions and a ∼50× increase (9.8 ± 0.8 W⋅m−1·K−1) when strained. This exceptional combination of thermal and mechanical properties is enabled by a unique thermal−mechanical coupling that exploits the deformability of the LM inclusions to create thermally conductive pathways in situ. Moreover, these materials offer possibilities for passive heat exchange in stretchable electronics and bioinspired robotics, which we demonstrate through the rapid heat dissipation of an elastomer-mounted extreme high-power LED lamp and a swimming soft robot.

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High thermal conductivity in soft elastomers with elongated liquid metal inclusions.

On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results

Nonlinear finite element analysis of solids and structures by M.A. Crisfield

https://kashanu.ac.ir/Files/Content/New%20exact%20solutions%20for%20free%20vibrations%20of%20thin%20orthotropic%20rectangular%20plates.PDF

New exact solutions for free vibrations of thin orthotropic rectangular plates

SUMMARY Based on the differential quadrature (DQ) rule, the Gauss Lobatto quadrature rule and the variational principle, a DQ finite element method (DQFEM) is proposed for the free vibration analysis of thin plates. The DQFEM is a highly accurate and rapidly converging approach, and is distinct from the differential quadrature element method (DQEM) and the quadrature element method (QEM) by employing the function values themselves in the trial function for the title problem. The DQFEM, without using shape functions, essentially combines the high accuracy of the differential quadrature method (DQM) with the generality of the standard finite element formulation, and has superior accuracy to the standard FEM and FDM, and superior efficiency to the p-version FEM and QEM in calculating the stiffness and mass matrices. By incorporating the reformulated DQ rules for general curvilinear quadrilaterals domains into the DQFEM, a curvilinear quadrilateral DQ finite plate element is also proposed. The inter-element compatibility conditions as well as multiple boundary conditions can be implemented, simply and conveniently as in FEM, through modifying the nodal parameters when required at boundary grid points using the DQ rules. Thus, the DQFEM is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter-element compatibilities. A series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the DQFEM. Copyright q 2009 John Wiley & Sons, Ltd.

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method

Exact solutions for the free in-plane vibrations of rectangular plates

This paper studies the differential quadrature finite element method (DQFEM) systematically, as a combination of differential quadrature method (DQM) and standard finite element method (FEM), and formulates one- to three-dimensional (1-D to 3-D) element matrices of DQFEM. It is shown that the mass matrices of C0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems. The Lagrange polynomials are used as the trial functions for both C0 and C1 differential quadrature finite elements (DQFE) with regular and/or irregular shapes, this unifies the selection of trial functions of FEM. The DQFE matrices are simply computed by algebraic operations of the given weighting coefficient matrices of the differential quadrature (DQ) rules and Gauss-Lobatto quadrature rules, which greatly simplifies the constructions of higher order finite elements. The inter-element compatibility requirements for problems with C1 continuity are implemented through modifying the nodal parameters using DQ rules. The reformulated DQ rules for curvilinear quadrilateral domain and its implementation are also presented due to the requirements of application. Numerical comparison studies of 2-D and 3-D static and dynamic problems demonstrate the high accuracy and rapid convergence of the DQFEM.

Yufeng Xing

Papers

New exact solutions for free vibrations of thin orthotropic rectangular plates

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method

Exact solutions for the free in-plane vibrations of rectangular plates

A differential quadrature finite element method