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The non-linear hygrothermal and mechanical buckling responses of FG sandwich plates resting on two-parameter elastic foundations are presented in this study. Non-linear Fourier temperature distribution is considered as a special case. A hyperbolic displacement model is proposed in the present investigation. The present model involves four unknown variables, and the shear stresses on the bottom and top of the plate surfaces are equal to zero. The effective material properties of the FG sandwich face sheets are presumed to be varied in the direction of the thickness using a simple power law distribution, while the core is supposed to be purely ceramic. The stability equations are deduced by the principle of virtual work, containing the effect of foundations interaction and hygrothermal effects based on the present model. The hygrothermal effects are considered as non-linear, linear and uniform distribution through the plate thickness. Comparison examples are presented to verify the accuracy of the present model. The effects played by the temperature rise, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio of the plate, the inhomogeneity parameter on the critical buckling of FG sandwich plates are investigated. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for vibration and buckling of functionally graded (FG) sandwich beams using various quasi-3D theories, which consider effects of both shear and normal deformation. Sandwich beams with FG skins–homogeneous core and homogeneous skins–FG core are considered. By using the Hamilton’s principle, governing equations of motion are derived. An analytical solution is presented, and the obtained results by various quasi-3D theories are compared with each other and with the available solutions in the literature. The effects of normal strain, power-law indexes, skin–core–skin thickness and slenderness ratios on vibration and buckling behaviour of sandwich beams are investigated. [ABSTRACT FROM AUTHOR]

This article presents an analytical approach for evaluating the buckling load of sandwich panels made of hybrid laminated faces and a transversely flexible core. Useful design indications are obtained once the influence of main parameters influencing the structural response is examined. The proposed model is based on a priori assumption of the displacement field through the thickness, which is composed of two sets of modal configurations, one symmetric and one antisymmetric, besides a pure compressive mode. An equivalent `single layer approach', considering all displacement components (u, v, w) that linearly vary across the panel thickness, is used. For simply supported flat sandwich panels subjected to in-plane biaxial and shear loads, the Rayleigh-Ritz method is used to evaluate the buckling loads. Predictions of the proposed model are compared with those obtained by other available theoretical models and with experimental results. Finally, the best arrangement of sandwich panels, corresponding to the maximum buckling loads, is investigated by varying the parameters of both the faces and the core material. [ABSTRACT FROM AUTHOR]

This article deals with the linear static and buckling analysis of an asymmetric square sandwich plate with orthotropic stiffness properties in the face layers. Two analytical formulations related to thin and thick face layers, respectively, have been taken from (Zenkert, D. (1995). An Introduction to Sandwich Construction, Chameleon Press Ltd, London, UK (ISBN 0 947817 77 8)), slightly modified to account for unequal faces, orthotropic properties in the face layers, and individual Poisson's ratios, and applied to square sandwich plates of I m lateral dimension and a variety of different face layer thickness. All cases assume simply supported edges. The obtained deflections and buckling loads are compared with the results of a 3D analysis (Meyer-Piening, H.-R. (2004). Application of the Elasticity Solution to Linear Sandwich Beam, Plate and Shell Analyses, J. of Sandwich Structures & Materials, 6(4): 295-312) and of finite element calculations. The objectives of this study are to gain insight into the limits of validity of the published formulas in view of unequal thick face layers and orthotropic properties. The obtained results are meant to serve as a benchmark for further studies. [ABSTRACT FROM AUTHOR]

The buckling behavior of a disbond in a sandwich beam is analyzed by modeling the sandwich as a beam on a Winkler foundation. The foundation stiffness is derived through a stress function approach, modeling the core as a two-dimensional, orthotropic material in plane strain. When the resulting stiffness term is used in the Winkler foundation model, the predicted buckling loads vary from the specimen test results by only 1.7% (with a standard deviation of 2.3%). This is the most accurate published prediction of disbond buckling and is discussed in terms of previous studies. An extensive specimen test program is described, the results of which are used to validate the Winkler foundation model. The buckling load, as a function of core thickness, is found to have a minimum when the core thickness is approximately equal to the natural wrinkling half-wavelength of the sandwich. Further, a characteristic curve is found using the wrinkling wavelength and the Euler buckling load as normalizing values. A semi-empirical formula for the buckling load is developed from a non-dimensional analysis and predicts the specimen test results to within 2.8% (standard deviation of 3.6%). [ABSTRACT FROM AUTHOR]

This paper is dedicated to the study of global (at the sandwich scale) and local (at the component scale) buckling in sandwich structures. This approach relies on the basis of an analytical model able to capture both local and global instabilities [Léotoing, L., Drapier, S. and Vautrin, A. (2002). First Applications of a Novel Unified Model for Global and Local Buckling of Sandwich Columns, European Journal of Mechanics A/SOLIDS, 21(4): 683-701]. Results from this model are used to provide simple design rules by assessing the combinations of geometrical and material parameters which control these instabilities. From there, design diagrams are extracted which permit very quickly to select sandwich configurations more susceptible to develop local or global phenomena. These design diagrams constitute a precious guide at the predesign stage of sandwich structures. Then, two distinct FE models are presented and compared. The ability of a reduced size FE model to capture local as well as global instabilities is demonstrated. Eventually, the predicted loads and wavelengths from both FE simplified model and analytical model are shown to correlate very well. Thus, analytical wavelengths give accurate evaluations of the mesh element size for a low time-consuming but accurate FE model which can be easily extended to fully non-linear computations of sandwich panels. [ABSTRACT FROM AUTHOR]

The novelty of this paper is the use of a new four-variable refined plate theory for thermal buckling analysis of functionally graded material (FGM) sandwich plates. Unlike any other theory, the present new theory is variationally consistent and gives four governing equations. The number of unknown functions involved is only four, as against five in case of other shear deformation theories. In addition, the theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear, and nonlinear temperature rises across the thickness direction. The effects of aspect and thickness ratios, gradient index, loading type, and sandwich plate type on the critical buckling are all discussed. [ABSTRACT FROM PUBLISHER]

Vibration and buckling of sandwich laminates are studied for different degrees of imperfections at the layer interfaces using a refined plate theory. In this plate theory, the through-thickness variation of transverse shear stresses is represented by piecewise parabolic functions, where the continuity of these stresses is satisfied at the layer interfaces. The transverse shear stresses free condition at the top and bottom surfaces of the plate is also satisfied. The interlaminar imperfections are represented by in-plane displacement jumps at the layer interfaces by a linear spring layer model. Many new results are generated that should be useful for future research as there is no such published result on imperfect sandwich plates. [ABSTRACT FROM AUTHOR]

An experimental study of the in-plane compression failure of sandwich panels consisting of glass/epoxy face sheets over a range of PVC foam cores (H45, H100, and H200) and a balsa wood core containing one or two circular or square interfacial debonds is conducted. For the great majority of the specimens, failure occurred by local buckling of the debonded lace sheet followed by rapid debond growth towards the panel edges, perpendicular to the applied load. Panels with the largest debond (10cm diameter or 9cm length) displayed some post-buckling strength. Examination of the face and core failure surfaces after total separation showed that the tendency for interface (core/resin) failure increases with increasing core density. It was found that the compression strength strongly decreases with decreasing core stiffness and increasing debond size. The compression strength of panels with H45 core decreased with reduced core thickness. Failure loads for panels with symmetric debonds at both face/core interfaces were practically the same as those for panels containing a single debond. Panels with square debonds failed at lower loads than those with circular debonds of the same area. Circular debonds of 50 mm diameter and square debonds of 45 mm length set the threshold for debond failure of the panels considered here. [ABSTRACT FROM AUTHOR]

Compared to other core materials, honeycomb materials provide impressive mechanical performance for sandwich panels, but with less weight added to the structures. In this article, the out-of-plane compressive properties of the thermoplastic hexagonal honeycombs are investigated by using finite element analysis (FEA). Due to the fact that the vertical cell walls of the honeycombs are not perfectly straight, the out-of-plane compressive modulus and strength cannot be predicted correctly by conventional theories. Therefore, FEA methods are used in this study attempting to evaluate the compressive properties. Initially, linear buckling analysis (eigenvalue problem) is applied on the honeycomb models with various numbers of cells to obtain the relationship between the single hexagonal unit cell and the infinite honeycomb. Based on this, nonlinear large deformation FEA is performed on the unit cell model with/without imperfect geometry to obtain honeycomb compressive properties. Finally, the resulting modulus and strength of the honeycomb are compared to the other analytical results and experimental data. The FEA method shows some advantages over these conventional theories. [ABSTRACT FROM AUTHOR]

Sandwich panels manufactured using thermoplastic fiber-metal laminates (FML) skins and an aluminum foam core were tested under quasi-static and low-velocity impact loading conditions. The quasi-static properties of the sandwich beams were evaluated using the three-point bend test geometry. Energy absorbing mechanisms such as buckling and interfacial delamination in the FML skin, as well as indentation, crushing, and densification in the aluminum foam have been observed to contribute to the excellent energy absorbing characteristics offered by these systems. The low-velocity impact behavior of the sandwich panels was evaluated using an instrumented dropping weight impact tower and modeled using an energy balance approach. A breakdown of the energy absorption revealed that these sandwich structures absorb much of the impact energy due to contact and bending effects. Finally, four-point bend testing after low-velocity impact revealed that these systems offer excellent residual flexural strength with relative values remaining close to 80% of the original strength after a 32 J impact. [ABSTRACT FROM AUTHOR]

The works that have been already published on sandwich face wrinkling consider isotropic or almost isotropic sandwich configurations. Hence, only the critical wrinkling load needs to be evaluated in the principal compressive stress direction. This is insufficient for a sandwich panel with a higher degree of anisotropy. This paper presents a method for estimating the wrinkling behavior of highly anisotropic sandwich panels under biaxial loading. The method is based on the assumption that wrinkling occurs at the angle where the ratio of applied load to sustainable wrinkling loads reaches a global maximum. In addition to the description of the analytical theories, the paper presents comparisons with finite element calculations and testing of real sandwich configurations. The results indicate that the derived model works excellently both for uni- and biaxial loadings, though a small factor of safety is required as with all other standard wrinkling theories. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling behaviors of eccentrically stiffened sandwich plates on elastic foundations subjected to in-plane compressive loads, thermal loads, or thermomechanical loads are presented analytically by using the Reddy’s third-order shear deformation plate theory with von Karman geometrical nonlinearity. Four cases of general Sigmoid and power laws are considered. The material properties of the facesheets, the core layer, and stiffeners are assumed to be temperature-dependent. Theoretical formulations based on the smeared stiffeners technique and third-order shear deformation plate theory are derived. The expressions of thermal parameters are found in the analytical form. Applying the Galerkin method, the expressions for determination of the critical buckling load and analysis of the postbuckling mechanical and thermal load–deflection curves are obtained. The iterative algorithm is presented for the case of temperature-dependent plate material properties. In addition, the influences of thermal element, functionally graded material stiffeners, the facesheet thickness to total thickness ratio, initial imperfection, and foundations are clarified in detail. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

Compression failure of sandwich specimens with glass/vinylester face sheets over PVC foams has been experimentally examined using an end loading test fixture based on the ASTM C 364 standard. The main objective of the research was to examine the roles of the faces and core in the mechanism of failure and ultimate load carrying ability of the structure. A range of PVC foam densities, core thicknesses, and specimen lengths were examined. Failure modes were identified, and compression strengths were compared to analytical predictions. Short specimens failed by compression failure of the face sheets up to a gage length that increased with increased foam density, and decreasing core thickness. At intermediate gage lengths it was found that specimens with a thick low density core failed in an anti-symmetric face wrinkling mode, while long specimens failed by global buckling in the fundamental buckling mode. Predictions of the failure loads were found to be in reasonable agreement with experimental results. [ABSTRACT FROM AUTHOR]

The effects of time and stress state on fracture behaviors and mechanisms of polyvinyl chloride foam have been evaluated by varying displacement rates (0.1 to 1000 mm/min) and specimen thicknesses (5 to 37.5 mm). For thin specimens, the crack tips were under plane-stress condition at all displacement rates. The excessive deformation under plane-stress condition induced severe damages of cell walls around the crack tip, which resulted in low fracture toughness. For thick specimens at low displacement rate, the crack tips were under plane-stress condition. The marginal inelastic deformation under plane-stress condition was high enough to cause crack-tip blunting. Thus, relatively high fracture toughnesses were observed. For thick specimens at high displacement rate, the crack tips were under plane-strain condition. Brittle fracture of cell walls around crack tip was observed. The fracture toughnesses were lower than those of thick specimens at low displacement rate. [ABSTRACT FROM PUBLISHER]

A new idea for fabricating a truss periodic cellular metal (PCM) is described. Namely, an octet-like truss PCM named 'M-octet' is fabricated by folding expanded metals. Its strengths under compression and shear load estimated by elementary mechanics are compared with experimental results and those of other competing cellular metals. When employed as a core in a sandwich panel, the load capacity subjected to bending load is predicted by an energy-based approach for various failure modes. For a given core height, a failure mode map is constructed with the nondimensional parameters such as geometric variables, material parameter (yield strain), load index, and weight index. Based on the failure mode map, three designs are chosen for maximum load per weight ratio. The predicted failure loads for the three different geometric designs are compared with the values measured through the experiments which are performed with sandwich specimens with the tetrahedral truss cores made of a wrought steel SS41. The measured equivalent normal yield and shear yield stresses agree fairly well with those predicted by the analytic solutions. In the three-point bending tests, the design with the thickest core truss and face sheets shows the peak load point delayed the most, which gives benefits in terms of the energy absorption and deformation stability after the peak load point. [ABSTRACT FROM AUTHOR]

This study shows that a simple approach to stiffness tailoring of composite face sheets can improve the performance of sandwich panels under compressive loading when delaminations are present. The simple stiffness tailoring concept used here is to reposition of all 0° material (aligned with the loading direction) into regions of certain width near the edges of the sandwich panel. This concept has been shown to improve the buckling and postbuckling performance of solid plates and to offer control of delamination growth. To evaluate this tailoring design concept in sandwich panels, numerical simulations of onset and propagation of the delamination growth were conducted with uniform face sheets and tailored face sheets. The delamination front tracing method previously developed by the authors was used to perform the delamination growth analysis. The interfacial elements, which allow the growth of the delamination front to be traced, are placed at the interface between the top face sheet and the core in the undelaminated region. They enable calculation of the strain energy release rates and application of a fracture mechanics delamination growth criterion. Gap elements were used to avoid interfacial overlap. Based on the numerical study, the improvement in the ultimate load provided by the simple stiffness tailoring concept ranges from 80% to 100%, depending on the extent of tailoring. Substantial improvements in the residual strength and stiffness, after significant delamination growth, can also be observed. Therefore, this article provides a potential design concept that can improve the damage tolerance of sandwich panels without adding weight. [ABSTRACT FROM AUTHOR]

The problem of face wrinkling in sandwich structures was identified as an important failure mode and first analyzed in 1940 by Gough et al., who used a Winkler-type elastic foundation to model the core. This work was followed by experiments and further analysis by many others. Until 1966 all of the research was devoted to uniaxial compression loading. However, in many applications, such as naval and aircraft structures, panels are subjected to biaxial loading. Such loadings were first analyzed by Plantema in 1966 for the case of sandwich constructed of isotropic materials. Sullins et al. suggested an interaction equation that can be used as a criterion of wrinkling under compression in the principal directions. This equation is formulated in terms of the ratios of the principal compressive stresses to the corresponding wrinkling stresses. More recently Fagerberg and Vonach and Rammerstorfer considered the case of sandwich with orthotropic facings. The present work attacks the subject problem using three different models for the core. One model uses a simple Winkler elastic foundation approach. The second model, following Hoff and Mautner [Hoff, N.J. and Mautner, S.E. (1945). The Buckling of Sandwich-Type Panels, Journal of the Aeronautical Sciences, 12: 285-297.], uses a linear model for the decay in deformation from the core-facing interface, while the third model, following Plantema [Plantema, F.J. (1966). Sandwich Construction, John Wiley & Sons, Inc., New York.], uses an exponential decay. [ABSTRACT FROM AUTHOR]

To develop lightweight and biomimetic structural materials, in this paper, the compressive deformation and mechanical properties of the grid beetle elytron plate (GBEP) with the same core volume as the end-trabecular beetle elytron plate (EBEP) under compression were investigated for the first time. (1) The B-type deformation mode of trabeculae is clarified, which is a higher stage of independent deformation than the Φ-type deformation mode in the beetle elytron plate (BEP). Additionally, the four deformation modes of the BEP are divided into three stages in succession from easy to difficult: C-type, Φ-type and S (B)-type deformation. This paper verifies that the compressive strength and energy absorption capacity of the GBEP increase by 35% and 87%, respectively, relative to those of the grid plate (GP) with the same volume. (2) Although the number of trabeculae of the GBEP is significantly less than that of the EBEP, each trabecula in the GBEP has one more honeycomb wall constraint than each trabecula in the EBEP. The increase range of the compressive properties of the GBEP relative to the GP is greater than that of the EBEP relative to the honeycomb plate (HP). This confirms the prediction that the compressive properties can be effectively improved by appropriately increasing the constraints on the trabeculae. This paper deepens and enriches the knowledge regarding the biomimetic application system of BEPs, lays the foundation for GBEPs, whose preparation is convenient, and accelerates the applications of GBEPs. [ABSTRACT FROM AUTHOR]

In this article, the static analysis of sandwich plates is performed by radial basis functions collocation, according to the Murakami's Zig-Zag function theory. The Murakami's Zig-Zag function theory accounts for through-the-thickness deformation, by considering a Zig-Zag evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carrera's unified formulation, and further interpolated by collocation with radial basis functions. [ABSTRACT FROM PUBLISHER]

This article presents a study of the linear transient response of composite plates using radial basis functions and collocation method. We use the Kansa method and radial basis functions in a pseudo-spectral framework. The first-order and a third-order shear deformation plate theories are used. It is shown that the present method produces highly accurate displacements and stresses when compared with the available results in the literature. [ABSTRACT FROM PUBLISHER]

In this study, the bending responses of metallic sandwich plates with a sheared dimple core were investigated through the 3-point bending tests and dynamic plane bending tests. It was experimentally shown from the uniaxial tensile tests that the yield and tensile strengths of the brazed face sheet were weaker than those of the welded face sheet. A mild steel sheared dimple core was fabricated by the sectional forming process and then bonded with DP590 face sheets by multi-point resistance welding. Analysis for large deformation of a sandwich plate subject to 3-point bending was carried out, where frictional work was considered and a face sheet was treated as a rigid-plastic material based on Hollomon’s flow rule. Load—deflection curves and the deformed shapes of the finite element method computations and the experiments were efficiently predicted by the proposed analysis. The effect of frictional work on the peak load and energy absorption increases as the bending angle increases. The dynamic bending responses of the sandwich plates, such as the effect of a deformed shape, failure mode, energy absorption and absorption ratio were compared with those of a high-strength steel sheet. It was demonstrated that a bendable sandwich plate was stronger construction than a high-strength steel sheet under the tested conditions, despite the weight reduction and weaker properties. [ABSTRACT FROM AUTHOR]

Corrugated sandwich panels are widely used in engineering applications for their excellent energy absorption and lightweight. In this research, the mechanical response of aluminum corrugated sandwich panels subjected to three-point bending is investigated experimentally, numerically, and theoretically. In the experiments, the sandwich panels were loaded under two conditions, namely base indentation and node indentation. A parametric study is conducted by ABAQUS/explicit to investigate the effects of geometric configurations (corrugation angle, core height, and core thickness) on the deformation mode, peak force, and energy absorption. Both peak force and specific energy absorption vary with the geometric parameters. Theoretical models are further developed to predict the force–displacement curves of the panels under the two loading conditions. The theoretically predicted crushing force is in good agreement with both the experimental and simulated results. Finally, the non-dominated sorting genetic algorithm II is adopted to optimize the geometric configuration to improve the specific energy absorption and reduce the weight of corrugated sandwich panels. [ABSTRACT FROM AUTHOR]

In this article, an experimental investigation is carried out to understand the behaviour of sandwich deep beams. The shear strength, load transfer mechanism, integral action and failure modes are reported. Primary variables of this study include distribution of web reinforcement, beam geometry and type of loading. Twelve full-scale beams were tested with simply supported end conditions classifying them into two groups. Each series consists of six beams with rectangular and I-shaped cross-sectional geometry. Two types of loading, i.e. concentrated and uniformly distributed loads, were adopted to understand the influence of distribution of horizontal reinforcement along the depth of beam in the web. Using both types of cross-sections, two beams were tested under uniformly distributed loads, and all the remaining beams were subjected to concentrated load with two different shear span-to-depth ratios (a/d). Observations of the study with respect to strength and serviceability include initial cracking load, ultimate load, crack width, transverse deflection and out-of-plane deformations. The test results indicated that confined or unconfined I-beams in the web failed due to punching shear under concentrated or distributed loads. The modes of failure of rectangular beams with web confinement were diagonal splitting and shear-compression, whereas the unconfined beams failed in flexure. Shear strength expression for conventional deep beams is refined for sandwich beams, and the predicted shear strength agrees well with the experimental results. [ABSTRACT FROM AUTHOR]

Auxetic cellular solids in the forms of honeycombs under blast load have great potential in a diverse range of applications, including core material in sandwich plates composite components. Based on Reddy’s first-order shear deformation plate theory, this paper presents an analysis of the nonlinear dynamic response and vibration of sandwich plates with negative Poisson’s ratio in auxetic honeycombes on elastic foundations subjected to blast and mechanical loads. A three-layer sandwich plate is considered discretized in the thickness direction by using analytical methods (stress function method, approximate solution), Galerkin method, and fourth-order Runge-Kutta method. The results show the effects of geometrical parameters, material properties, mechanical and elastic foundations on the nonlinear dynamic response, and vibration of sandwich plates. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear dynamic response of higher order shear deformable sandwich functionally graded circular cylindrical shells with outer surface-bonded piezoelectric actuator on elastic foundations subjected to thermo-electro-mechanical and damping loads. The sigmoid functionally graded material shells are made of the metal–ceramic–metal layers with temperature-dependent material properties. The governing equations are established based on Reddy’s third-order shear deformation theory using the stress function, the Galerkin method and the fourth-order Runge–Kutta method. Numerical results are given to demonstrate the influence of geometrical parameters, material properties, imperfection, elastic foundations, and thermo-electro-mechanical and damping loads on the nonlinear dynamic response of the shells. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature. [ABSTRACT FROM AUTHOR]

Free vibration analysis of a sandwich beam with soft core and carbon nanotube reinforced composite face sheets, hitherto not reported in the literature, based on extended high-order sandwich panel theory is presented. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded. In this theory, the face sheets follow the first-order shear deformation theory. Besides, the two-dimensional elasticity is used for the core. The field equations are derived via the Ritz-based solution which is suitable for any essential boundary conditions. Chebyshev polynomials multiplying boundary R-functions are used as admissible functions and evidence of their good performance is given. A detailed parametric study is conducted to study the effects of nanotube volume fraction and their distribution pattern, core-to-face sheet thickness ratio, and boundary conditions on the natural frequencies and mode shapes of sandwich beams with functionally graded carbon nanotube reinforced composite face sheets and soft cores. Since the extended high-order sandwich panel theory can be used with any combinations of core and face sheets and not only the soft cores that the other theories demand, the results for the same beam with functionally graded carbon nanotube reinforced composite face sheets and stiff core are also provided for comparison. It is concluded that the sandwich beam with X and V distribution figures of face sheets, no matter what the boundary conditions, has higher vibration performance than the beam with UD-CNTRC face sheets. [ABSTRACT FROM AUTHOR]

Using harmonic differential quadrature method, an approach to analyze sandwich cylindrical shell panels with any sort of boundary conditions under a generally distributed static loading, undergoing elasto-plastic deformation is proposed. The faces of the sandwich shell panel are made of some isotropic materials with linear work hardening behavior while the core is assumed to be an isotropic material experiencing only elastic behavior. The faces are modeled as thin cylindrical shells obeying the Kirchhoff–Love assumptions. For the core material, it is assumed to be thick and the in-plane stresses are negligible. Upon application of an inner and outer general lateral loading, the governing equations are derived using the principle of virtual displacements. Using an iterative approach, named elasto-plastic harmonic differential quadrature method (EP-HDQM), the equations are solved. The obtained results are compared with the results from finite element software Ansys for different sandwich shell panel configurations. Then, the effects of changing different parameters on the stress and displacement components of sandwich cylindrical shell panels in different elasto-plastic conditions are investigated. [ABSTRACT FROM AUTHOR]

Radar domes are the cover structures over the radar antenna systems to provide environmental protection to the sensitive parts such as electronics, steering hardware, wave guide, additional equipments, and antenna itself. Composite dielectric materials are preferred solutions for radome construction because of their negligible effects on electromagnetic transmission of enclosed antenna. Very recently, the effect of interlaminar stress distribution and radome geometry over the transmission capabilities is reported by several researchers. The aim of this study is to present an efficient solution methodology with minimized mathematical effort for the analytical solution of sandwich composite dielectric materials for radome structures with one and double core layers. Analytical solution methodology for the analyses of stresses and deformations is based on Third-Order Shear Deformation Theory (TSDT). Double Fourier series which are specialized for boundary discontinuity are used to solve highly coupled linear partial differential equations. Numerical solutions for the designed spherical radome geometry with one and double core layers are presented for laminated sandwich shells to provide benchmark results for the pre-design activities of radome structures. [ABSTRACT FROM AUTHOR]

A simplified three-unknown shear and normal deformations nonlocal beam theory for thermo-electro-magneto mechanical bending analysis of a nanobeam with a functionally graded material core and two functionally piezomagnetic layers is studied in this paper. The assumed structure is subjected to mechanical, thermal, electrical, and magnetic loads. An initial applied voltage and magnetic load is considered on the functionally graded piezomagnetic material layers. Eringen’s nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using the principle of virtual displacements. The numerical results including the deflection, electric, and magnetic potential distribution are calculated in terms of important parameters of the problem such as applied electric and magnetic potentials, two parameters of temperature distribution, and nonlocal parameter. The numerical results indicate that increase in applied electric potential increases the deflection unlike the applied magnetic potential that decreases the deflection. Furthermore, it can be concluded that increasing the nonlocal parameter leads to increase in the deflection. [ABSTRACT FROM AUTHOR]

This paper focuses for the first time on the static analysis of sandwich plates with functionally graded faces and homogeneous core by an nth-order shear deformation theory and meshless global collocation method. The meshless global collocation method approximates the solutions of governing differential equations based on the nth-order shear deformation theory using all nodes in the problem domain. The deflection and stress of a simply supported sandwich plates under sinusoidal load are calculated to verify the accuracy and efficiency of the present theory. [ABSTRACT FROM AUTHOR]

An accurate discrete model is presented here for the analysis of simply supported web-core sandwich plates. In this model, the face plates are analysed using the equations of 3D elasticity and for the webs a plane stress idealization is used to model the kinematics of transverse bending while simple one-dimensional classical models are employed for lateral bending and torsion. Thus, this model accounts for the non-classical effects of transverse shear deformation and transverse thickness-stretch in the face-plates and the webs. It is shown that this model is capable of accurately capturing the effects of secondary local bending of the face-plates between the webs on the displacement and stress fields. Results obtained by this rigorous approach are used to highlight the errors of the commonly used model based on the classical hairbrush hypothesis for the face-plates. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened sandwich plate with functionally graded material (FGM) on elastic foundation using both of the first-order shear deformation plate theory and stress function with full motion equations (not using Volmir's assumptions). The thick sandwich plates are assumed to rest on elastic foundation and subjected to mechanical loads in thermal environment. Numerical results for dynamic response of the eccentrically stiffened thick sandwich plates are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, material properties, imperfections, the elastic foundations, eccentric stiffeners, mechanical loads and temperature on the nonlinear dynamic response and nonlinear vibration of functionally graded sandwich plates. The numerical results in this paper are compared with the results reported in other publications. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration analysis of composite thick rectangular plates, based on Reddy’s higher order shear deformation theory (HSDT). The plate theory ensures a zero shear-stress condition at the top and bottom surfaces of the plate and do not requires a shear correction factor. Although the plate theory is quite attractive, it could not be used in the finite element analysis. This is due to the difficulties associated with the satisfaction of the C1 continuity requirement. To overcome this problem associated with Reddy’s HSDT, a new C1-HSDT p-element with eight degrees of freedom per node is developed and used to find natural frequencies of thick composite plates. The formulation is easily implemented into simple and efficient finite element programs in which the trigonometric hierarchical shape functions are used. A fast convergence and excellent agreement with the known results in the literature are obtained using only one element. Besides, the effects of the boundary conditions, core to face sheet thickness ratio, Young’s modulus ratio on the natural frequencies are investigated through the analysis of these numerical results. [ABSTRACT FROM AUTHOR]

In this article, the geometrical nonlinear free vibration behaviour of shear deformable laminated composite single/doubly curved shell panel in hygrothermal environment is investigated. A general nonlinear mathematical model of laminated composite doubly curved shallow shell panel has been developed based on the higher order shear deformation theory and Green-Lagrange geometric nonlinear kinematics. All the nonlinear higher order terms have been included in the present mathematical model to achieve a realistic case. In addition to that, the composite material properties are considered as temperature and moisture dependent through hygro-thermo-elastic constitutive relations. The governing equation of laminated composite curved panel is obtained using Hamilton’s principle and discretised using nonlinear finite element steps. The desired responses are computed numerically using a direct iterative method. The convergence behaviour of present numerical model has been checked and validated by comparing the responses with those available published results. The effect of different geometrical and/or material parameters on nonlinear vibration behaviour of laminated composite doubly curved shell panel under hygrothermal environment is computed and discussed in detail. [ABSTRACT FROM AUTHOR]

In this work, the functionally graded honeycomb structures with defects are investigated. It is shown how the patterns and locations of defects, as well as the density gradients, can affect the in-plane dynamic crushing behavior of honeycombs. Numerical results show that due to missing vertical cell walls, the deformation process for the transverse-vertical mixing defects is more complicated than that for pure vertical defects. For the honeycombs with negative density gradient, the I-shape deformation band is dominant during the dynamic crushing. However, the honeycombs with positive density gradient are crushed to densification with the combination of the first and second deformation bands. It is revealed that the ability of energy absorption could be improved by introducing the functional graded property. Moreover, under a high impact velocity, the gradient displays a high sensitivity on the energy-absorption capability of the honeycomb structures. At the early stage of crushing, the honeycomb structures with the positive density gradient behave the stronger capacity on energy absorption than those with the negative one. The energy-absorption curves for systems with positive and negative densities are symmetric about the homogeneous structures. As the compression proceeds, for the honeycombs with positive and negative density gradients, the trends of energy-absorptive abilities go into reverse. [ABSTRACT FROM PUBLISHER]

The increasing application of functionally graded materials in the aerospace structures requires the adoption of accurate modeling strategies. The original formulation of the Refined Zigzag Theory is here extended to the bending and free vibration analysis of sandwich plates embedding functionally graded layers, either as faces or core. Extensive numerical investigation shows the superior predictive capabilities of Refined Zigzag Theory over both First-order Shear Deformation Theory and Third-order Shear Deformation Theory, if compared with the reference three-dimensional elasticity or high-fidelity FEM solutions. In virtue of its accuracy and of the C0–continuity requirement for shape functions, Refined Zigzag Theory can be adopted to formulate reliable and computationally efficient finite elements suited for large-scale analyses of both traditional and functionally graded structures. [ABSTRACT FROM PUBLISHER]

This paper analyzes the bending response of functionally graded skew sandwich plates with graded layer as face sheet/core using higher order shear deformation theory in the frame work of finite element method considering through-the-thickness variation of displacements. The assumed kinematics field incorporates the quadratic variation of thickness co-ordinate in defining the transverse displacement. The C0 finite element formulation has been done efficiently to overcome the problem of C1 continuity associated with the higher order shear deformation theory. For this, a rectangular isoparametic Lagrangian element with nine nodes and 13 nodal unknowns at each node is developed. Two types of plates are modeled: functionally graded skew plates with graded face sheets and graded layer as core part. By considering the symmetry of the plate, different combinations of bottom-core-top thickness has been considered for the numerical study. Wide variety of numerical problems are presented for functionally graded sandwich plates with various skew angles, thickness schemes, aspect ratio, thickness ratio and boundary conditions. It is noticed that isotropic plates exhibit diverge response in comparison with graded plates. Also, power law exponent and skew angle are vital parameters that dictate the response of the plate under bending. [ABSTRACT FROM AUTHOR]

In this paper, a new higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed. The number of unknown functions involved in the present theory is only five, as against six or more in case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The boundary conditions for the plate are assumed to be simply supported in all edges and in the static analysis, the plate is assumed to be subjected to a sinusoidally distributed load. Both symmetric and non-symmetric sandwich plates are considered. The equations of motion are obtained using Hamilton’s principle. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and efficient in predicting the bending and free vibration responses of sandwich plates with functionally graded isotropic face sheets. [ABSTRACT FROM PUBLISHER]

The failure modes of open weave (latticed) sandwich skins under biaxial compression load are analysed. Due to the latticed structure of these sandwich face sheets, they are able to transfer loads in both directions. Tests show a distinct non-linear correlation between load and deformation. This non-linear load-deflection-behavior indicates that the failure may be induced by geometrical imperfections. Based on this assumption and measured geometrical imperfections, a mathematical model for the latticed face sheet consisting of beams under compression is derived. Several beams are combined within one or two cells of the honeycomb core to describe the failure modes. Furthermore, biaxial loading is analysed by using the finite element method. Experimental results are in good agreement with failure loads derived by analytical and by finite element method analyses as well. [ABSTRACT FROM PUBLISHER]

A refined trigonometric higher-order plate theory is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The effects of transverse shear strains as well as the transverse normal strain are taken into account. The number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformations theories. Several types of the present symmetric and non-symmetric sandwich plates are used. The faces are assumed to be functionally graded through the thickness, while the core layer is still homogeneous and made of an isotropic material. The present refined plate theory is used to derive the field equations of the functionally graded sandwich plates. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses. [ABSTRACT FROM PUBLISHER]

An elastic-plastic model was developed for predicting the blast response of a foam-core, curved composite sandwich panel. A multi-layered approach was used to distinguish facesheets and core deformations. Core compressibility and transverse shear through the thickness were accounted for using linear displacement fields through the thickness. The predicted solution from the elastic-plastic model was shown to compare well with FEA from ABAQUS Implicit. A parametric study showed that blast resistance of the sandwich shell is increased by allowing cores to undergo plastic crushing. Very thick and shallow shells derive much of their resistance to blast from core crushing. Strong, dense foam cores did not increase the blast resistance of the curved sandwich panel but allowed facesheets to fracture while the core remained elastic. [ABSTRACT FROM PUBLISHER]

The dynamic behavior of soft-core sandwich plates is investigated. A high-order finite element concept that has been developed for the dynamic analysis of multi-layered plate structures with stiff and compliant layers is applied to the soft-core sandwich plate. The application to sandwich plates aims to validate the general model through comparison with experimental and analytical benchmarks and to throw light on the unique structural response of the sandwich plate. The model introduces the core’s three-dimensional stress and deformation fields using a high-order kinematic assumption that is based on the closed-form solution of the static governing equations of the core. The first-order shear deformation laminated plate theory is used for the face sheets. The combination of the high-order theory with the finite element concept aims to extend the application of the theory to more general layouts, to reduce the computation effort needed for a three-dimensional analysis, and to address some of the obstacles due to differences in length scales and elastic properties. The validity and the capabilities of the formulation are examined through comparison with experimental and analytical results taken from the literature. In addition, the static, free vibration, and dynamic behaviors of an ‘L’ shaped sandwich plate subjected to localized loads and boundary conditions are numerically studied. The formulation, the comparison with experimental and analytical benchmarks, and the numerical study highlight the three-dimensional effects and reveal unique aspects of the dynamic response of soft-core sandwich plates. [ABSTRACT FROM AUTHOR]

In the present study, vibration and damping analysis of cylindrical sandwich panels containing a viscoelastic flexible core based on the high-order theory of sandwich structures is investigated. A layerwise formulation is developed to study the applicability of the high-order theory. The face sheets are considered as composite laminates with cross-ply layup that follow first-order shear deformation assumption and the core is considered as a linear viscoelastic medium with out-of-plane stresses only. The field equations along with the boundary conditions are derived via the application of Hamilton’s principle. A closed-form solution is developed for simply supported boundary conditions and a comparison is made with available results in the literature to verify the high-order and layerwise solution results. Finally, the influence of parameters including the core stiffness, the core to the face sheets thickness ratio, and the core damping on the applicability of the high-order theory, and variation of natural frequencies and modal loss factors of the sandwich panel are investigated. The results demonstrate a good agreement between the high-order and layerwise theories for small core stiffnesses, and for a wide range of the core to the face sheet thickness ratio and core damping. [ABSTRACT FROM AUTHOR]

This article presents a theoretical analysis for predicting the initial stiffness E*, and plastic collapse strength σ*pl of BCC micro-lattice blocks under compressive loading. This theoretical analysis is based on the observed deformation mechanisms, and can, in principle, be developed to predict the elastic properties of other micro-lattice structures. The analytical solutions are verified by comparing the predictions with FEM data using 1D beam and 3D solid elements and uniaxial compression tests on samples fabricated by selective laser melting. The FEM predictions using the 3D solid elements agree well with the experimental data for a wide range of strut aspect ratios, d/L. In addition, the range of applicability of the analytical model and the FEM predictions using beam elements are clarified. [ABSTRACT FROM AUTHOR]

Three-point bending tests in the elastic domain were carried out on sandwich specimens with the facings made of unidirectional T800H/3900-2 laminates, and the core of a soft and thin viscoelastic layer, varying the slenderness ratio. A closed-form formula available in the literature, developed for sandwich beams with thick facings, was used to predict the rigidities in flexure, adopting three different methods for the calculation of the shear rigidity. The best results were obtained by the classical sandwich theory, which provided reasonably good correlation with the experimental results, slightly overestimating the actual values. A finite element model consisting of three layers, made of standard CQUAD4 and CHEXA8 elements for facings and core, respectively, was developed, accurately predicting beam bending behavior. From the numerical results, the inability of classical sandwich theory to correctly estimate the bending rigidity is correlated with the through-the-thickness shear deformation of facings, not accounted for in the analysis. [ABSTRACT FROM AUTHOR]

Following paper Part I, this article investigates the last step of ThermHex process namely fusion bonding. The critical point of the fusion bonding step is to prevent catastrophic deformation (collapsing) of cell walls under heat and pressure. This demands a rapid heating rate and short heating time to keep sufficient stiffness for the inner part of cell walls against the pressure applied on the honeycomb. Hence, in this work the transient heat transfer behavior during the fusion bonding is investigated by using a finite element model for the detailed hexagonal unit cell. Furthermore, a mathematical model is developed to analyze the deformation of molten cell walls and their gradual contact to the skin strips. The experiments based on the talc-filled polypropylene material have been performed to validate the analytical model. Consequently, the optimal fusion bonding conditions can be determined to ensure good quality for the final products. [ABSTRACT FROM AUTHOR]

This article presents an approach to facilitate comparison and optimization of sandwich material combinations. Equivalent homogenized sandwich material properties (bending stiffness, density, and cost) are presented graphically in material selection charts to enable an efficient performance per cost evaluation. The effects of core shear deformations and panel production costs can be included in those sandwich material selection charts. [ABSTRACT FROM AUTHOR]

The energy absorption of an aluminum foam sandwich structure and a conventional polymer foam sandwich structure is similar for impacts ranging from 5 to 25 J. The polymer foam-based samples exhibit localized damage in the form of skin fracture and core crushing, but with negligible permanent out-of-plane deformation. In contrast, the aluminum foam-based samples show little fracture but exhibit extensive out-of-plane deformation radiating from the impact point. This deformation suggests that the impact damage could be more easily detectable in the aluminum foam sandwich structure. Surface strains are lower in the aluminum foam sandwich samples during post-impact loading in a single cantilever beam test, suggesting improved damage tolerance. [ABSTRACT FROM AUTHOR]