Analysis of Compression Stress of a Filler and Bending of a Sandwich Panel under Multipoint Loading

The distribution of transverse stresses in the midlayer of a composite sandwich panel under multipoint loading is investigated. The stresses averaged across the thickness of a soft filler are estimated using a discrete model. Finite expressions for the compression of the filler along the length of the panel are derived by means of superposition of the local effects from the bending of face layers under an infinite system of transverse point forces constant across the panel thickness. The effects of compression and transverse extension of the filler, in the case of a high distribution frequency of these forces, i.e., when the distance between the forces is comparable to the panel thickness, are revealed. Compression of the panel by two systems of forces applied symmetrically or nonsymmetrically to the upper and lower faces is considered. The bending characteristics in the cases of loading with point forces and piecewise distributed loads are compared. The formulas obtained are used to determine the length of a small region on the panel surface for which the local effects from the distributed pressure and the point force are equivalent. The corresponding estimates are obtained in a closed form. The analysis, carried out with varied parameters of the structure, allows us to elucidate the peculiarities of the effect of discontinuous loads on the design characteristics in the local zones, using finite expressions derived by the operational method.     

Free-edge effects in a cylindrical sandwich panel with a flexible core and laminated composite face sheets

In the present study, the static response of cylindrical sandwich panels with a flexible core is investigated. The face sheets are considered as composite laminates with a cross-ply lay-up and the core as a flexible elastic medium. The flexibility of the low-strength core leads to high stress concentrations in terms of peeling stresses between the face sheets and the core at edges of the sandwich panel. To take into account the compressibility of the core and to determine the free-edge stresses of sandwich structures accurately, the Reddy layerwise theory (LWT) is used in this paper. The paper outlines the mathematical formulation, along with a numerical study, of a cylindrical sandwich panel with two simply supported and two free edges under a transverse load. The formulation includes the derivation of field equations along with boundary conditions. A Levy-type solution procedure is performed to determine the distributions of stresses and strains. In the numerical study, first a comparison is made with results from the commercial finite-element software ANSYS to verify the LWT results. Finally, a parametric study is conducted, and the effect caused by varying different parameters, such as the radii of curvature and the core to face sheet thickness ratio, on the results are investigated. The results obtained demonstrate a good agreement between LWT and FEM solutions and show increasing interlaminar stresses in the free edge of the sandwich panel     

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.     

An effective computer modelling approach to the study of aeroelastic characteristics of an aircraft composite wing with high aspect ratio

Static aeroelastic and flutter characteristics of an aircraft composite wing with high aspect ratio were analysed by an effective Computational Fluid Dynamics and Computational Structure Dynamics coupled method. Effects of stiffness distribution on aeroelastic characteristics were considered. Honeycomb core sandwich composite was considered to be equivalent to an orthotropic material by stiffness and inertance equivalent method to allow highly efficient numerical simulation, which was used for analysis of bending and torsional stiffness distribution. The results showed that the redistributed aerodynamic load leads to a decrease of pressure difference between the upper and lower airfoils. The flutter speed of the composite wing is near 0.64 Ma. Both bending and torsional stiffness increases with a small increase of beam size. Stiffness of the wing root has a major influence generally on the static aeroelastic characteristics. Both the lift coefficient and the loss percent decrease with a small increase of beam size. Effects of stiffness distribution on frequency are not obvious. Flutter speed remains close to the initial value when the beam size is changed.     

Optimization of the thickness of layers of sandwich conical shells

We deal with an optimal control problem for variational inequalities, where the linear operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for optimal control is applied to optimal design problems for sandwich conical shells where a variable thickness of given layers appears as a control variable.     

Optimization of axisymmetric membrane shells

Problems of the joint optimization of the shape and distribution along the meridian of the thickness of membrane shells of revolution under the action of axisymmetric loads are considered, taking account of the constraints concerning the strength of the shell and the volume of its cavity. General formulations of problems of the optimal design of shells of revolution are given and the optimal shape of a shell and the corresponding thickness distribution are investigated. Results of the exact solution of problems of the optimal design of closed shells of revolution when there is an internal pressure are presented. The simultaneous introduction of two control functions, describing the shape of the shell and the distribution of its thickness, not only ensures a substantial reduction in the mass of a shell but also leads to significant mathematical simplifications, which enable the solution of the optimization problem being considered to be obtained in an analytical form.     

Panel Flutter of a Variable-Thickness Composite Shell

Mechanics of Composite Materials - Systems of equations are obtained to study the onset of panel flutter of a composite shell with a linearly varying thickness. Using a model developed, the...     

Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method

Nonlinear flexural vibration of a symmetric rectangular honeycomb sandwich thin panel with simply supported along all four edges is studied in this paper. The nonlinear governing equations of the symmetric rectangular honeycomb sandwich panel subjected to transverse excitations are simplified to a set of two ordinary differential equations by the Galerkin method. Based on the homotopy analysis method, the average equations of the primary resonance and harmonic resonance are obtained. The influence of structural parameters, the transverse exciting force amplitude, and transverse damping to the symmetric rectangular honeycomb sandwich panel are discussed by using the analytic approximation method. Compared with the results obtained by single‐mode modeling technique, the results obtained by double‐mode modeling technique change the softening and hardening nonlinear characteristics when Ω ≈ ω₁, ω₁/3, and ω₂/3.     

Waves of Transverse Stresses under a Plane Impact on the Surface of a Sandwich Panel (Acoustic Approximation)

The wave process arising in a sandwich panel with a free back surface under the action of a short-term dynamic load on the front surface of the upper layer (plane deformation) is investigated. The calculation procedure for displacements, rates, and stresses under a rectangular short-time pulse, whose duration does not exceed the double time of wave travel within a layer, is based on the representation of the solution to the one-dimensional wave equation in terms of characteristics. The transmission and reflection coefficients of the pressure pulses on the contact surfaces of layers with different physical properties are determined. The expressions for tensile stresses in the panel face layers and filler, which are responsible for the material failure by spalling, are presented. The stresses in relation to the geometry and dynamic parameters of the sandwich structure are analyzed. In the case of a symmetric panel structure, the stress pattern in the midlayer and on its contact boundaries is given, which takes into account the branching and superposition of pulses.     

Deformation of sandwich panels in cylindrical bending by point forces. 1. Analytical construction

A refined model for bending of a three-layered panel with a soft filler is proposed. The modified model permits us to consider the asymmetry of elastic properties and thickness of the outer layer relative to the middle plane of the panel in a composite sandwich structure. In constructing the deformation mechanism, a heterogeneous kinematic model was adopted, which, in contrast to the assumptions for the deformation of the whole stack of layers, features four degrees of displacement freedom permitting consideration of the separate nature of the deformation of the outer layers in bending and of the intermediate layer in transverse compression combined with shear. This approach is postulated according to an energetic evaluation of the deformation of the layers [2]. The specific features of the stress from point forces in cylindrical bending are considered using the operational Laplace method, which avoids the additional difficulties in analyzing the solution convergence arising when it is represented by a series of eigenfunctions of the boundary value problem. The fundamental functions of a twelfth-order set of equations are used to construct the boundary problem reduced to a Cauchy problem. Various boundary effects of the point stress are described using a generalized Dirac function. Variants are examined for the limiting transformation of the model parameters leading to a qualitative change in its kinematics and the corresponding simplified bending models. Institute of Polymer Mechanics, Latvian Academy of Sciences, LV-1006 Riga, Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 588–611, September–October, 1996.     

On the optimal structural design for a nonconservative,elastic stability problem

The design of a cantilever column under a follower load is considered with the aim of maximizing the critical value of the load. The optimality condition is derived, and a modified Ritz method is used to determine an approximate solution for the bending stiffness. Results are obtained numerically for the case of a sandwich column with constant bending stiffness in each of two segments. It is found that, for the same structural weight, the optimal design yields a critical load significantly higher than that for a uniform column.This research was supported in part by the US Army Research Office–Durham and in part by the United States Navy under Grant No. NONR N00014-67-A-0191-0009.     

Aplicación de métodos computacionales en la evaluación de la respuesta aeroelástica de puentes soportados por cables

The possibilities of computational methods for assessing the response of cable supported bridges under wind action are considered in this work. The main objective is to study the possibilities of substituting wind tunnel campaigns by computer based analyses, particularly at the early design stage. The preliminary proposed design for a continuous cable-stayed bridge with two main spans of 650 m and a single box girder deck has been considered as a case study. The force coefficients of the deck cross-section have been computed and the unsteady response associated to vortex-shedding has been simulated using CFD commercial software. Furthermore, an in-house piece of software has been employed to obtain the response for flutter and buffeting phenomena adopting the hybrid approach; with that purpose the experimental flutter functions of a similar box girder deck were adopted. The computational results have been validated by comparison with similar experimental results published by other researchers. It has been verified that the set of adopted methods offers reliable results with moderate costs; therefore, the proposed approach is very suitable at the early design stage of long span bridges or at conceptual design works.     

Elastic-plastic sandwich beams with optimized properties for the impact case

An approach for the design of lightweight sandwich beams with optimal performance under low velocity impact loading is presented. Exemplary for beams with stainless steel faces and aluminium foam cores a procedure is proposed that bases on simulation results using an explicit finite element code. Experimental tests assure the accuracy of numerical analyses and provide data to fit the applied plastic compressible material model. By means of a multicriteria optimization method failure mechanisms are identified which dissipate a maximum of energy and lead to minimal deflections as well as to minimal beam thickness and weight at the same time. Face and core thicknesses are used as design variables. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

2D elastic analysis of the sandwich panel buckling problem: benchmark solutions and accurate finite element formulations

This paper is concerned with the elastic stability of a sandwich beam panel using classical elasticity. An exact solution for the buckling problem of a sandwich panel (wide beam) in uniaxial compression is presented. Various formulations that correspond to the use of different pairs of energetically conjugate stress and strain measures for the infinitesimal elastic stability of the sandwich panel are discussed. Results from the present two-dimensional analyses to predict the global and local buckling of a sandwich panel are compared with previous theoretical and experimental results. A new finite element formulation for the bifurcation buckling problem is also introduced. In this new formulation, terms that influence the buckling load, which have been omitted in popular commercial codes are pointed out and their significance in influencing the buckling load is identified. The formulation and results presented here can be used as a benchmark solution to establish the accuracy of numerical methods for computing the buckling behavior of thick, orthotropic solids.     

Free edge stress prediction in thick laminated cylindrical shell panel subjected to bending moment

A thick composite cylindrical shell panel with general layer stacking is studied to investigate the free edge and 3D stresses in the panel which is subjected to pure bending moment. To this aim, a Galerkin based layerwise formulation is presented to discretize the governing equation of the panel to ordinary differential equations. Employing a reduced displacement field for the cylindrical panel, the governing equations for thick panel are developed in terms of displacements and a set of coupled ordinary differential equations is obtained. The governing equations are solved analytically for free edge boundary conditions and applied pure bending moment. The accuracy of numerical results is examined and the distribution of interlaminar and in-plane stresses is studied. The free edge stresses are studied and the effect of radius to thickness ratio, width to thickness ratio and layer stacking on the distribution of stresses is investigated. The focus of numerical results is on the prediction of boundary layer and free edge stress distribution.     

Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling

In this paper, we design an attribute np control chart using multiple deferred state (MDS) sampling under Weibull distribution based on time truncated life test. This chart is constructed for monitoring the variation of mean life of the product in a manufacturing process. The optimal parameters of MDS sampling and the control limit coefficients are determined so that the in‐control average run length (ARL) is as close as to the target ARL. The optimal parameters of MDS sampling are sample size and number of successive subgroups required for declaring the current state of process. Out‐of‐control ARL is considered as a measure of the performance of proposed chart and reported with determined optimal parameters for various shift constants. The out‐of‐control ARL of the proposed chart obtained under various distributions is compared with each other. The performance of proposed control chart is compared with the performance of the existing control chart designed under single sampling. In addition, the economic design of proposed chart using variable sampling interval scheme is discussed, and sensitivity analysis on expected costs is also investigated.     

Analysis of Guided Lamb Wave Propagation (GW) in Honeycomb Sandwich Panels

The paper aims to introduce the guided lamb wave propagation (GW) in a honeycomb sandwich panels to be used in the health monitoring applications. Honeycomb sandwich panels are well-known as lightweight structures with a good stiffness behavior and a wide range of applications in different industries. Due to the complex geometry and complicated boundary conditions in such a structure, the development of analytical solutions for describing the wave propagation and the interaction of waves with damages is hardly possible. Therefore dimensional finite element simulations have been used to model GW for different frequency ranges and different sandwich panels with different geometrical properties. The waves, which are highly dispersive, have been excited by thin piezoelectric patches attached to the surface of the structure. In the first step, the honeycomb panel has been simplified as an orthotropic layered continuum medium. The required material data have been calculated by applying a numerical homogenization method for the honeycomb core layer. The wave propagation has been compared in the homogenized model with the real geometry of a honeycomb sandwich panel. Such calculations of high frequency ultrasonic waves are costly, both in creating a proper finite element model as well as in the required calculation time. In this paper the influence of changes in the geometry of the sandwich panel on the wave propagation is presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Degenerate cases of stability loss of an elastic fluid-conveying tube

The two-dimensional non-linear dynamics of a liquid-filled tube is considered. The tube is clamped at the upper end, a point mass is fixed to its free lower end and laterally it is supported by two springs. The uniform flow velocity of the fluid, the end mass, the spring constant and the vertical position of the springs are considered as the distinguished parameters of the problem. A linear stability analysis shows that the (degenerate) case of a Takens-Bogdanov-Hopf bifurcation exists, which is associated with a high frequency flutter movement superimposed on a low frequency flutter around a statically buckled state of the tube. We account for this degenerate case by indicating the parameter regime necessary for its occurence and and give the bifurcation diagram for the trivial equilibrium position of the tube. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design and Fabrication of Composite Smart Structures with High Electric and Mechanical Performances for Future Mobile Communication

In this paper, we have developed a load-bearing outer skin for antennas, which is termed a composite smart structure (CSS). The CSS is a multilayer composite sandwich structure in which antenna layers are inserted. A direct-feed stacked patch antenna is considered. A design procedure including the structure design, material selection, and design of antenna elements in order to obtain high electric and mechanical performances is presented. An optimized honeycomb thickness is selected for efficient radiation and impedance characteristics. High gain conditions can be obtained by placing the outer facesheet in the resonance position, which is at about a half wavelength distance from the ground plane. The measured electrical performances show that the CSS has a great bandwidth (over 10%) and a higher gain than an antenna without a facesheet and has excellent mechanical performances, owing to the composite laminates and honeycomb cores. The CSS concept can be extended to give a useful guide for manufacturers of structural body panels and for antenna designers.     

2D elastic analysis of the sandwich panel buckling problem: benchmark solutions and accurate finite element formulations

This paper is concerned with the elastic stability of a sandwich beam panel using classical elasticity. An exact solution for the buckling problem of a sandwich panel (wide beam) in uniaxial compression is presented. Various formulations that correspond to the use of different pairs of energetically conjugate stress and strain measures for the infinitesimal elastic stability of the sandwich panel are discussed. Results from the present two-dimensional analyses to predict the global and local buckling of a sandwich panel are compared with previous theoretical and experimental results. A new finite element formulation for the bifurcation buckling problem is also introduced. In this new formulation, terms that influence the buckling load, which have been omitted in popular commercial codes are pointed out and their significance in influencing the buckling load is identified. The formulation and results presented here can be used as a benchmark solution to establish the accuracy of numerical methods for computing the buckling behavior of thick, orthotropic solids.