Bending Of Sandwich Beams Research Articles

Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov's foundation

The aim of this research is to analyze buckling and bending behavior of a sandwich Reddy beam with porous core and composite face sheets reinforced by boron nitride nanotubes (BNNTs) and shape memory alloy (SMA) wires resting on Vlasov\'s foundation. To this end, first, displacement field\'s equations are written based on the higher-order shear deformation theory (HSDT). And also, to model the SMA wire properties, constitutive equation of Brinson is used. Then, by utilizing the principle of minimum potential energy, the governing equations are derived and also, Navier\'s analytical solution is applied to solve the governing equations of the sandwich beam. The effect of some important parameters such as SMA temperature, the volume fraction of SMA, the coefficient of porosity, different patterns of BNNTs and porous distributions on the behavior of buckling and bending of the sandwich beam are investigated. The obtained results show that when SMA wires are in martensite phase, the maximum deflection of the sandwich beam decreases and the critical buckling load increases significantly. Furthermore, the porosity coefficient plays an important role in the maximum deflection and the critical buckling load. It is concluded that increasing porosity coefficient, regardless of porous distribution, leads to an increase in the critical buckling load and a decrease in the maximum deflection of the sandwich beam.

Finite element prediction of stress-strain fields on sandwich composites

The main objective of this study was the assessment of the stress-strain fields of the sandwich core during bending tests. Finite element models (FEM) using Siemens NX10 and digital image correlation (DIC) were used to predict the behavior of sandwich beams in 3 and 4 point bending. Two different core thickness and two different sandwich length (short and long beams) with basalt fiber reinforced polymer (BFRP) faces were simulated. The numerical simulation using 3D finite element were compared and validated with experimental results obtained previously by DIC. This work validated innovative numerical simulations and experimental techniques for determining stress-strain fields in composite sandwich beams subjected to bending. The correlation between experience and analysis allowed a better knowledge and understanding of the complex stress-strain fields along the core thickness of sandwich beams in bending.

Failure mechanism of PMI foam core sandwich beam in bending

Polymethacrylimide (PMI) foams have been widely applied in aerospace engineering as the core material of sandwich structures. This paper proposes a modified model to predict the constitutive relation of PMI foams and compares it to existing testing data. The study is then applied to the investigation of the failure mechanism of PMI foam core sandwich beams in bending. Corresponding bending tests were carried out where a complex failure process was observed through a high-speed camera. Numerical model of the foregoing sandwich beam is developed, in which the maximum principal stress criteria is used to predict damage propagation in PMI foam core. Both results from tests and numerical simulation validate the reliability of the theoretical prediction of the failure of PMI foam core sandwich beam using the proposed modified model of PMI foams. This study provides a theoretic tool for the design of sandwich structures with PMI foam core.

복소 전단탄성계수를 갖는 다층 감쇠보의 유한요소 진동 해석

In this paper, the general equation of motion of damped sandwich beam with multi-viscoelastic material layer was derived based on the equation presented by Mead and Markus. The viscoelastic layer, which has characteristics of complex shear modulus, was assumed to be dominantly under shear deformation. The equation of motion of n-layered damped sandwich beam in bending could be represented by (n+3)th order ordinary differential equation. Finite element model for the n-layered damped sandwich beam was formulated and programmed using higher order shape functions. Several numerical examples were implemented to show the effects of damped material.

A comparison of three population-based optimization techniques for the design of composite sandwich materials

Three population-based optimization techniques — particle swarm optimization, ant colony optimization, and simulated annealing — are applied to the multi-objective design of sandwich materials. The formulation of the algorithms is described, along with metrics for quantifying their performance. For the case study considered of a sandwich beam in bending, it is shown that the ant colony technique out-performs the other two algorithms with respect to identifying optimal geometries, materials, and lay-ups for a stiff sandwich in which low mass and low cost are the design objectives. The particle swarm and simulated annealing algorithms were found to have particular difficulties in handling the optimization of multi-ply oriented fiber-reinforced polymer facing laminates.

Quasi-Static and Low-Velocity Impact Response of Fully Backed or Simply Supported Sandwich Beams

The present paper describes analysis of low-velocity transverse impact on sandwich beam, with composite faces from Eglass/epoxy and cores from Polyurethane or PVC. Boundary conditions are fully backed rigid or simply supported. This research is based on a step by step study to generate more reliable impact results. Indentation of laminated beam, indentation of sandwich beams, and three-point loading have been analyzed with existing theories and modeled with the FE code ABAQUS, also their results are compared with experimental results. In quasi-static three-point bending, energy is consumed through three mechanisms: indentation of laminated beam, indentation of sandwich beam, and bending of sandwich beam. Impact on fully backed specimen is modeled in two cases of impactor energies using mass spring model of SDOF (single-degree-of-freedom) and indentation stiffness, lower energy of impactor for elastic indentation of sandwich beams, and higher energy for indentation in plastic area. TDOF (two-degree-of-freedom) with flexural and contact stiffnesses are used for impact on simply supported beams. Impacts are simulated by ABAQUS, as well. Results can describe response of beam and impactor displacements in terms of core and faces thicknesses, core material, and impactor energies for static and impact results. The experimental results are in good agreement with the analytical and FE analyses.

Planar Bending of Sandwich Beams with Transverse Loads off the Centroidal Axis

Conventional analysis methods for beams do not distinguish between transverse loads that are applied at the beam centroidal axis and those acting either above or below the centroidal axis. In contrast, this paper formulates a sandwich beam finite element solution which models the effect of load height relative to the centroidal axis. Towards this goal, the governing equilibrium equations and associated boundary conditions are derived based on a Timoshenko beam formulation for the core material. Special shape functions satisfying the homogeneous form of the equilibrium equations are derived and subsequently used to formulate exact stiffness matrices. By omitting the stiffness terms related to the faces, the formulation for a homogeneous Timoshenko beam can be recovered. Also, the Euler-Bernoulli counterpart of the formulation is recovered as a limiting case of the current Timoshenko beam formulation. Effects of load height relative to the centroid are observed to have similarities with those induced by axial forces in beam-columns. For a simply supported beam, downward acting loads located below the centroidal axis are found to induce a stiffening effect while those acting above the centroidal axis are found to induce a softening effect, resulting in higher transverse displacements.

Equivalence of the Analyses of Sandwich Beams with or without Interlayer Slip

ABSTRACT Dynamic plane bending of sandwich beams composed of three symmetrically arranged layers is studied. Analyzing two special cases of interlaminar connections, namely, “perfect bond” and “elastic interlayer slip,” a complete analogy between the corresponding initial-boundary-value problems is derived. Hence, the response of the beam with elastic interlayer slip can be determined directly from the solution of the perfectly bonded sandwich beam with moderately thick faces.

Holographic interferometry assessment of stress distribution in sandwich beams in bending

Abstract It is well known that there is a lack of experimental results on the thickness distributions of the displacements, strains and stresses in sandwich beams in bending. The present work aims to fill partially this lacuna through an experimental investigation. Use is made of a technique based on holographic interferometry. Some experimental results quantifying the thickness distributions of the displacements are presented and the limitations of the adopted technique are discussed. The investigation also highlights some interesting effect of the core deformability, which are essential in understanding the failure phenomena of sandwich structures subjected to concentrated loads.

Theoretical and experimental investigation of bending of sandwich beams

We present the results of theoretical and experimental investigation of problems on bending of composite inhomogeneous sandwich beams. The theoretical results obtained by using the basic equations of the stress-strain state deduced within the framework of classical and refined nonclassical theories of bending of composite beams were compared with the experimental data. The nonclassical theory is based on a hypothesis taking into account the effect of deplanation of cross sections of the beam caused by transversal shear deformations. As experimental data, we use the results of experimental investigation of the process of bending of sandwich beams.

Stresses and failure patterns in the bending of sandwich beams with transversely flexible cores and laminated composite skins

The stresses and failure maps in a sandwich beam that consists of a transversely flexible compressible core between two laminated composite skins, are presented. The stresses and the failure maps are determined using a general, systematic rigorous, and high-order analysis that is based on variational principles, and includes the flexibility effects of the core on the global and local bending behavior of the beam. The analysis uses closed form solutions for any type of skin construction, symmetric or unsymmetric laminated composite layups, any type of core, compressible or incompressible, any type of loading, concentrated or distributed, and any types of boundary and continuity conditions that may differ from one skin to the other, even in the same section. Failure patterns are determined with the aid of the analytical description of the longitudinal stresses in the skins and the principal stresses through the thickness of the core. The stresses in the core and the skins, along with an appropriate failure criteria, for a specified three point bending beam, are demonstrated in the form of principal stresses, failure and failure load maps, that indicate possible failure patterns and locations.

Bending of curved sandwich beams, a numerical approach

Curved sandwich beams in bending are analysed with the finite element method (FEM) and compared to simple analytical formulae and solutions to Airy's stress function. It is shown that the curvature can have a significant influence on the circumferential stresses in the faces and the radial stress in the core. It is also shown that there is very good correspondence between the exact elasticity solution and numerical results far away from stress concentrations. In design and sizing of curved sandwich members the results show that special considerations have to be taken to the stress concentrations that are present at the interface between the straight and curved parts of sandwich beams with both straight and curved segments. The use of layered sandwich shell elements and layered brick elements on curved sandwich beams in bending is investigated. The results with the layered elements show that poor correlation in stress levels to the analytical results can be expected for low to medium radius of curvature to sandwich thickness ratios.

Bending of curved sandwich beams

Curved sandwich beams in bending are analyzed with analytical elasticity methods and compared to simple analytical formulae and FEM calculations. Solutions to Airy's stress function in polar co-ordinates are used to obtain the stress distributions in the radial and circumferential directions. Plane stress and plane strain solutions are given with isotropic and orthotropic material models. It is shown that the properties of the core can have a significant influence on the circumferential stresses of the faces, but that the radial stress of the core is nearly constant with varying core properties. The radius of curvature can have a large influence on the circumferential stresses of the faces when the radius of curvature to sandwich thickness ratio is small to moderate. It is shown that simple analytical methods can be utilised to calculate the radial stresses in the core and the circumferential stresses of the faces for beams with large to moderate radii of curvature and thin to moderately thick faces.

High‐Order Bending of Sandwich Beams with Transversely Flexible Core and Nonparallel Skins

The bending behavior of a general tapered sandwich beam with a flexible core in the vertical direction and a piecewise uniform sandwich beam with tapered transition zones between the uniform regions is analytically investigated. The structure is modeled as a combination of a core that is assumed to be a two- dimensional elastic medium, in the longitudinal and transverse directions, and skins considered as one-dimensional inclined beams. Thus the effects of the flexibility of the core in the vertical direction and that of the vertical component of the longitudinal and the shear forces in the inclined skins on the local and the overall behavior are considered. The field equations and the boundary and the continuity conditions are rigorously derived using variational principles. The proposed analysis accounts for higher-order effects due to the flexibility of the core in the form of nonlinear displacements fields through its height that comprises a parabolic distri- bution of the vertical deformation, which changes the distance between the skins, as well as the height of the core and a cubic variation of the longitudinal displace- ment. These high-order effects are especially pronounced in the vicinity of con- centrated or localized distributed loads or supports as well as at the ends of tapered transition zones and are usually associated with stress concentration in the form of high peeling and shear stresses at the skin-core interfaces and high bending stresses in the skins. These effects also exist at the ends of taper transition zones of a piecewise uniform beam due to the concentrated resultant of the shear and lon- gitudinal internal forces of the skins even in the case of a distributed load. The characteristic behavior of a tapered sandwich beam and a piecewise uniform beam with a tapered transition region are studied in terms of deflections, shear forces and bending moments in the skins, normal transverse and shear stresses in the core, and shear and peeling stresses at the interfaces between the core and the skins. Numerical results of stress concentration effects for some typical cases are presented and discussed.

On stress concentration in the bending of sandwich beams with transversely flexible core

Stress concentrations in sandwich beams with a ‘soft’ core subjected to bending loading are investigated and the level of stresses is analytically determined. The cases discussed include stress concentration effects (i) in the vicinity of concentrated loads and supporting zones; (ii) at the edges of debonding regions-edge and inner delamination types at the interface layer between the skins and the core; and in the vicinity of vertical cut-off connections; and (iii) at the location of diaphragms that are bonded and unbonded with the adjacent core and embedded in it. The results are determined with the aid of a variational rigorous, analytical, systematic elastic high-order theory that uses closed form solutions. This theory is applicable to any type of sandwich construction with and without discrete diaphragms (i) to any type of loading, concentrated or distributed; and (ii) to any type of boundary conditions including cases in which at the same section the conditions at the upper skin are different from those at the lower skin. The stress concentration effects are presented in terms of deflections, internal forces and normal stresses (peeling) in the interface layers between the skin and the core. A parametric study is conducted and investigates the level of stresses as a result of (i) the vertical modulus of elasticity of the core; (ii) the delamination length; (iii) the reinforcing diaphragm in a typical connection; and (iv) the presence of diaphragms, either bonded or unbonded with the adjacent core, at specific locations.

Strength and stiffness of sandwich beams in bending

This investigation is concerned with the experimental versus analytical correlation of the mechanical properties of sandwich-beam specimens. Such sandwich structures are commonly employed in the aircraft industry. Four-point and three-point load tests were conducted on a large number of sandwich-beam specimens, fabricated by using fiber-glass reinforced plastics (both unidirectional and woven-glass cloth) and DTD 685 aluminum alloy for the facings with aluminum honeycomb core and polyurethane foam cores and the indigenously available Araldite as the bonding medium between the core and the facings.

Bending of sandwich beams with transversely flexible core

The bending behavior of a sandwich beam with a foam core is analytically investigated. The beam consists of upper and lower skins, metallic or composite laminated, and a soft core. The loading pattern consists of concentrated as well as distributed loads exerted at the upper or the lower skin or a combination of the two. The analysis includes the effects of the flexibility of the core in the vertical direction on the overall bending behavior. The main parameters affecting the overall behavior and particularly the peeling and the shear stresses between the skins and the core are studied. ANDWICH beams have been used in various industries for many years. A typical beam consists of two skins made of metal or laminated composite and a core. The core is usually made of honeycomb, metallic or nonmetallic, which is stiff in the vertical direction and flexible in the horizontal one. In recent years, plastic foams are used for cores in sandwich structures. In this case, the effect of the transverse flexibility of the core on the mechanical behavior of the beam should be taken into account. This flexibility affects the transverse bend- ing behavior of the beam and leads to unequal deflections of the upper and lower symmetrical skins (see Fig. 1). Sandwich beams with honeycomb cores were considered by many researchers. Reissner1'2 included the shear strain effect on the bending, but only the average bending behavior of the composite beam is considered. Many researchers3'5 dealt with the analysis of beams with an antiplane core, i.e., a core with shear rigidity only. The Hexcel designer manual6 outlines the design procedures for beams with honeycomb cores only. An antiplane-cor e approach with anisotropic and composite skin appears in Refs. 7-9. Ojalvo10 assumed different deflec- tions to the two skins, but neglected the peeling stresses. Ogorkiewicz and Sayigh11 dealt with a foam core by replacing it with an ordinary beam with equivalent properties. In this paper, the proposed analysis includes the effects of the transverse flexibility of the core and the peeling stresses between the skin face and the core on the overall bending behavior. The analysis is general and applicable to metallic or com- posite laminated identical skins. The behavior is described in terms of the deflections, the peeling, and the shear stresses in the adhesive layers. The effect of the variables that govern the behavior is incorporated through a parametric study. The mathematical formulation and the boundary conditions are discussed. The analytical solution for the various types of loading with different boundary conditions is presented.

Interlaminar shear test by hybrid sandwich specimen under distributed load

AbstractA new method is proposed for the determination of the interlaminar shear strength of composites. The method is particularly pertinent to composites of high interlaminar shear strengths, where the ratio of tensile (compressive) strength to shear strength is relatively low. In such materials, including unidirectional composites with improved fiber/matrix bond strength and angle‐ply laminates, an analysis based on a short beam interlaminar shear test is highly problematic and may, in fact, be erroneous. The test method is based on the use of a sandwich composite structure with a core made of layers of the tested composite and skins made of an elastic, strong unidirectional composite. A proper design procedure determines the choice of the skin material and of the relative thicknesses, so that flexural testing under distributed load leads to the intended core failure in shear. Calculations of the stress profile in a hybrid sandwich beam in bending and of the stress ratios under distributed load are presented. Also presented are experimental results recorded with sandwich hybrids made of unidirectional carbon‐fiber‐reinforced epoxy skins and a ±θ aramid‐fiber‐reinforced epoxy angle‐ply core.

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