Curved Sandwich Panels Research Articles

Closed-form elasticity solution for smart curved sandwich panels with soft core

Due to the rapid development of intelligent engineering structure, the demand for high performance smart structures has been increased in recent years. In this paper, an exact elasticity solution for bending analysis of sandwich panel with generally orthotropic facings and core is developed. Two electro-orthotropic piezoelectric layers in the top and bottom surfaces of sandwich panel as sensor and actuator are considered. From practical point of view, an initially curved sectorial geometry is considered for smart sandwich panel. In this regard, the constitutive relations and governing equations are considered in polar coordinate and coupled Euler–Cauchy Equations are derived. The characteristic equations are determined and closed-form basis functions of displacements and stresses are achieved for various material and geometrical conditions. Furthermore, based on classical and first-order shell theories, the governing equations of smart curved sandwich panels are derived. The governing equations are solved analytically and compared with exact elasticity solution. Several parametric studies are performed on both material and geometrical properties such as angular span, facing and core thickness, and external electrical voltage.

Thermal vibration analysis of SMA hybrid composite double curved sandwich panels

This work analyses the thermal vibration of a double curved sandwich panel (DCSP) with embedded pre-strained shape memory alloy (SMA) wires hybrid composite face sheets and soft core. The von Karman nonlinear displacement–strain relationships are here applied to handle large deflections due to a thermal loading. The equations of motion are derived by applying the Hamilton’s principle and the first order shear deformation theory (FSDT) for the composite face sheets and core layer. This last one features the displacement field of the Frostig's second model here, used to model the DCSP. The material properties of the DCSP are assumed to be both temperature-dependent (TD) and/or temperature-independent (TI). The effect of the SMA wires is captured by adding a stress recovery within the formulation. This term is determined by using a one-dimensional Brinson’s model in the constitutive equations of the SMA composite face sheets during the phase transformation of the pre-strained SMA wires. It is verified that SMAs can play a key role within DCSPs subjected to a thermal loading condition, whereby the proposed formulation is validated comparatively against the available literature. We also explore the sensitivity of the vibration response for a varying SMA activation temperature, volume fraction, and pre-strain, as well as for different curvature ratios, thickness ratios and different sequences in composite layers.

Forming characteristics analysis and springback prediction of bi-directional trapezoidal sandwich panels in the multi-point bend-forming

Bend-forming is an efficient and economical method to manufacture curved sandwich panels, and the major concerns for fabricating precise products are forming characteristics and springback prediction. In this paper, numerical simulation, analytical approach, and forming experiments were conducted to assess the multi-point cylindrical bend-forming process of bi-directional trapezoidal sandwich panel. Analysis was performed on the deformation characteristics, regularity, and forming defects of sandwich panel in the early stage. And afterwards, equivalent elastic constants of the core layer were deduced by the semi-analytic approach combined with finite element method (FEM). On this basis, a theoretical model was established to calculate bending moments and predict springback within formable range. The results indicate that the stress of face sheet in the welded area was obviously lower than that in the suspended area. The core cell was primarily deformed by changing the angle between the inclined plane and the platform, and the deformation of the cell layer mainly occurred in the transition surface area. The dimple and straight plane effect are the most common forming defects during the bending process. The main factors that affect the forming defects are face sheet thickness and bending radius. The springback amount of the sandwich panel approximates the equivalent thickness plate. Thus, it is easy to control the forming precision for small springback, and the springback ratio increases with the increase of bending curvature radius. The springback in theoretical model and experiment has an error of less than 1.0 mm, verifying the accuracy of the theoretical prediction model.

Preliminary studies for alternative lattice core design for FDM 3D Printed Sandwich Panels

Lattice structures with different types of open cell topologies are attracting interest as millimeter cell sized lightweight core structures for sandwich panel constructions. Lattices appear to be an alternative improvement to honeycomb structures with flexible and amenable to the creation of single or compound curved sandwich panels. Currently, lattice structures design is limited to folding fabrication. Hence, Fused Deposition Modeling (FDM) 3D printing technologies allow more complex and advanced lattices design. The purpose of this research is to design and compare the capacity of different lattice structures. Z-ULTRAT material was used to simulate the 3D printed materials. All designs will undergo buckling test to simulate the real-world applications of sandwich core panels.

First-Order Shear Deformation Theory Variants for Curved Sandwich Panels

Due to the curvature, the first-order shear deformation theory for curved sandwich panels is not a direct extension of the corresponding one for flat panels; thus, it is formulated accordingly, and its unique features, such as the reference curve, are discussed. Three versions of the first-order shear deformation theory are formulated: the one based on a direct variational formulation based on the assumed through-thickness displacement field (termed “basic”); one based on the definition of an equivalent shear modulus for the section (termed “”); and one based on derivation of a shear correction factor, which is considered in conjunction with the equivalent shear modulus. A comparison of the results between a previously formulated benchmark elasticity solution and the three variants of the first-order shear deformation theory is presented. In addition, the results are compared with the classical theory for curved sandwich panels, which does not include transverse shear. The shear correction factor formula derived for sandwich curved panels is proven to converge to the homogeneous flat-plate value of in the limit.

Experimental and numerical analysis of vibration frequency in sandwich composites with different radii of curvature

In this study, free vibration responses of sandwich composite panels with different radius of curvature were presented numerically. The studies were carried out on square flat and curved sandwich panels made of E-glass/epoxy face sheets and polyvinyl chloride foam with three different radii of curvature. Experimental studies were used to verify the numerical results. Vibration tests were performed on flat and curved sandwich panels under free–free boundary conditions. The experimental data were then compared with finite element simulation, which was conducted by ANSYS finite element software and it was shown that the numerical analysis results agree well with the experimental ones. Effect of the curvature on natural frequencies under different boundary conditions (all edge free, simply supported, and fully clamped) was investigated numerically. Results indicated that the natural frequencies and corresponding mode shapes were affected by boundary conditions and curvature of the panel. For all boundary conditions, the variation of curvature had smaller effect on the natural frequency of the first mode than those of the other modes.

Extended High-Order Theory for Curved Sandwich Panels and Comparison With Elasticity

A new one-dimensional high-order sandwich panel theory for curved panels is presented and compared with the theory of elasticity. The theory accounts for the sandwich core compressibility in the radial direction as well as the core circumferential rigidity. Two distinct core displacement fields are proposed and investigated. One is a logarithmic (it includes terms that are linear, inverse, and logarithmic functions of the radial coordinate). The other is a polynomial (it consists of second and third-order polynomials of the radial coordinate), and it is an extension of the corresponding field for the flat panel. In both formulations, the two thin curved face sheets are assumed to be perfectly bonded to the core and follow the classical Euler–Bernoulli beam assumptions. The relative merits of these two approaches are assessed by comparing the results to an elasticity solution. The case examined is a simply supported curved sandwich panel subjected to a distributed transverse load, for which a closed-form elasticity solution can be formulated. It is shown that the logarithmic formulation is more accurate than the polynomial especially for the stiffer cores and for curved panels of smaller radius.

General equations for free vibrations of thick doubly curved sandwich panels with compressible and incompressible core using higher order shear deformation theory

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element (1 ± z/R) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

Higher order flutter analysis of doubly curved sandwich panels with variable thickness under aerothermoelastic loading

In this study, the supersonic panel flutter of doubly curved composite sandwich panels with variable thickness is considered under aerothermoelastic loading. Considering different radii of curvatures of the face sheets in this paper, the thickness of the core is a function of plane coordinates (x,y), which is unique. For the first time in the current model, the continuity conditions of the transverse shear stress, transverse normal stress and transverse normal stress gradient at the layer interfaces, as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the sandwich panel are satisfied. The formulation is based on an enhanced higher order sandwich panel theory and the vertical displacement component of the face sheets is assumed as a quadratic one, while a cubic pattern is used for the in-plane displacement components of the face sheets and the all displacement components of the core. The formulation is based on the von Karman nonlinear approximation, the one-dimensional Fourier equation of the heat conduction along the thickness direction, and the first-order piston theory. The equations of motion and boundary conditions are derived using the Hamilton principle and the results are validated by the latest results published in the literature.

Curved sandwich composites with layer-wise graded cores under impact loads

Sandwich composites with single type foam are very much prevalent in the applications to absorb energy under impact load. However, there is increasing awareness that graded cores in sandwich composites can significantly affect the impact performance. In this work, the perforation energy and failure modes of curved sandwich composites with layer wise graded cores are studied experimentally. Three types of foam were used for flat and curved sandwich composites with layered cores. A series of six different core layer arrangements were studied. The contact forces, displacements and corresponding perforation energies of square panels were measured and failure modes after perforation were observed. The results indicate that the perforation energies of the sandwich panels are dependent on various geometrical and material parameters. The perforation energies of the curved panels with single type foam were increased compared to similar flat panels, whereas panels with graded foam behaved differently due to the foam layer arrangements. Furthermore, it was observed that the failure modes were not similar when the panels were perforated. Contribution of present study to current literature is the use of different core layer arrangements to increase the impact performance of curved sandwich panels which are inevitable parts of various applications.

The effect of curvature on the impact response of foam-based sandwich composite panels

The aim of this study is to investigate the impact behavior and impact-induced damage of sandwich composites made of E-glass/epoxy face sheets and PVC foam. The studies were carried out on square flat and curved sandwich panels with two different radius of curvatures. Impact tests were performed under impact energies of 10 J, 25 J and 80 J using an instrumented drop-weight machine. Contact force and displacement versus time and contact force- displacement graphs of sandwich panels were presented to determine the panel response. Through these graphs, the energy absorbing capacity of the sandwich panels was determined. The impact responses and failure modes of flat and curved sandwich panels were compared and the effect of curvature on sandwich composite panel was demonstrated. Testing has shown that the maximum contact force decrease while displacement increases with increasing of panel curvature and curved panels exhibits mixed failure mode, with cylindrical and cone cracking.

Non-linear response of curved sandwich panels – extended high-order approach

The geometrical non-linear behavior a curved sandwich panel with a stiff or compliant core when subjected to a pressure load using the Extended High-Order Sandwich Panel theory (EHSAPT), is presented. The formulation follows the EHSAPT procedure where the in-plane. i.e circumferential rigidity of the core is considered and the distribution of the displacements through the depth of the core are presumed. These displacement distributions are the closed-form solutions of the 2D governing equations of the curved core without circumferential rigidity that appear in the HSAPT curved sandwich panel model. The mathematical formulation includes the field equations along with the appropriate boundary and continuity conditions that take into account the high-order stress resultants in the core due to the presumed distributions. Finally a numerical study is conducted for a panel loaded by a distributed pressure at the upper face sheet. It reveals that the post-buckling response of a curved sandwich panels is associated with shallow to deep wrinkling deformations of the upper face sheet in the case of a simply-supported panel or a general non-linear pattern without wrinkles in the case of pinned supports with a short span. In both cases a stable post-buckling response is observed similar to that of a plate one.

Load and frequency interaction effects in dynamic buckling of soft core sandwich structures

The present study is concerned with an analysis of load and frequency interaction effects in the dynamic buckling of sandwich plates and shells with a soft, transversely flexible core. The analysis is based of a general geometrically nonlinear soft-core sandwich model presented and a corresponding extended Galerkin solution strategy presented earlier. In the present study, the formalism is adopted and transformed into an eigenvalue problem. Assuming large transverse average displacements but small amplitudes for the vibration problem, a partially decoupled problem is obtained where in a first step the static buckling and face wrinkling problems can be addressed without consideration of the dynamic problem. In a second step, the dynamic eigenvalue problem can be solved, using the static solution as input parameters. The model is applied in parametric studies on the vibration response of plane and doubly curved sandwich panels with rectangular projection. In all cases, strong interaction effects between the external static preload and the natural frequencies are observed. The development of overall buckling or local face wrinkling instabilities enabled due to the transverse flexibility of the core result in distinct drops of the first natural frequency.

Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory

In this paper, the supersonic flutter characteristics of doubly curved sandwich shell panels, viz., cylindrical and spherical shells, with carbon nanotube (CNT) reinforced facesheets are investigated using QUAD-8 shear flexible shell element developed based on higher-order structural theory. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacement at the interface. The strain–displacement relation is accurately introduced in the formulation. The first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The solutions of the complex eigenvalue problem, developed based on Lagrange’s equation of motion, are obtained by QR algorithm. The accuracy of the present formulation is validated considering the problems for which solutions are available in the literature. A detailed numerical study is conducted to highlight the significance of the higher-order model over the first-order theory and also to examine the influence of the volume fraction of the CNT, core-to-face sheet thickness, the shell thickness and the aspect ratio, radius-to-thickness ratio, and temperature on the flutter boundaries.

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.

Dynamic response and optimal design of curved metallic sandwich panels under blast loading.

It is important to understand the effect of curvature on the blast response of curved structures so as to seek the optimal configurations of such structures with improved blast resistance. In this study, the dynamic response and protective performance of a type of curved metallic sandwich panel subjected to air blast loading were examined using LS-DYNA. The numerical methods were validated using experimental data in the literature. The curved panel consisted of an aluminum alloy outer face and a rolled homogeneous armour (RHA) steel inner face in addition to a closed-cell aluminum foam core. The results showed that the configuration of a “soft” outer face and a “hard” inner face worked well for the curved sandwich panel against air blast loading in terms of maximum deflection (MaxD) and energy absorption. The panel curvature was found to have a monotonic effect on the specific energy absorption (SEA) and a nonmonotonic effect on the MaxD of the panel. Based on artificial neural network (ANN) metamodels, multiobjective optimization designs of the panel were carried out. The optimization results revealed the trade-off relationships between the blast-resistant and the lightweight objectives and showed the great use of Pareto front in such design circumstances.

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.

Local facesheet pulse buckling in a curved, composite sandwich panel

Local facesheet buckling of a curved sandwich panel subjected to external pressure pulse loading was investigated in this paper. Equations of motion for the facesheet transient deformations in the sandwich shell were derived from Lagrange’s equations of motion, and solutions using this approach compared well with FEA results from ABAQUS Standard. Both facesheet fracture during stable deformation response and local dynamic pulse buckling of facesheets were considered as possible modes of failure in the curved sandwich panel. Parametric studies indicated that local facesheets buckling is more likely to occur than facesheet fracture in thin and deep curved sandwich panels. The facesheet laminate layup can also be adjusted to improve the local buckling resistance of the curve panel.

Foam-core, curved composite sandwich panels under blast

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.

Experimental investigation into the thermoelastic spring-in of curved sandwich panels

An investigation into the thermoelastic spring-in of curved sandwich panels has been conducted. Sandwich panels incorporating solid foam cores and biaxial glass–epoxy skins were manufactured and spring-in measured. The major contributors to spring-in were found to be the thermal expansion and Poisson’s ratio of the foam which were subsequently characterised. Also important was the development of resin rich regions on the surface of the panel. Experimental findings were implemented into a finite element (FE) model developed using 3-dimensional elements in ANSYS. The investigation was extended to panels including a core with machined slots. A refined FE model highlighted the influence of in-plane restraint reduction within the core, as well as the effect of a much thicker resin rich region caused by core segmentation. Results showed good agreement with experiment and provided a good basis for shape prediction of sandwich panels.