A spectral element for wave propagation in honeycomb sandwich construction considering core flexibility

Spectral elements are found to be extremely resourceful to study the wave propagation characteristics of structures at high frequencies. Most of the aerospace structures use honeycomb sandwich constructions. The existing spectral elements use single layer theories for a sandwich construction wherein the two face sheets vibrate together and this model is sufficient for low frequency excitations. At high frequencies, the two face sheets vibrate independently. The Extended Higher order SAndwich Plate theory (EHSaPT) is suitable for representing the independent motion of the face sheets. A 1D spectral element based on EHSaPT is developed in this work. The wave number and the wave speed characteristics are obtained using the developed spectral element. It is shown that the developed spectral element is capable of representing independent wave motions of the face sheets. The propagation speeds of a high frequency modulated pulse in the face sheets and the core of a honeycomb sandwich are demonstrated. Responses of a typical honeycomb sandwich beam to high frequency shock loads are obtained using the developed spectral element and the response match very well with the finite element results. It is shown that the developed spectral element is able to represent the flexibility of the core resulting into independent wave motions in the face sheets, for which a finite element method needs huge degrees of freedom. (C) 2015 Elsevier Ltd. All rights reserved.

COMPUTATIONAL MODELING OF A MULTI-LAYERED PIEZO-COMPOSITE BEAM MADE UP OF MFC

The Variational Asymptotic Method (VAM) is used for modeling a coupled non-linear electromechanical problem finding applications in aircrafts and Micro Aerial Vehicle (MAV) development. VAM coupled with geometrically exact kinematics forms a powerful tool for analyzing a complex nonlinear phenomena as shown previously by many in the literature 3 - 7] for various challenging problems like modeling of an initially twisted helicopter rotor blades, matrix crack propagation in a composite, modeling of hyper elastic plates and various multi-physics problems. The problem consists of design and analysis of a piezocomposite laminate applied with electrical voltage(s) which can induce direct and planar distributed shear stresses and strains in the structure. The deformations are large and conventional beam theories are inappropriate for the analysis. The behavior of an elastic body is completely understood by its energy. This energy must be integrated over the cross-sectional area to obtain the 1-D behavior as is typical in a beam analysis. VAM can be used efficiently to approximate 3-D strain energy as closely as possible. To perform this simplification, VAM makes use of thickness to width, width to length, width multiplied by initial twist and strain as small parameters embedded in the problem definition and provides a way to approach the exact solution asymptotically. In this work, above mentioned electromechanical problem is modeled using VAM which breaks down the 3-D elasticity problem into two parts, namely a 2-D non-linear cross-sectional analysis and a 1-D non-linear analysis, along the reference curve. The recovery relations obtained as a by-product in the cross-sectional analysis earlier are used to obtain 3-D stresses, displacements and velocity contours. The piezo-composite laminate which is chosen for an initial phase of computational modeling is made up of commercially available Macro Fiber Composites (MFCs) stacked together in an arbitrary lay-up and applied with electrical voltages for actuation. The expressions of sectional forces and moments as obtained from cross-sectional analysis in closed-form show the electro-mechanical coupling and relative contribution of electric field in individual layers of the piezo-composite laminate. The spatial and temporal constitutive law as obtained from the cross-sectional analysis are substituted into 1-D fully intrinsic, geometrically exact equilibrium equations of motion and 1-D intrinsic kinematical equations to solve for all 1-D generalized variables as function of time and an along the reference curve co-ordinate, x(1).

Quasi-static three-point bending of carbon fiber sandwich beams with square honeycomb cores

Sandwich beams comprising identical face sheets and a square honeycomb core were manufactured from carbon fiber composite sheets. Analytical expressions were derived for four competing collapse mechanisms of simply supported and clamped sandwich beams in three-point bending: core shear, face microbuckling, face wrinkling, and indentation. Selected geometries of sandwich beams were tested to illustrate these collapse modes, with good agreement between analytic predictions and measurements of the failure load. Finite element (FE) simulations of the three-point bending responses of these beams were also conducted by constructing a FE model by laying up unidirectional plies in appropriate orientations. The initiation and growth of damage in the laminates were included in the FE calculations. With this embellishment, the FE model was able to predict the measured load versus displacement response and the failure sequence in each of the composite beams. © 2011 American Society of Mechanical Engineers.

Composite materials dynamic fracture studies by generalized Shmuely difference algorithm

The generalized Shmuely Difference Algorithm (GSDA) is presented here to analyze the dynamic fracture performance of orthogonal-anisotropic composite materials, such as glass fibre reinforced phenolplast. The difference recurrence Formulae and boundary condition difference extrapolation formulae are derived and programmed. The dynamic stress intensity factors (DSIF) of the isotropic and anisotropic centrally cracked plates are computed respectively using GSDA and compared with that published previously. GSDA is proved effective and reliable. Copyright (C) 1996 Elsevier Science Ltd.

Vibration analysis of laminated plates using a refined shear deformation-theory

A previously published discrete-layer shear deformation theory is used to analyze free vibration of laminated plates. The theory includes the assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory has the same dependent variables as first order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibration of simply supported symmetric and antisymmetric cross-ply plates is calculated. The numerical results are in good agreement with those from three-dimensional elasticity theory.

Dynamic compressive response of composite square honeycombs

Carbon fibre-epoxy composite square honeycombs, and the parent composite material, were tested in quasi-static compression at a strain rate of 10 -3 s -1 and in dynamic compression at strain rates of 10 3-10 4 s -1 using an instrumented Kolsky bar arrangement. Taken together, these tests provide an assessment of the potential of this composite topology for use as a lightweight sandwich core. The honeycombs had two relative densities, 0.12 and 0.24, and two material orientations, ±45° and 0/90° with respect to the prismatic, loading direction of the honeycomb. Honeycomb manufacture was by slotting, assembling and bonding together carbon fibre/epoxy woven plies of composite sheets of 2 × 2 twill weave construction. The peak value of wall stress in the honeycombs was about one third that of the parent material, for all strain rates. An elastic finite element analysis was used to trace the source of this knock-down in strength: a stress concentration exists at the root of the slots and leads to premature failure by microbuckling. Shock-wave effects were evident at impact velocities exceeding 50 ms -1 for the honeycomb of relative density 0.12. This was traced to stubbing of the buckled cell walls against the face of the Kolsky bar. © 2011 Elsevier Ltd. All rights reserved.

Deformation and fracture of impulsively loaded sandwich panels

Light metal sandwich panel structures with cellular cores have attracted interest for multifunctional applications which exploit their high bend strength and impact energy absorption. This concept has been explored here using a model 6061-T6 aluminum alloy system fabricated by friction stir weld joining extruded sandwich panels with a triangular corrugated core. Micro-hardness and miniature tensile coupon testing revealed that friction stir welding reduced the strength and ductility in the welds and a narrow heat affected zone on either side of the weld by approximately 30%. Square, edge clamped sandwich panels and solid plates of equal mass per unit area were subjected to localized impulsive loading by the impact of explosively accelerated, water saturated, sand shells. The hydrodynamic load and impulse applied by the sand were gradually increased by reducing the stand-off distance between the test charge and panel surfaces. The sandwich panels suffered global bending and stretching, and localized core crushing. As the pressure applied by the sand increased, face sheet fracture by a combination of tensile stretching and shear-off occurred first at the two clamped edges of the panels that were parallel with the corrugation and weld direction. The plane of these fractures always lay within the heat affected zone of the longitudinal welds. For the most intensively loaded panels additional cracks occurred at the other clamped boundaries and in the center of the panel. To investigate the dynamic deformation and fracture processes, a particle-based method has been used to simulate the impulsive loading of the panels. This has been combined with a finite element analysis utilizing a modified Johnson-Cook constitutive relation and a Cockcroft-Latham fracture criterion that accounted for local variation in material properties. The fully coupled simulation approach enabled the relationships between the soil-explosive test charge design, panel geometry, spatially varying material properties and the panel's deformation and dynamic failure responses to be explored. This comprehensive study reveals the existence of a strong instability in the loading that results from changes in sand particle reflection during dynamic evolution of the panel's surface topology. Significant fluid-structure interaction effects are also discovered at the sample sides and corners due to changes of the sand reflection angle by the edge clamping system. © 2012 Elsevier Ltd. All rights reserved.