High-order Sandwich Beam Theory Research Articles

Bending analysis of simply-supported sandwich beam using Chebyshev quadrature element method

Based on the higher-order sandwich beam theory, the Chebyshev quadrature sandwich beam element is established for the bending analysis of the simply-supported sandwich beam. Gauss Lobatto sampling is adopted as element nodes. The discrete governing equation of the sandwich beam is obtained by the principle of minimum potential energy. A series of numerical examples are carried out on simply-supported sandwich beams under sinusoidal loading. The results are compared with the finite element method, showing that the proposed method can yield very accurate displacements and stresses. This method is suitable for the static analysis of simply-supported sandwich beams with different materials and different geometric parameters.

Static analysis of defective sandwich beam by Chebyshev quadrature element method

This paper proposes a quadrature element method based on Chebyshev polynomials for the static analysis of the defective sandwich beam with general boundary conditions. Gauss-Lobatto nodes are utilized. The discrete governing equation is obtained by the high-order sandwich beam theory and the principle of minimum potential energy. A series of numerical examples of the defective sandwich beam with different boundary conditions, geometric parameters, and material properties subjected to various loadings are carried out. The results are compared with the existing methods and the finite element method to verify the proposed method, demonstrating that the present approach can converge exponentially and yield very accurate displacements and stresses. The influence of the defect on the stiffness of the sandwich beam is analyzed. The current method can provide a theoretical basis for the design of the multifunctional beam structure.

Measurement of adhesive shear properties by short beam shear test based on higher order beam theory

This paper refers to the measurement of the shear properties of adhesive bonding by a new beam theory using the short beam shear (SBS) test configuration. A novel higher-order sandwich beam theory has been developed to analyze the adhesive bonded beam that consists of two adhered laminates and a single layer of adhesive in between. The closed form analytical solution for the SBS test model of the adhesively bonded beam is obtained in terms of deflection and stress distribution. The present theory has been used for calculating the adhesive shear modulus from the structural compliance. The initiation of stiffness degradation for the short beam shear test model was used as the critical load value for deriving the adhesive shear strength. A finite element model is built for validating the present model, and to evaluate its suitability for measuring adhesive shear properties. The present theory shows better accuracy for measuring the shear modulus than existing theories for both thin and thick adhesive layers. The measured strength values are more accurate than those obtained from the single lap joint shear test model. This theory can be used for adhesive materials with linear elastic deformation behavior.

Effect of geometrical and mechanical properties on behaviour of sandwich beams with functionally graded face sheets under indentation loading

Improved high-order sandwich beam theory is used to model the local deformation ofsandwich beams with aluminium/alumina functionally graded (FG) face sheets loaded by central indentor. First-order shear deformation theory is used for the FG face sheets while three-dimensional elasticity is used for the flexible core. Using the model to consider the way in which different wavelengths of sinusoidal pressure loading on the upper FG face sheet are transmitted to the core and lower FG face sheet, two spreading length scales λt and λb are introduced and calculated; λt and λb, which are two functions of the beam material and geometrical properties, characterize the length over which a load on the upper surface of a beam is spread out by the face sheets and the core. Comparison of the semi-wavelength of the sinusoidal pressure loading ( L/m) on the upper FG face sheet with length scales λt and λb illustrate the importance of these length scales in describing whether the face sheets act in a rigid or a flexible manner. When the semi-wavelength ( L/m) of the applied load in the present example is higher than λt (or λb), 10–90 per cent (or 5–70 per cent) of the contact load is transmitted locally to the core (or from the core to the lower FG face sheet) for the geometries and materials analysed. Conversely, when L/m is lower than λt (or λ1b), the contact load from the upper FG face sheet with a maximum of 58 per cent (or 70 per cent) is spread out over a wider area of the core (or from the core is spread out over a wider area of the lower FG face sheet). Reasonable agreement is found between the theoretical predictions in this study and finite element method results by ANSYS and the results published in literature for special cases.

Dynamic Instability of MRE Embedded Soft Cored Sandwich Beam with Non-Conductive Skins

In this work the governing temporal equations of motions with complex coefficients have been derived for a three-layered unsymmetric sandwich beam with nonconductive skins and magnetorheological elastomer (MRE) embedded soft-viscoelastic core subjected to periodic axial loads using higher order sandwich beam theory, extended Hamilton's principle, and generalized Galerkin's method. The parametric instability regions for principal parametric and combination parametric resonances for first three modes have been determined for various end conditions with different shear modulus, core loss factors, number of MRE patches and different skin thickness. This work will find application in the design and application of sandwich structures for active and passive vibration control using soft core and MRE patches.

Dynamic Instability of MRE Embedded Soft Cored Sandwich Beam with Non-Conductive Skins

In this work the governing temporal equations of motions with complex coefficients have been derived for a three-layered unsymmetric sandwich beam with nonconductive skins and magnetorheological elastomer (MRE) embedded soft-viscoelastic core subjected to periodic axial loads using higher order sandwich beam theory, extended Hamilton's principle, and generalized Galerkin's method. The parametric instability regions for principal parametric and combination parametric resonances for first three modes have been determined for various end conditions with different shear modulus, core loss factors, number of MRE patches and different skin thickness. This work will find application in the design and application of sandwich structures for active and passive vibration control using soft core and MRE patches.

Vibration Characteristics of Sandwich Beams with Steel Skins and Magnetorheological Elastomer Cores

Magnetorheological elastomer (MRE) cored sandwich beams with steel skins offer potentially advantageous features when used in the context of structural dynamics. Modelling of the dynamic behaviour is undertaken in this investigation by adopting a higher order sandwich beam theory. Frequency responses from the theoretical modelling are compared with experimental results on MRE cored sandwich beams. The experimental responses are generated from a specially designed test rig to study dynamic behaviour, damping effects, localised magnetic field effects and energy dissipation with varying topology. A numerically based parametric study is conducted to find the optimum geometry for skins and core material to enhance damping performance. Under the same magnetic field strength, sandwich beams with thinner skins and thicker MRE core dissapate more vibration energy. Correlation between the experimental results and numerical studies has been found to be reasonably good.

Modeling and Dynamics of Sandwich Beams with a Viscoelastic Soft Core

The dynamic behavior of sandwich beams with a viscoelastic soft core is analytically studied. The analysis combines the concepts of viscoelasticity with those of the high-order sandwich beam theory and accounts for the shear and transverse (through the thickness) deformability and the viscoelastic effects through the constitutive laws of the core material. The beam model assumes no variation through the width. The viscoelastic response is introduced through the Kelvin-Voigt and Maxwell models, which characterize different materials and provide some of the fundamental building blocks for more refined viscoelastic theories. The governing equations that correspond to the two models and the solution procedures that combine time integration through Newmark's method with a numerical solution in space are derived. The formulation of a refined viscoelastic model based on the building blocks developed in the paper is analytically demonstrated. The capabilities of the model are studied numerically with emphasis on the time variation of the deflections and the interfacial shear and vertical normal stresses under step, impulse, and harmonic loads. A comparison between the theoretical results and experimental results available in the literature is also presented. The analytical models and the numerical study highlight some unique aspects of the dynamic response of sandwich beams with viscoelastic soft cores and provide fundamental analytical tools for their modeling.

Optimal design of acoustical sandwich panels with a genetic algorithm

Abstract An optimization study is performed to design a sandwich panel with a balance of acoustical and mechanical properties at minimal weight. An acoustical model based on higher-order sandwich beam theory is used with mechanical analysis of the maximum deflection at the center of the sandwich panel under a concentrated force. First, a parametric study is performed to determine the effects of individual design variables on the sound transmission loss of the sandwich panel. Next, by constraining the acoustical and mechanical behavior of the sandwich panel, the area mass density of the sandwich panel is minimized using a genetic algorithm. The sandwich panels are constructed from eight face-sheet and sixteen core materials, with varying thicknesses of the face sheets and the core. The resulting design is a light-weight, mechanically efficient sound insulator with strength and stiffness comparable to sandwich structures commonly used in structural applications.

Nonlinear analysis of a curved sandwich beam joined with a straight sandwich beam

The buckling behaviour of straight sandwich beams joined with curved sandwich beams loaded in pure bending is investigated using two different models. One is based on a high order sandwich beam theory and the other model is based on finite element analysis. The analyses are applied to a numerical example and the results are compared with experimental results.

High Order Analysis of Junction Between Straight and Curved Sandwich Panels

When curved and straight sandwich panels are joined, localized bending effects arise in the vicinity of the curvature discontinuity. To investigate this the problem is analyzed using a high order sandwich beam theory. This, however, is not straight forward because the continuity conditions at a junction cannot be fulfilled in an exact sense. Instead an averaging scheme is suggested and used to obtain a set of approximate continuity conditions. The accuracy of these approximate continuity conditions is estimated and a numerical example is conducted and compared with finite element analyses. The results prove to be within the estimates of the inaccuracy. A parametric study is conducted to identify possible ways to reduce the localized bending effects.

Indentation failure analysis of sandwich beams

Failure of sandwich honeycomb structures under indentation loading is considered. A failure criterion for Nomex honeycombs subjected to combined compressive and shear stresses is determined using biaxial tests. By combining this with a theoretical calculation of the stress distribution in the core due to indentation loading, found from a high-order sandwich beam theory (HOSBT), the indentation failure load of the sandwich beam due to core failure can be predicted. It is assumed that both the skin and core are elastic up to failure, which is a reasonable approximation for the GFRP skins and Nomex cores considered. Short beam 3-point bending tests are used to validate the theoretical predictions, using beams made with GFRP skins and Nomex cores with densities between 29 and 128 kg/ m 3 . Theoretical predictions of indentation failure load are in excellent agreement with measured values. Inclusion of shear stresses in the failure criterion significantly improves the predictions, correctly modelling the observed stronger behaviour of cores with a longitudinal ribbon direction.

Indentation resistance of sandwich beams

High-order sandwich beam theory is used to model the local deformation under the central indentor for sandwich beams loaded under three-point bending. `High-order' refers to the non-linear variations of in-plane and vertical displacements through the height of the core which the model incorporates. The analysis is elastic, which is appropriate to describe the beam response up to peak load for the material combination of GFRP skins and Nomex honeycomb core which is the focus of this paper. Reasonable agreement is found between theoretical predictions of the displacement field under the indentor and experimental measurements using a beam with GFRP skins and Nomex honeycomb core. By using the model to consider the way in which different wavelengths of sinusoidal pressure loading on the top skin are transmitted to the core, a spreading length scale λ is introduced. λ, which is a function of the beam material and geometric properties, characterises the length over which a load on the top surface of a beam is spread out by the skin. Calculations of the effect of roller diameter on indentation behaviour illustrate the importance of this length scale. When λ is small compared with the roller radius R, corresponding to a flexible skin, the contact load at the roller-skin interface is transmitted relatively unchanged to the core. Conversely, when λ/ R is greater than about 0.25, corresponding to a relatively rigid skin, the load from the roller is spread out by the skin and the pressure in the core is distributed over a length of the order of λ.