Multilayer Sandwich Beams Research Articles

Underwater impulsive response of sandwich structure with multilayer foam core

Abstract The coupling between fluid-solid interaction and structural response is a crucial factor in understanding the resistance of sandwich structures to underwater blasts. In this study, we present a theoretical model that predicts the dynamic response of multilayer foam core sandwich beams subjected to underwater impulses. We carried out a time-scale intercoupling analysis by considering the compressible core in both incident impulse and structural response. In the incident impulse coupling phase, the one-dimensional fluid-structure interaction in terms of cavitation evolution is conducted to obtain the incident pressure profile. A four inter-stages response model is proposed for further analyze the structural response coupling phase and its coupling with core strength. Explicit finite element calculations are performed to verify the theoretical results in terms of the velocity profile, transverse deflection, and core compression. The results suggest that the interaction between the four stages of the dynamic response is significantly influenced by the impulsive intensity and core strength, and the sandwich beam does not undergo all the four stages. The equivalent core strength used in the theoretical analysis is confirmed accurate to predicts impact resistance of the corresponding graded core sandwich beam, which is inferior to the sandwich beam with uniform cores, despite having the same areal mass.

Dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact

The paper focuses on the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact with heavy-mass using analytical and numerical methods. Based on the yield criterion for the multilayer sandwich structure, the circumscribing and inscribing loci of sandwich structure are obtained. Considering the interaction of bending and stretching, the analytical solution and “bound” solution for the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores are developed. The numerical calculations are used to verify the analytical solutions, and all lie within the analytical “bound” predications. Then, the influences of impact position, foam strength and face-sheet thickness on the dynamic response of multilayer sandwich beams are discussed in detail by theoretical model. For a given deflection, the impact force decreases with impact position closer to the midspan, the impact force increases with the increase of foam strength and face-sheet thickness. The present analytical model can effectively predict the dynamic response of fully clamped multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact.

Large deflection of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores

The paper used the analytical and numerical methods to analyze large deflection of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores. Considering both the strength of metal foam and corrugated core, we obtained a yield criterion for the multilayer sandwich structure foam-filled trapezoidal corrugated and foam cores. Based on proposed yield criterion, we further presented an analytical solution for large deflection of such multilayer sandwich beam under transverse loading. Well agreement is achieved between analytical and numerical results. What is more, we discussed the effects of foam strength, punch size, face-sheet thickness and middle foam thickness on the plastic behaviors.

Dynamic response of slender multilayer sandwich beams with fiber-metal laminate face-sheets subjected to low-velocity impact

Low-velocity impact of slender multilayer sandwich beams, which formed by fiber-metal laminate (FML) face-sheets and metal foam cores, is theoretically and numerically investigated. Based on the modified rigid plastic model, the analytical solution for dynamic response of the slender multilayer FML foam sandwich beam under low-velocity impact is obtained. Numerical calculations are conducted, the analytical solutions capture numerical results. Effects of the strength ratio of composite and metal layers, core strength, and metal volume fraction are discussed for impact resistance of multilayer FML foam sandwich beams. Finally, the optimal design map by minimizing the mass of multilayer FML foam sandwich beam is conducted.

Shape sensing of multilayered composite and sandwich beams based on Refined Zigzag Theory and inverse finite element method

An accurate and effective reconstruction method, which is commonly known as “shape sensing”, is presented for real-time reconstructing the deformation field of multilayered composite and sandwich laminated beam using the measured surface strains is presented. The proposed strategy uses the inverse finite element (iFEM) as a general framework and the Refine Zigzag Theory (RZT) as improved theory. Compared to the traditional iFEM, an additional kinematic variable is introduced to improve reconstruction accuracy of the axial displacement through the depth of the beam. Initially, the displacement fields, strain fields and equilibrium relations are presented. Then, the deformed displacement fields are described by the isogeometric analysis method, where the order of kinematic variables can be determined based on the equilibrium relations and the criteria for element interpolations. Next, transformation relationships are established between measured surface strains and section strains. And the number of strain sensor is further reduced through the boundary conditions. Finally, a least-square function is employed to establish the strain–displacement model. A cantilevered beam is used as a case to compare the reconstructed displacements with the theoretical displacement solutions. The numerical results demonstrate the superior accuracy capability and potential applicability of presented approach for performing accurate shape prediction of the RZT beam.

A novel magnetorheological elastomer-based adaptive tuned vibration absorber: design, analysis and experimental characterization

The present study aims at the development of a novel semi-active adaptive tuned vibration absorber (SATVA) capable of tuning its natural frequency adaptively in low frequency range. The absorber consists of a multilayer sandwich beam featuring magnetorheological elastomer (MRE) and integrated U-shaped electromagnets which are attached at the top and bottom layers of the sandwich beam. Electromagnets are designed to provide the required magnetic field to alter the stiffness of the MRE layers while also acting as the active mass of the absorber. Based on the characterization of the shear and loss modulus of the fabricated MRE samples, the finite element (FE) model of the proposed SATVA has been developed to analyze the absorber to meet the design requirements and also to evaluate its dynamic performance. The proposed SATVA is then fabricated and experimental set-ups are designed to validate the electromagnet and FE models. The frequency response function of the proposed SATVA is then investigated under different levels of the applied current to the electromagnets. It has been shown that good agreement exists between simulation and FE results. A frequency-shift of approximately 9% was achieved while maintaining a reasonable factor of safety for material constraints. Finally, using the validated FE mode, a parametric study has been conducted to investigate the effect of different design parameters.

Vibration characteristics of novel multilayer sandwich beams: Modelling, analysis and experimental validations

Multilayer sandwich structures have been extensively studied. However, very few results are reported on the vibration issues of some novel multilayer sandwich structures with lattice truss cores in the literature. To this aim, in this paper, the dynamic modellings of multilayer sandwich beams with pyramidal lattice truss cores are developed, and the vibration characteristics of multilayer lattice sandwich beams are numerically investigated and validated by vibration experiments. The deformation relations of multilayer sandwich beams are theoretically developed in this study, and consequently the constitutive relations of the truss core layers of multilayer sandwich beams are derived by using such a deformation energy based method. Hamilton’s principle and the assumed mode method are used to derive the equations of motion of the multilayer sandwich beams. The natural frequencies of the multilayer lattice sandwich beams are obtained and compared with those from the finite element method (FEM) and experimental tests, which all verified the correctness and feasibility of the proposed numerical method. Contributions of this study lie in the development of the novel deformation relations of multilayer sandwich beams, establishment of the dynamic models, and systematic analysis of vibration characteristics with both the numerical and experimental methods. The present work would facilitate the application of multilayer truss core sandwich structures in engineering fields.

Comparison and experimental verification of simplified one-dimensional linear elastic models of multilayer sandwich beams

Three analytical one-dimensional linear elastic models of composite laminated beams are considered – composite Bernoulli-Euler beam (BE), composite Timoshenko beam (T) and multilayer sandwich beam model (MS). They are compared with results obtained via finite element method for a two-dimensional model in plane stress state. Overall system stiffness is verified with experimental data obtained for two statical configurations – three-point bending and four-point bending. The first configuration concerned 8 types of three-panel cross-laminated timber (CLT) beams accounting for various materials and thickness of timber panels as well as various materials and thickness of adhesive layer, while the second one concerned 5 types of two-panel aluminium laminated beams accounting for different thickness of adhesive layer. Simplified multilayer sandwich model is found to be in good accordance with FEA results and with experimental data, while simple BE and T models are shown to provide erroneous estimates.

Free vibration analysis of cracked functionally graded non-uniform beams

This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams

This study deals with the analysis of multilayer composite and functionally graded materials (FGM) structures. The material properties of the FGM beam are assumed to vary according to the power law distribution of its constituent’s volume fraction over the cross section. The analytical analysis seems to be cumbersome. A finite element approach is investigated in this work for the static and free vibration behaviors of the 2D FGM beams with variable constituents over the cross section. The analyses are carried out in arbitrary axes and the axial, bending and shear couplings are considered. In this study, the classical beam theory, Timoshenko first-order and higher order shear models are described and implemented. The different models are compared to benchmark solutions found in the literature. Effects of boundary conditions, slenderness ratio, and the FGM power law parameter are investigated under static and free vibration analyses. FGM and multilayer sandwich beams are also analyzed. It is proven that the axial bending and shear coupling affect the behavior of the FGM beams in both statics and dynamics. In the presence of short beams, shear effect is important and leads to cross-section warping. The classical beam theory fails in this context. All models are close in the case of slender beams.

Finite Element Approach of Bending and Buckling Analysis of FG Beams Based on Refined Zigzag Theory

This is the first attempt to utilize the refined zigzag theory (RZT) to study the bending and buckling behavior of a functional graded (metal/ceramic) thick beam. RZT, which has been exploited for the analysis of multilayered composite and sandwich beams does not employ shear correction factor. Furthermore, the number of kinematics variables of the RZT is not dependent to the number of layers in comparison with the layerwise theory. With regarding to the numerical solution, RZT, also requires C0 continuity interpolation, which leads to the development of this theory in finite element method. It is assumed that the mechanical properties of the beam varies through the thickness. According to the volume fraction of metal and ceramic, it is discretized across the thickness; consequently, the functionally graded beam (FGB) is modeled as a multi-layered one. The beam subjected to uniformly transverse and axial loadings. The equilibrium equations are established using the principle of virtual work. Using the shape functions of the first and second order forms, the non-isoparametric finite element consisting of three nodes and nine degrees of freedom are extracted. To confirm the excellent accuracy of the present approach, some numerical examples are provided and compared with those available in the literature that reveals that RZT is a trusty and validated theory to analyze the FG thick beams.

Nonlinear static response analysis of sandwich beams using the Refined Zigzag Theory

The Refined Zigzag Theory (RZT) is assessed for the buckling and nonlinear static response analysis of multilayered composite and sandwich beams. A nonlinear formulation of the RZT is developed taking into account geometric imperfections and nonlinearities using the Von Kármán nonlinear strain-displacement relations. FE analyses are conducted employing C0-beam elements based on the RZT and the Timoshenko Beam Theory (TBT) to model three sandwich beams with different core materials and slenderness ratios, in both simply supported and cantilever configurations. The reference solutions are obtained by high-fidelity FE commercial codes, Abaqus® and Nastran®. The first two buckling loads are evaluated for the beams without initial imperfections. Several shapes are then assumed as geometric imperfections to calculate the beams’ nonlinear response to axial-compressive loads. The comparisons show the very high accuracy of the RZT (comparable to high fidelity FE commercial codes) for both the buckling and nonlinear static analyses and its superior capability with respect to the TBT to deal with sandwich beams with low slenderness ratio and higher face-to-core stiffness ratio.

Large deflections of multilayer sandwich beams with metal foam cores under transverse loading

In this paper, large deflections of fully clamped multilayer sandwich beams with metal foam cores are investigated. Based on the yield criteria, analytical solutions are derived for the plastic behavior of fully clamped multilayer sandwich beams loaded by a punch, in which the effects of local denting and core strength on the overall bending are considered. The finite element method is employed to predict the large deflection behavior of multilayer sandwich beams, and the analytical model captures numerical results reasonably well. The effects of core strength, multilayer factor, the size of the loading punch and loading location on the plastic analysis of multilayer sandwich beams are discussed. It is demonstrated that the load-carrying capacity of multilayer sandwich beams increases with a decrease in the multilayer factor and an increase in the core strength and that loading location and the size of the loading punch play important roles in plastic analysis.

Low-velocity impact of multilayer sandwich beams with metal foam cores: Analytical, experimental, and numerical investigations

This paper uses the analytical, experimental and numerical methods to investigate the low-velocity impact response of fully clamped multilayer sandwich beams with metal foam cores struck by a heavy mass. Using the quasi-static method, analytical solutions for dynamic response of the fully clamped multilayer sandwich beams are derived including the interaction between bending and stretching induced by large deflections. Effects of local denting and core strength on the overall bending are considered. The low-velocity impact experiments and numerical calculations are carried out to validate the analytical model. The present analytical model captures experimental and numerical results reasonably. It is shown that the energy absorption of multilayer sandwich beams increases with decrease of multilayer factor and increase of the core strength.

Evaluation of apparent shear modulus of multilayer PUF cored sandwich beams using novel experimental technique

This experimental investigation was mainly concerned with the evaluation of apparent shear modulus (Gc) of multi-layered polyurethane foam core sandwichbeams using a novel experimental technique. Aiming to this goal, some experimental three-point bending tests were conducted on sandwich beams made up of composite face sheets and multi-layered polyurethane foam cores of differentlayer density. Various core configurations in a stack of three layered core was experimented to study the effect of layer density and core configuration on apparent shear modulus.Priorto actual task, to get more confidence on proposed technique and also to understand the experimental procedure necessary for the present investigation, some samples of single PUF core sandwich beams of known densities were tested to evaluate the shear modulus(Gc) and compared the results with existing results. Series of multi-layered cored beams of different span length and configurations were tested to cater the demand of experimental procedure and to study the effect of layer density and ply order on apparent shear modulus.From the present investigation it is observed that the apparent shear modulus of linearly ordered multi-layered core i.e. core layers arranged in order of lower density to higher density from face sheet of tension side to compression side(configuration-2) could be a better option. Furthermore the apparent shear modulus of linearly ordered multi-layered core sandwich beam was comparatively better than other core configurations and single cored beams of differentcore densities used for multi-layer construction.

The plastic behavior of sandwich beams with core gradation

The objective of this paper is to establish yielding criteria for a slender sandwich beam with two-layer metal foam cores under transverse loading. A unified yielding criterion for this geometrical or physical asymmetry four-layer metallic sandwich beam is established. Based on the yield criteria, an analytical solution for large deformation of fully clamped multilayer sandwich beams under transverse loading is presented. Comparisons of present solutions with numerical results are given and good agreements are obtained. Finally, the effects of core strength and thickness ratios on the large deflection responses of the sandwich beams with core gradation are discussed in detail. It is demonstrated that the present analytical model can reasonably predict the behavior of the plastic deformation of four layer sandwich beams.

Vibration and damping behaviors of symmetric layered functional graded sandwich beams

In this study, free vibration and damping behaviors of multilayered symmetric sandwich beams and single layered beams made of Functionally Graded Materials were investigated, experimentally and numerically. The beams were composed of Aluminum and Silicon Carbide powders and they were produced by powder metallurgy. Three beam models were used in the experiments. The first model was isotropic, homogeneous beams produced by using different mixing ratios. In the second model, the pure metal layers were taken in the middle of the beam and the weight fraction of the ceramic powder of each layer was increased towards to the surfaces of the beam in the thickness direction. In the third model, the pure metal layers were taken in the surfaces of the beam and the weight fraction of the ceramic powder of each layer was increased towards to middle of the beam. Then the vibration tests were performed. Consequently, the effects of stacking sequence and mixing ratio on the natural frequencies and damping responses of functionally graded beams were discussed from the results obtained. Furthermore, the results obtained from the tests were supported with a finite-element-based commercial program, and it was found to be in harmony.

Behavior of a Sandwich Beam Subjected to Bending in Terms of the Core's Shape and Density

Problem of the multi-layer sandwich beams, subjected to bending, is considered in this paper. The influence of the density and shape of the sandwich beam core on the beam behavior was studied. The two beam configurations were analyzed: the beam whose cross-section is constant along its length and the beam with periodically varying cross-section along the length. Each of the two configurations was considered for the two different core shapes - with the square and the circular holes. The diagrams of the beam deflection in terms of the number of the core unit cells are presented for the two beam configurations and the two core shapes. Based on results presented in this paper, one can conclude that in the given loading conditions, the core density, after reaching certain critical value, ceases to affect the bent sandwich beam behavior. Comparison of the two cores shapes leads to conclusion that, in the same loading conditions, the core with the square holes provides for the better sandwich beam's characteristics, i.e. such a beam has smaller deflection with respect to the beam with the core with the circular holes.

Dynamic response of slender multilayer sandwich beams with metal foam cores subjected to low-velocity impact

Multilayer sandwich panel is a new potential lightweight structure in practical engineering applications. Dynamic response of fully clamped slender metal foam core multilayer sandwich beams struck by a low-velocity heavy mass is investigated. Based on the yield criteria for the multilayer metal sandwich cross-sections, analytical solutions and ‘bounds’ of analytical solutions for large deflection of the fully clamped slender sandwich beams are derived, in which interaction of bending and stretching induced by large deflections is considered. Numerical calculations are carried out and good agreement is achieved between the analytical solutions and numerical results. The dynamic solution approaches the quasi-static one when the mass ratio of the striker to the beam is large enough. Using the analytical formulae, optimal design charts are constructed to minimize the mass of multilayer sandwich beams for a given low-velocity impact resistance. It is shown that the dynamic and quasi-static solutions can capture the low-velocity heavy-mass impact response of fully clamped slender multilayer sandwich beams.

Plastic analysis of multilayer sandwich beams with metal foam cores

The plastic behavior of fully clamped multilayer sandwich beams with metal foam cores is investigated. A plastic yield criterion for multilayer sandwich structures with metal foam cores is proposed. Analytical solutions are derived for the multilayer sandwich beams transversely loaded by a flat punch considering the interaction of bending and stretching induced by large deflections. Numerical calculations are carried out, and good agreement is achieved between the analytical solutions and numerical results. The effects of the multilayer, punch size and core strength are discussed. Using the analytical formulae, optimal design charts are constructed to maximize the load-carrying capacity of the multilayer sandwich beams for a given mass. It is demonstrated that the present analytical model can reasonably predict the post-yield behavior of the multilayer sandwich beams with metal foam cores.