Sandwich Panel Theory Research Articles

High Order Impact Elastic Analysis of Circular Thick Cylindrical Sandwich Panels Subjected to Multi-mass Impacts

THIS STUDY DEALT WITH THE DYNAMIC MODEL OF COMPOSITE CYLINDRICAL SANDWICH PANELS WITH FLEXIBLE CORES AND SIMPLY SUPPORTED BOUNDARY CONDITIONS UNDER LOW VELOCITY IMPACTS OF MULTIPLE LARGE OR SMALL MASSES USING A NEW IMPROVED HIGHER ORDER SANDWICH PANEL THEORY (IHSAPT). IN-PLANE STRESSES WERE CONSIDERED FOR THE CORE AND FACE SHEETS. FORMULATION WAS BASED ON THE FIRST ORDER SHEAR DEFORMATION THEORY FOR THE COMPOSITE FACE SHEETS AND POLYNOMIAL DESCRIPTION OF THE DISPLACEMENT FIELDS IN THE CORE THAT WAS BASED ON THE SECOND FROSTIG'S MODEL. FULLY DYNAMIC EFFECTS OF THE SOFT CORE AND FACE-SHEETS WERE CONSIDERED IN THIS INVESTIGATION. IMPACTS WERE ASSUMED TO OCCUR SIMULTANEOUSLY AND NORMALLY OVER THE TOP FACE-SHEET WITH ARBITRARILY DIFFERENT MASSES AND INITIAL VELOCITIES. THE CONTACT FORCES BETWEEN THE PANEL AND IMPACTORS WERE TREATED AS THE INTERNAL FORCES OF THE SYSTEM. IN THIS PAPER, NONLINEAR CONTACT STIFFNESS WAS LINEARIZED WITH A NEWLY PRESENTED IMPROVED ANALYTICAL METHOD. NUMERICAL RESULTS OF THE MENTIONED STRUCTURES WERE COMPARED WITH FINITE ELEMENT MODEL USING ABAQUS CODE.

A parametric study on the stress analysis and transient response of thick-laminated-faced cylindrical sandwich panels with transversely flexible core

In the present work the effects of important parameters such as core thickness, radius of curvature and sector angle on the static and dynamic response of composite cylindrical sandwich panels have been investigated using a higher-order sandwich panel theory (HSAPT). The presented higher-order theory, which applies first-order shear deformation shell theory (FSDT) for the face sheets and the equivalent elasticity theory for the core, is a rigorous approach that includes the higher-order effects incurred by the nonlinearity of the in-plane and transverse displacements of core. Equations of motion along with associated boundary conditions are derived by using Hamilton's principle. For simply-supported panels closed-form solutions can be achieved by Navier techniques. However, for dynamic analysis, the solution is obtained in the time domain by implementing Newmark method. Finally numerical parametric studies are performed to provide some insight into the roles of key variables that influence the static and dynamic response of sandwich panels.

Extended high order sandwich panel theory for bending analysis of sandwich beams with carbon nanotube reinforced face sheets

Bending analysis of a sandwich beam with soft core and carbon nanotube reinforced composite (CNTRC) face sheets in the literature is presented based on Extended High order Sandwich Panel Theory (EHSAPT). Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded (FG). In this theory the face sheets follow the first order shear deformation theory (FSDT). 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 condition. The influences of boundary conditions on bending response of the sandwich panel with soft core and CNTRC face sheet are investigated. In each type of boundary condition the effect of distribution pattern of CNTRCs on many essential involved parameters of the sandwich beam with functionally graded carbon nanotube reinforced composite (FG- CNTRC) face sheets are studied in detail. Finally, experimental result have been compared with those obtained based on developed solution method. It is concluded that, the sandwich beam with X distribution figure of face sheets is the strongest with the smallest transverse displacement, and followed by the UD, O and ∧-ones, respectively.

An advanced high-order theory for bending analysis of moderately thick faced sandwich beams

Abstract An advanced high order sandwich panel theory (AHSAPT) for bending analysis of moderately thick faced sandwich beams with soft core is introduced. In this new theory, stress compatibility conditions at the interface are satisfied. The transverse shear stresses and the transverse normal stresses vanish on the top and bottom surfaces. Considering mentioned concepts improves high order sandwich panel theories for bending analysis of moderately thick faced sandwich panels. Comparison of transverse stresses at the top and bottom interfaces due to the AHSAPT and high order sandwich panel theories indicates that the discontinuity of the transverse stresses at the top and bottom interfaces are significant for the thickness ratio of the face sheet to the core more than 0.1. So, it is important to apply the presented theory for static analysis of moderately thick faced sandwich panels. The results of analytical solutions are compared with experimental data as well as the results of finite element simulation.

Bending behavior of sandwich structures with flexible functionally graded core based on high-order sandwich panel theory

In this study the problem of a sandwich beam with functionally graded (FG) core is attended with use of higher order sandwich panel theory forcing no pre-determined assumptions setting limits to the displacement and stress fields in the core. Face-sheets are analyzed using classical beam theory and the core is subjected to elasticity formulation. Governing equations and boundary conditions are derived using the principle of virtual displacements and governing equations based on five primary variables are solved using Navier’s solution. This method yields nonlinear patterns of displacements in the core and as a result it can manage to present localized effects of the core including the change in the core thickness under the load point which is an improvement on the previous classical and higher order theories. This present theory can handle any type of loadings distributed or concentrated and also any type of boundary conditions even when at the same edge, upper and lower face-sheets do not have the same boundary conditions. The solution is compared with present literature for a beam with conventional core. The results indicate positive effects of using FG core to reduce the possibility of delamination of the structure at interfaces between the upper and lower face-sheets and the core.

Free vibration analysis of soft-core sandwich beams by the novel weak form quadrature element method

The free vibration of soft-core sandwich beams is analyzed by using the weak form quadrature element method. An N-node novel weak form quadrature sandwich beam element is established based on the extended high-order sandwich panel theory and the differential quadrature rule. Gauss quadrature is used to obtain the element stiffness and consistent mass matrices numerically. Detailed formulations are given. Convergence study shows the fast rate of convergence. The validity and the capability of the novel beam element are examined through comparison with analytic results based on the same theory and two-dimensional finite element data. It is shown that one proposed beam element can yield very accurate frequencies with a relatively small number of nodal points. New data of soft-core sandwich beams with boundary conditions other than the simply supported one, not available in literature, are provided. These data may be referential with which other researchers can compare their results during developing new numerical methods.

Modal density of sandwich panels based on an improved ordinary sandwich panel theory

Modal density of sandwich panels with composite face sheets and orthotropic core is presented based on an improved ordinary sandwich panel theory. The governing equations are derived by applying the Hamilton’s principle, where in-plane rigidity of the core is considered and the material and reference axes are not limited to be identical to each other. Modal density is obtained using wavenumber space integration, and the effects of boundary conditions on both modal density and mode counts are also studied. The accuracy of the proposed models is validated by comparing with the existing modal density expressions, piecewise shear deformation theory and finite element models. Parametric studies are performed in order to investigate the influence of the ply angle of face sheets and the core, in-plane rigidity of the core, transverse shear rigidity and boundary conditions on modal density. The proposed modal density formula has a wider application scope and will be beneficial to the predication of sound transmission and radiation of sandwich panels.

Finite Element Formulation Based on the Extended High-Order Sandwich Panel Theory

The extended high-order sandwich panel theory was formulated in its one-dimensional version for orthotropic elastic sandwich beams. This theory includes the in-plane rigidity of the core, and the compressibility of the soft core in the transverse direction is also considered. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core, and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. The theory was derived so that all core/face displacement continuity conditions are fulfilled. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases of the other available sandwich computational models cannot correctly predict the stress fields involved. In this paper, a linear finite element is formulated based on the extended high-order sandwich panel theory. The element equations are outlined, and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. The comparison among these numerical results shows that, with a relatively small number of elements, the results are very close to the elasticity ones in terms of both the displacements and stress or strains. Thus, the finite element version of the extended high-order sandwich panel theory constitutes a very powerful analytical tool for sandwich panels.

Geometrically nonlinear creep behavior of debonded sandwich panels with a compliant core

The paper investigates the effects of creep of the core material on the geometrically nonlinear behavior of sandwich panels with debond at one of the core–face interfaces within the framework of the high-order sandwich panel theory (HSAPT). The theoretical model accounts for the viscoelasticity of the core via an incremental exponential law that corresponds to the rheological generalized Maxwell model obtained from the expansion of the relaxation moduli into Prony series. The HSAPT structural modeling accounts for the deformability of the core in shear and through its thickness, as well as for the large displacements of the facesheets. An incremental time-stepping analysis is conducted, which accounts for the time variations of the stresses, deformations, and the geometrically nonlinear effects. The incremental governing equations and the stresses and deformations fields through the thickness of the core are derived, and the capabilities of the model are studied numerically. The results show that creep of the core leads to significant variations in the deformations and stresses over time, which when combined with the geometrically nonlinear effects of the debonded facesheet, can have an important influence on the performance of sandwich panels under sustained loads. It is shown that stress relaxation due to creep and/or contact may restrain the buckling of the debonded facesheet in some cases.

Dynamic Response of Composite Sandwich Beams With Arbitrary Functionally Graded Cores Subjected to Low-Velocity Impact

Using an improved higher-order sandwich panel theory (IHSAPT), the dynamic response of a sandwich beam with arbitrary cores (foam or functionally graded materials) subjected to single impact at arbitrary impacted face sheet and arbitrary locations is studied. The formulation uses the first-order shear deformation theory for the composite face sheets and a polynomial description of the displacements fields in the core, which is based on the displacement field of the second Frostig's model. The unknowns are the coefficients of these polynomials in addition to the displacements of the various face sheets. It is assumed that the impactor impacted normally and simultaneously over the top or bottom face sheets. The impact force between the impacted face sheet and the impactor is treated as the internal force of the system and in this study, for the first time, in order to simulate the impact phenomena, two models are presented: first, the linearized spring–mass model with two degrees of freedom (simply called TDOF), which can be solved by a new analytical method; second, the modified Hertz's model, which uses the perfect form of contact law (perfect model). An impact problem of sandwich beam is first solved and the results obtained from TDOF and perfect models are validated by comparing them with the analytical and numerical results published in the literature and also together. The agreement between the results is quite good. Then, the effect of various types of FGM function and its power and core to beam thickness ratio on the dynamic behavior of sandwich beam are studied.

Blast Response of Sandwich Plates with a Compressible Core: Extended High-Order Approach

The transient blast response of a sandwich panel that consists of a compressible core with in-plane rigidity using the extended high-order sandwich panel theory is presented and compared with elasticity closed-form solutions. The mathematical formulation of the extended high-order sandwich panel theory for the transient dynamic response of sandwich plates is described along with a numerical investigation. The extended high-order sandwich panel theory formulation takes into account the shear resistance of the core and its compressibility, which is envisaged through nonidentical displacements of the upper and the lower facesheets and its in-plane rigidity. The equations of motion and the appropriate boundary conditions are derived using the Hamilton’s principle. A numerical investigation is conducted on a simply supported sandwich panel, and its results are compared with a benchmark elasticity closed-form solution. The results include deformed shapes at the first millisecond at various time steps; displacements of the various constituents, as well as various stress resultants in the facesheets; and stress distributions within the core and at its interfaces with the facesheets. The extended high-order sandwich panel theory and the elasticity benchmark results correlate very well. Finally, a summary is presented and conclusions are drawn.

Improved high order analysis of sandwich beams by considering a bilinear elasto-plastic behavior of core: An analytical and experimental investigation

Nonlinear material response of a sandwich beam with bilinear elasto-plastic constitutive relations for the transverse normal and shear stresses of the core is studied based on a proposed improved high order sandwich panel theory (IHSAPT). In this theory the face sheets follow the first order shear deformation theory (FSDT). Besides, the two dimensional elasticity is used for the core. In this work, the behavior of the faces follows the linear elastic assumption. The field equations are derived via the Ritz based solution which is suitable for any essential boundary condition. The influences of boundary conditions on bilinear material response of the sandwich panel are investigated. In each type of boundary condition the effects of plastic modulus of the core on transverse normal stress distribution within the core, transverse shear stress, and displacement components through the thickness of the core as well as the force and moment resultants and transverse displacements in the face sheets are studied in detail. Finally, some experiments have been carried out under conditions of three point bending on sandwich beams. Load–midspan displacement predicted by analytical model based on assumed bilinear material behavior of the core is in good agreement with that obtained by experimental result. Besides, for the case study of the three point bending, the results of the constitutive model are compared with finite element simulation.

Influence of thermomechanical interaction effects on the failure behaviour of polymer foam cored sandwich panels

The paper presents an experimentally based and numerically supported investigation of the collapse behaviour of polymer foam cored sandwich beams subjected to combined mechanical and thermal loading. Recent analytical and numerical modelling results available in the literature have ascertained that collapse may be due to loss of stability induced by nonlinear interactions between mechanical loads and thermally induced deformations, when accounting for the reduction of the polymer foam core mechanical properties with increasing temperature. In the paper, experiments are devised whereby a thermal gradient is introduced into a sandwich beam specimen loaded in three-point bending. The experiments cover a range of temperatures where one face sheet is heated from room temperature (25℃) to just below the glass transition temperature of the polymer foam core (70℃) and the other face sheet remains at room temperature. Digital image correlation (DIC) is used to obtain the local displacement field of the sandwich beam and its temperature is monitored using an infrared detector and thermocouples. The experimental results are compared with the predictions of both a generally nonlinear finite element model and an analytical so-called high-order sandwich panel theory (HSAPT) model. It is important to note that the HSAPT model has clear limitations as it takes into account only the geometric nonlinearity and thermal degradation of the foam core elastic properties, and it further assumes that the sandwich constituents are linear elastic with infinite straining capability. The HSAPT model predicts the occurrence of a strongly nonlinear load response leading to loss of stability (limit point behaviour). However, the experiments show that for the investigated sandwich beam configuration, it is necessary to include the nonlinear material properties in the modelling, as the nonlinear beam response leading to failure and collapse is significantly influenced by plastic deformations in the constituent materials. Thus, core indentation and extensive plasticity precede the transition to loss of stability driven by geometric nonlinearity and thermomechanical interaction effects. Finite element analyses that include both geometric and material nonlinearities provide results that correlate closely with the experimental observations. The work presented lays the foundation of a methodology for validating complex thermomechanical behaviour in sandwich structures using non-contact full-field measurement systems, and it demonstrates that analytical or numerical models based on the assumption of linear elastic material behaviour (such as the HSAPT model referenced in the paper) generally cannot adequately describe the thermomechanical behaviour of foam-cored sandwich structures.

Transient Blast Response of Sandwich Plates by Dynamic Elasticity

The three-dimensional linear dynamic elasticity problem formulation and solution for a generally asymmetric sandwich plate consisting of core and face sheets that are orthotropic, and subjected to blast loading, is presented. Laplace transforms are used to obtain ordinary differential equations in the complex Laplace space (with the variable being the through-thickness coordinate), which are subsequently solved in closed form for a simply supported plate, with the solution involving a cubic characteristic equation with complex coefficients. Subsequently, the time response is obtained by a numerical inverse Laplace transform by use of the Euler method. A realistic material and blast case is used to demonstrate the transient behavior for the displacements and face sheet/core interfacial transverse normal and shear stresses. The elasticity results are compared with the predictions of the first-order shear deformation plate theory as well as a high-order sandwich panel theory. This dynamic elasticity solution can serve as a benchmark in assessing the accuracy of sandwich-plate theories.

High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core

Free vibration analysis of functionally graded material sandwich plates is studied using a refined higher order sandwich panel theory. A new type of FGM sandwich plates, namely, both functionally graded face sheets and functionally graded flexible core are considered. The functionally graded material properties follow a power-law function. The first order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for the core. On the basis of continuities of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are obtained by using Hamilton’s principle. The accuracy of the present approach is validated by comparing the analytical results obtained for a degradation model (functionally graded face sheets and homogeneous flexible core) with ones published in the literatures, as well as the numerical results obtained by finite element method and good agreements are reached. Then, parametric study is conducted to investigate the effect of distribution of functionally graded material properties, thickness to side ratio on the vibration frequencies.

Improved extended high order analysis of sandwich beams with a bilinear core shear behavior

The response of a sandwich panel with bilinear constitutive behavior for shear stress of a core is presented based on a proposed improved extended high order sandwich panel theory. In this theory the face sheets are analyzed based on the first order shear deformation theory that is hitherto not applied in the conventional extended high order sandwich panel theory. Besides, the two-dimensional (2D) elasticity is used for the core. The field equations are derived using the Ritz-based solution which is suitable for any essential boundary condition. In each type of boundary conditions, the effects of plastic shear modulus of the core on transverse shear stress distribution within the core, transverse normal stresses at top and bottom face sheet–core interfaces, displacement components through the thickness of the core, as well as the force and moment resultants and transverse displacements in the face sheets are studied in detail. Also, all results based on the bilinear material assumption of the core are compared with the linear elastic ones. The results reveal that initial plastic regions are created at core edges. Furthermore, the absolute value of shear stresses in the plastic zones based on the bilinear analysis is lower than those obtained from linear elastic one for both types of the boundary conditions. It is seen that, unlike the case of the clamped edges, the plastic regions predicted by bilinear material behavior are much more extensive than ones resulted from elastic material behavior in the simply supported case. Finally, in the case of the linear elastic analysis, the results of the transverse deflections and shear stresses are compared with finite element simulation.

The buckling of truncated conical sandwich panels under axial compression and external pressure

Based on a new improved higher-order sandwich panel theory, the buckling analysis of a truncated conical composite sandwich panel with simply supported and fully clamped boundary conditions was performed for the first time. This panel was subjected to axial compression and external pressures. The governing equations were derived by using the principle of minimum potential energy. The first-order shear deformation theory was used for the composite face sheets, and for the core, a polynomial description of the displacement fields was assumed. Geometry was used for the consideration of different radii curvatures of the face sheets and the core was unique. The effects of types of boundary conditions, conical angles, length to smaller radius of core ratio, core to panel thickness ratio, and smaller radius of core to panel thickness ratio on the buckling response of truncated conical composite sandwich panels were also studied. The results were validated by the results published in the literature and the presented FE results were obtained by ABAQUS software.

Axial Loading Tests and Simplified Modeling of Sandwich Panels with GFRP Skins and Soft Core at Various Slenderness Ratios

AbstractExperimental and analytical studies were conducted to investigate the axial strength and failure modes of sandwich panels with glass fiber reinforced polymer (GFRP) skins and soft polyurethane core. A total of 45 specimens of 78×150 mm cross-section and of lengths Le varying from 500 to 2,400 mm [i.e., slenderness ratio (KLe∶r) of 15–70, where r is the radius of gyration] were tested concentrically using pin-ends (K=1). The effects of skin thickness and an internal GFRP rib on axial behavior were studied. The study first assessed the level of out-of-straightness and concluded that all specimens generally fall within an acceptable limit of span/1,000. A model based on sandwich panel theory, accounting for excessive shear deformations of the soft core, was used to predict axial strength at a wide range of KLe∶r and then used in a parametric study. It was shown that short panels with KLe∶r of 15–17 experienced local failure, outwards skin wrinkling in non-ribbed panels, or skin crushing in ribbed pa...

Geometrically nonlinear extended high order analysis for sandwich beams based on elastic–plastic core shear behavior

Geometrically nonlinear response of a sandwich panel based on elastic–linear plastic (bilinear) shear behavior of the core is presented. The extended high order sandwich panel theory (EHSAPT) is applied to obtain governing equations. The nonlinear Von Karman type relations for strains of face sheets and the core are adopted. The face sheets follow first order shear deformation theory along with the linear elastic assumption. A Ritz based solution which is suitable for any essential boundary condition is implemented. Two types of boundary conditions are considered simply supported and immovable clamped at both edges. In each type of boundary conditions, the effects of plastic shear modulus of bilinear material behavior on transverse shear stress distribution along with detection of the elastic and plastic regions within the core, force and moment resultants, transverse displacement distributions in the face sheets, in-plane and vertical displacements through the thickness of the core are studied in detail. Besides, all results based on the bilinear material assumption of the core are compared with the linear elastic ones. Finally, for the case study of the simply supported beam, the results of the constitutive model are compared with finite element simulation.

Static analysis of higher order sandwich beams by weak form quadrature element method

Based on the extended high order sandwich panel theory (EHSAPT) and differential quadrature rule, an N-node novel weak form quadrature sandwich beam element is established. Gauss Lobatto Legendre (GLL) points are utilized as element nodes and GLL quadrature is used to obtain the element stiffness matrix and work equivalent load. Detailed formulations are given. Convergence study is performed. Numerical results are presented for sandwich beams with different boundary conditions subjected to distributed loadings. Different materials for the face sheets and core of the beam structure are considered. It is shown that the proposed beam element can yield very accurate displacements and stresses as compared to theoretical solutions.