Sandwich Panel Theory Research Articles

Experimental and finite element analysis of higher order behaviour of sandwich beams using digital projection moiré

This paper presents a new experimental procedure based on Digital Projection Moiré (DPM) for analyzing the non-linear behaviour of sandwich beam with compliant foam core. This kind of core is very flexible relative to the face sheets. Its behaviour is associated with localized effects in the form of displacements and stresses. These effects in turn influence the overall behaviour of the sandwich beam. In this study, the three-point bending results of sandwich beam are in agreement with FEA results obtained using the ABAQUS finite element code. The theoretical predictions based on the high-order sandwich panel theory (HSAPT) are also in good agreement with the experimental and FEM results. It is shown that the results from the proposed procedure are very accurate. Furthermore, it is suggested that the present method is advantageous for whole-field testing for many applications in evaluation of composite materials and sandwich structures and is more user-friendly.

Modeling of axial and shear stresses in multilayer sandwich beams with stiff core layers

In order to optimize the load-bearing behavior of sandwich structures and adapt it to specific requirements, their core may be composed of layers of different materials with tailored properties. These layers may consist not only of soft foam or honeycomb materials but also comprise stiff materials, e.g. timber, or even very stiff laminates in the case of fiber-reinforced polymer (FRP) materials. In this paper, new analytical models for predicting axial and shear stresses in multilayer sandwich structures composed of stiff core layers and intermediate laminates are presented. The models are based on new formulations for calculating the bending and shear stiffness of multilayer sandwiches. They have been validated by finite element modeling (FEM) and the results from four-point bending experiments on GFRP-balsa sandwich beams with complex core assembly. In contrast to existing models, e.g. the high-order sandwich panel theory (HSAPT), the new models are able to accurately predict axial and shear stresses in stiff cores and intermediate FRP laminate layers.

Static response of thermally loaded sandwich beams with confined horizontal displacements of faces at the supports

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Higher order impact analysis of sandwich panels with functionally graded flexible cores

This study deals with dynamic model of composite sandwich panels with functionally graded flexible cores under low velocity impacts of multiple large or small masses using a new improved higher order sandwich panel theory (IHSAPT). In-plane stresses were considered for the functionally graded core and face sheets. The formulation was based on the first order shear deformation theory for the composite face sheets and polynomial description of the displacement fields in the core that was based on the second Frostig's model. Fully dynamic effects of the functionally graded core and face-sheets were considered in this study. Impacts were assumed to occur simultaneously and normally over the top and/or bottom of the face-sheets with arbitrary different masses and initial velocities. The contact forces between the panel and impactors were treated as internal forces of the system. Nonlinear contact stiffness was linearized with a newly presented improved analytical method in this paper. The results were validated by comparing the analytical, numerical and experimental results published in the latest literature.

Improved high-order bending analysis of double curved sandwich panels subjected to multiple loading conditions

For the first time, the bending analysis of a double curved sandwich panel was presented which was subjected to point load, uniform distributed load on a patch, and harmonic distributed loads and was based on a new improved higher order sandwich panel theory. Since the cross-sectional warping was accurately modeled by this theory, it did not require any shear correction factor. Also, the present analysis incorporated trapezoidal shape factor (the 1+z/R terms) of a curved panel element. Geometry was used for the consideration of different radii curvatures of the face sheets, while the core was unique. Unlike most of other reference works, the core can have non-uniform thickness. The governing equations were derived by the principle of minimum potential energy. The effects of types of boundary conditions, types of applied loads, core to panel, and radii curvatures ratios on the bending response were also studied.

Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores

This paper dealt with free vibration analysis of thick double curved composite sandwich panels with simply supported or fully clamped boundary conditions based on a new improved higher order sandwich panel theory. The formulation used the first order shear deformation theory for composite face sheets and polynomial description for the displacement field in the core layer which was based on the displacement field of Frostig's second model. The fully dynamic effects of the core layer and face sheets were also considered in this study. Using the Hamilton's principle, the governing equations were derived. Moreover, effects of some important parameters like that of boundary conditions, thickness ratio of the core to panel, radii curvatures and composite lay-up sequences were investigated on free vibration response of the panel. The results were validated by those published in the literature and with the FE results obtained by ABAQUS software. It was shown that thicker panels with a thicker core provided greater resistance to resonant vibrations. Also, effect of increasing the core thickness in general was significant decreased fundamental natural frequency values.

A new nonlinear high order theory for sandwich beams: An analytical and experimental investigation

The paper presents a geometrically nonlinear sandwich panel theory for orthotropic sandwich beams in which the large deformation of face sheets and core is considered. The equations are derived based on high order sandwich panel theory in which the Green strain and the second Piola–Kirchhoff stress tensor are used. Nonlinear equations for a simply supported beam are derived using Ritz method in conjunction with minimum potential energy principle. The resulted set of equations is solved by the Newton–Raphson iterative technique. The results of numerical computation for beams in three point bending are presented and compared with experiments as well as with some other available results. Also simplification was used to obtain the results of linear model and in parametric studies the effect of geometric parameters on difference between results of linear and nonlinear models are discussed.Some experimental tests on sandwich beams with glass/epoxy face sheets and soft polymeric cores were performed. The experimental results of specimens with different arrangement support the claims which were based on analytical predictions about similarities and differences between linear and nonlinear models. In all cases good agreement is obtained between the nonlinear analytical predictions and experimental results.

Blast Response of a Sandwich Beam/Wide Plate Based on the Extended High-Order Sandwich Panel Theory and Comparison With Elasticity

This paper presents a one-dimensional analysis for the blast response of a sandwich beam/wide plate with a compressible core. The dynamic version of the recently developed extended high-order sandwich panel theory (EHSAPT) is first formulated. Material, geometric, and loading parameters are taken from blast experiments reported in literature. The novelty of EHSAPT is that it includes axial rigidity of the core and allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (shear stress in the core) of the earlier high-order sandwich panel theory (HSAPT). The solution procedure to determine the dynamic response to a general load applied on the top face sheet of a general asymmetric simply supported configuration is outlined. Although the dynamic EHSAPT is formulated in its full nonlinear version, the solution is for the linear problem so the accuracy of EHSAPT, along with the other theories, can be assessed by comparison to an available dynamic elasticity solution. Results show that the EHSAPT is very accurate and can capture the complex dynamic phenomena observed during the initial, transient phase of blast loading.

Free vibration of unidirectional sandwich panels, Part I: Compressible core

The free vibration response of a unidirectional sandwich panel with a compressible and incompressible core using the various computational models is presented and compared with closed-form elasticity solutions and finite element results. The mathematical formulations for various models along with the numerical investigation are presented in two parts. In the first part compressible core are considered using the elasticity closed-form solution and various high-order computational models such as the high-order sandwich panel theory (HSAPT) and the extended HSAPT model (EHSAPT). The second part is dedicated to incompressible cores and includes classical models, first-order and high-order shear deformable models, and zig-zag displacement pattern model, ordinary sandwich panel theory. The elasticity-based model serving as the benchmark solution (in first part) assumes isotropic, orthotropic, as well as layered core types. The mathematical formulation utilizes Hamilton’s principle to derive the general equations of motion. A closed-form solution of the elasticity model is available only for a simply-supported panel and it is compared with all various models numerically. The numerical investigation includes: eigenfrequencies, displacement modes along the length and through the depth of panel, as well as stress modes through the depth of panel. The results of the various models are compared with the 2D elasticity solution and finite element results of ADINA. In general, the lower mode correlates well for all models while for the higher modes only the EHSAPT and the HSAPT with displacement formulation compared well.

Free vibration of unidirectional sandwich panels, Part II: Incompressible core

The free vibration response of a unidirectional sandwich panel with an incompressible core using shear deformable and layered models is presented. The models considered include the layered model, ordinary sandwich panel theory that uses a zig-zag in-plane displacements distribution in addition to the shear deformations and the first and high-order shear deformable theories that adopt an approach which replaces the layered sandwich panel with a single layer with equivalent properties. The mathematical formulations use Hamilton’s principle to present the general equations of motion and the specific mass and stiffness matrices for a simply-supported panel. The results of the models are compared with the closed-form solution of the 2D elasticity equations of motion and finite element results of ADINA. The numerical comparison is described in terms of eigenfrequencies and eigenmodes of displacements and stresses and reveal a good correlation at the lower modes only.

Experiment and Simulation on the Flexural Properties of Fiber-Paper Honeycomb Sandwich Structure Compound Panel

Two equivalent models based on sandwich panel theory and equivalent panel theory were discussed in this paper. By analyzing the performance of fiber - paper honeycomb sandwich structure compound panel by bending load, the computational results are in accordance with test and Engineering software ANSYS. Therefore, it shows that the finite element equivalent models are reasonable and practical for the optimization design of fiber - paper honeycomb sandwich composites.

Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory

In the present work a non-linear dynamic response of a continuous sandwich beam with SMA hybrid composite face sheets and flexible core is analyzed taking into account the phase transformation and also the material non-linearity effects, for every point along the face sheets. The one-dimensional constitutive equation of SMA proposed by Brinson is employed. Equations of motion are derived using Hamilton’s principle and a new finite element is proposed based on a higher order sandwich panel theory. Due to the phase transformation, the equations of motion are coupled with the phase transformation’s kinetic equations of SMA wires. A new finite-element-based approach along with an iterative incremental method is developed to study the dynamic response of sandwich beam with SMA hybrid composite face sheets and flexible core. A damped response of the sandwich beam is observed, which is due to the hysteresis behavior of SMA wires. The influence of the SMA wires on the vibration suppression related to the resonance phenomena of a sandwich beam as well as the effect of the through thickness location of the SMA wires inside the composite face sheets and also the effect of different boundary conditions on the dynamic response are analyzed.

Global Buckling of Sandwich Beams Based on the Extended High-Order Theory

The focus of this paper is the application of the recently introduced extended high-order sandwich panel theory to the global buckling of a sandwich beam/wide panel. Three different solution approaches using the extended highorder sandwich panel theory are presented to investigate the effects of simplifying the loading case by applying loads just on the face sheets and by including or excluding nonlinear axial strains in the core. The results are also compared with results from a benchmark elasticity solution and, furthermore, from the simple sandwich buckling formula by the earlier extended high-order sandwich panel theory. It is found that all three theories are close to the elasticity solution for “soft” cores with Ec1=E f 1 0:001, the theories diverge and the extended high-order sandwich panel theory is the most accurate.

Wrinkling of sandwich wide panels/beams based on the extended high-order sandwich panel theory: formulation, comparison with elasticity and experiments

There exist several high-order sandwich panel theories, most notably, the first to be introduced high-order sandwich panel theory (HSAPT) assumes a constant shear stress in the core. Recently, the extended high-order sandwich panel theory (EHSAPT) was introduced, its novelty being that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (shear stress in the core) of the earlier theory. In this paper, the EHSAPT formulation for predicting the critical wrinkling load is presented for a simply supported sandwich of general asymmetric construction. The cases of (i) applying the loading just on the face sheets with a linear core assumption and (ii) applying uniform strain loading throughout the thickness of the panel and a nonlinear core assumption are examined. The results are compared with a benchmark elasticity solution. In addition, edgewise compression experiments were conducted on glass face/Nomex honeycomb core and the ensuing wrinkling point is compared with the theoretical predictions. A comparison is also made with earlier edgewise compression experiments on aluminum face/granulated-cork core reported in literature. Other wrinkling formulas that are included in the comparison are: Hoff–Mautner and the HSAPT.

The analysis of the influence of core compression effect on the determination of the shear modulus of the sandwich panel core

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core/face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout.

A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads

A new model based on the high order sandwich panel theory is proposed to study the effect of external loads on the free vibration of circular cylindrical composite sandwich shells with transversely compliant core, including also the calculation of the buckling loads. In the present model, in contrast to most of the available sandwich plate and shell theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core material are determined through a 3D elasticity solution. The performance of the present theory is compared with that of other sandwich theories by the presentation of comparative results obtained for several examples encompassing different material properties and geometric parameters. It is shown that the present model produce results of very high accuracy, and it is suggested that the present model, which is based on a 3D elasticity solution for the core material, can be used as a benchmark in future studies of the free vibration and buckling of circular cylindrical composite sandwich shells with a transversely compliant core.

Buckling of flat laminated glass panels under in-plane compression or shear

Because of evident aesthetic, lighting and architectural advantages, glass curtain walls are largely used to clad modern buildings. Since these elements are considered to constitute purely architectural systems, they are essentially designed to resist loads acting orthogonally to the plane of the façade (e.g. wind loads). Contrarily, glass elements are frequently used as structural components able to sustain in-plane loads (e.g. columns, stiffening fins, beam elements, stairs, etc.), thus to preserve their integrity a buckling verification could assume great importance.In order to overcome these problems, an analytical formulation is proposed for the estimation of the buckling resistance of flat laminated glass panels under in-plane compression or shear. Two different design approaches are taken into account and compared: the first one directly derives from the theory of sandwich panels, whereas the second one is based on the approximate concept of equivalent thickness. As discussed in the paper, this last approach constitutes a useful design expedient for the deformability and resistance check of buckled laminated panels under in-plane compression or shear, in presence of different boundary conditions. Since the resistance of such brittle elements directly depends on the level of connection between the glass panes offered by the interlayer, the effects of possible temperature and time-loading variations are highlighted. The obtained analytical results are in agreement with sophisticated numerical simulations.

Geometrically nonlinear thermomechanical response of circular sandwich plates with a compliant core

The geometrically nonlinear response of a circular sandwich plate that consists of two face sheets and a compliant (“soft”) core with mechanical properties that may be either independent or dependent of temperature and subjected to both mechanical loads and thermal induced deformations, but remain elastic linear throughout the loading process, is presented. The mathematical formulation follows the principles of the high-order sandwich panel theory (HSAPT) and includes the vertical flexibility of the core in addition to the temperature dependency of the mechanical properties of the core material. The mathematical formulation outlines the set of governing partial differential equations as well the appropriate boundary conditions for a general sandwich layout. The particular case of an axisymmetric circular sandwich plate subjected to axisymmetric mechanical and thermal loads, and with axisymmetric boundary conditions is studied analytically and numerically. The numerical study includes an interaction of mechanical and thermal loads which is presented through results within the plate for various load levels of various structural quantities as well as equilibrium curves of temperatures versus these structural quantities. The results reveal that the combination of mechanical and thermal loads along with a compliant core material with mechanical properties that degrade with increasing temperatures shifts the behavior from a linear and stable (strength controlled) response into a strongly nonlinear response with limit point behavior and associated loss of stability, when large displacements and large rotations (geometrical nonlinearity) are included in the modeling.

Indentation law for lightweight sandwich plates

Sandwich structures consisting of high-modulus thin skins and a low-modulus thick core are sensitive to local loading, which causes local indentation. Classical approaches determine the deflection of sandwich structures by a superposition method where the local compression of the core for a panel on a rigid foundation is added to global sandwich bending without core compression. In this article, a sandwich plate is analyzed using a higher-order sandwich panel theory (HOSPT) where the faces are modelled by classical laminate theory and the core by a three-dimensional elasticity solution. The results are obtained from 14 partial differential equations for displacements of the faces and core. HOSPT determines core compression with a second-order distribution of displacement through the core thickness. The force versus core compression relations in the fully backed and clamped states are compared and it is shown that the core compression assumed in the classical approach differs from the core compression in a clamped state. Results are verified by ANSYS® FEM software and experimental data. A few sandwich panel specimens were made with glass reinforced plastic (GRP) skins and a polyurethane foam core. Results from indentation tests on the panels are compared with finite element, HOSPT, and other theories.