Buckling and Postbuckling of Sandwich Beams With Delaminated Faces Based on Higher Order Core Theory

1999 ◽  
Author(s):  
R. F. Li ◽  
Y. Frostig ◽  
G. A. Kardomateas
Keyword(s):  
Nonlinear Distortion ◽  
Variational Principles ◽  
Vertical Direction ◽  
Initial Imperfection ◽  
Order Theory ◽  
Sandwich Beams ◽  
Postbuckling Behavior ◽  
The Core ◽  
Core Theory ◽  
The Face

Abstract Delaminations within the face sheets are often observed when a sandwich structure is exposed to impact loads. The buckling and postbuckling behavior of sandwich beams with delaminated faces is investigated in this work. The governing nonlinear equations, boundary conditions, and continuity conditions are formulated through variational principles. The beam construction consists of upper and lower, metallic or composite laminated symmetric skins, and a soft core of a foam or low strength honeycomb type. A high order theory is used for the core that accounts for the nonlinear distortion of the plane of section of the core and the compressibility in the vertical direction. The delamination considered is an interface crack, in which the substrate includes the transversely flexible core. The case of a debond at one of the skin-core interfaces is also included. The effects of the delamination length and location on the overall and local behavior are examined with an arbitrary initial imperfection.

scholarly journals Fundamental Frequency Analysis of Sandwich Beams with Functionally Graded Face and Metallic Foam Core

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lin Mu ◽  
Guiping Zhao
Keyword(s):  
Fundamental Frequency ◽  
Plate Theory ◽  
Order Theory ◽  
Functionally Graded ◽  
Face Sheet ◽  
Metallic Foam ◽  
Sandwich Beams ◽  
Classical Plate Theory ◽  
The Core ◽  
The Face

This study is interested in assessing a way to analyze fundamental frequency of sandwich beams with functionally graded face sheet and homogeneous core. The face sheet, which is an exponentially graded material (EGM) varying smoothly in the thickness direction only, is composed of a mixture of metal and ceramic. The core which is made of foam metal is homogeneous. The classical plate theory (CPT) is used to analyze the face sheet and a higher-order theory (HOT) is used to analyze the core of sandwich beams, in which both the transverse normal and shear strains of the core are considered. The extended Galerkin method is used to solve the governing equations to obtain the vibration equations of the sandwich beams suitable for numerical analysis. The fundamental frequency obtained by the theoretical model is validated by using the finite element code ABAQUS and comparison with earlier works. The influences of material and geometric properties on the fundamental frequency of the sandwich beams are analyzed.

Nonlinear Behavior of Sandwich Panels With Delamination Inside Face Sheets Based on Refined Higher Order Core Theory

2000 ◽  
Author(s):  
R. Li ◽  
V. La Saponara ◽  
G. A. Kardomateas
Keyword(s):  
Sandwich Structure ◽  
Nonlinear Distortion ◽  
Eigenvalue Problems ◽  
Continuation Method ◽  
Nonlinear Behavior ◽  
Higher Order ◽  
The Core ◽  
Core Theory ◽  
The Face ◽  
Inside Face

Abstract Sandwich construction, consisting of two stiff face sheets and a soft core of a foam or low strength honeycomb type while designed principally as efficient integral structures, can lose this quality when delaminations occur inside the face sheets, especially under compressive loading condition. A refined higher order core theory is developed for the core that accounts for the nonlinear distortion of the plane of section of the core and the compressibility in the vertical direction, and for the skins in which part of the transverse deflections is related to the core nonlinear distortion. Based on this core theory, nonlinear behavior of sandwich beams/panels with delaminated faces is studied. The nonlinear governing equations, boundary conditions, and continuity conditions are formulated for the compressed sandwich structure which includes initial imperfection and delamination in the face sheets. Solution arc length parameterization within Newton continuation method is employed in solving the bifurcation and nonlinear eigenvalue problems for critical loads and postbuckling behavior of the sandwich structure. The results suggest that delaminations inside face sheets have considerable influence on the global and local behavior of the whole sandwich con structure.

Finite Elements for Curved Sandwich Beams

1977 ◽  
Vol 28 (2) ◽  
pp. 123-141 ◽  
Author(s):  
P J Holt ◽  
J P H Webber
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Test Cases ◽  
Sandwich Beams ◽  
Honeycomb Core ◽  
The Core ◽  
The Face ◽  
Core Thickness ◽  
Displacement Approach ◽  
Circular Sandwich Ring

SummaryThe formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

Geometrical Nonlinear Effects in the Dynamic Response of Sandwich Beams

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Itay Odessa ◽  
Oded Rabinovitch ◽  
Yeoshua Frostig
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
High Order ◽  
Theory Approach ◽  
Nonlinear Frequency ◽  
Sandwich Beams ◽  
Nonlinear Dynamic Response ◽  
The Core ◽  
Geometrical Nonlinear ◽  
The Face

Abstract The geometrical nonlinear dynamic response of sandwich beams is studied using a dynamic high-order nonlinear model. The model is derived using the variational principle of virtual work and uses the Extended High-Order Sandwich Panel Theory approach with consideration of two interfaces between the three layers. A first-order shear deformation theory is adopted for the face sheets, while the kinematic assumption of high-order small deformations that account for out-of-plane compressibility are considered for the core layer. The nonlinearity of the dynamic model is introduced by considering geometrically nonlinear kinematic relations in the face sheets. The nonlinear kinematic relations and the dynamic modeling aim to evaluate the effects of the two features and their coupling on the response. The nonlinear dynamic response of sandwich beams is studied through two numerical cases and comparison of the nonlinear results with their linear counterparts. The first case looks into the coupling of the global geometrical nonlinear behavior with the dynamic behavior. The second case focuses on the local instability of the face sheets and its interaction with the compressibility of the core in the dynamic response of soft core sandwich beams. The comparison of linear and nonlinear dynamic response in the two cases sheds light on the coupling of the geometrical nonlinear and dynamic behaviors. Among other features, the latter is expressed by nonlinear attractors, higher modes response, nonlinear frequency response, and significant wrinkling response.

scholarly journals Simplified analytical model for tapered sandwich beams using variable stiffness materials

2016 ◽  
Vol 19 (1) ◽  
pp. 3-25 ◽  
Author(s):  
Qing Ai ◽  
Paul M Weaver
Keyword(s):  
Sandwich Beam ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Axial Stiffness ◽  
Beam Model ◽  
Sandwich Beams ◽  
Element Analysis ◽  
The Core ◽  
The Face ◽  
Potential Energy Method

A simplified layer-wise sandwich beam model to capture the effects of a combination of geometric taper and variable stiffness of the core on the static response of a sandwich beam is developed. In the present model, the face sheets are assumed to behave as Euler beams and the core is modelled with a first-order shear deformation theory. With geometrical compatibility enforced at both upper and lower skin/core interfaces, the beam’s field functions are reduced to only three, namely the extensional, transverse and rotational displacements at the mid-plane of the core. The minimum total potential energy method is used in combination with the Ritz technique to obtain an approximate solution. Geometrically nonlinear effects are considered in the present formulation by introducing von Kármán strains into the face sheets and core. Two types of sandwich beams, uniform and tapered, with different boundary conditions are studied. Results show that the proposed model provides accurate prediction of displacements and stresses, compared to three-dimensional finite element analysis. It is found that due to the axial stiffness variation in the core, displacements of beams and stresses of face sheets and core are significantly affected. The potential design space is shown to be expanded by utilizing variable stiffness materials in sandwich constructions.

On wrinkling of a sandwich panel with a compliant core and self-equilibrated loads

2011 ◽  
Vol 13 (6) ◽  
pp. 663-679 ◽  
Author(s):  
Y. Frostig
Keyword(s):  
Sandwich Panel ◽  
Variational Principles ◽  
Tensile Force ◽  
Mathematical Formulation ◽  
Compressive Load ◽  
Distribution Functions ◽  
The Core ◽  
The Face ◽  
Overall Buckling ◽  
Loading Scheme

The nonlinear response of a unidirectional sandwich panel that is associated with wrinkling of the face sheets, due to a self-equilibrated loading scheme is presented. This loading scheme may be a results of a manufacturing process where the core is tensioned first and the sandwich panel is formed through bonding of the face sheets to the tensioned core while wrinkling occurs as a result of the release of the tensile force of the core, i.e. similar to the manufacturing of electroactive polymers (EAPs) [Wantanaba et al. (2002)] or due to prestressing of the core which is associated with the pre-strain the edge of the core only. These self-equilibrated loads yield compression in the face sheets as well as in the core which may be associated with loss of stability as a result of overall buckling of the entire panel or wrinkling of the face sheets. Thus, for such loading scheme the longitudinal rigidity of the core must be considered although it is small as compared with that of the face sheets. The governing equations along with the appropriate boundary conditions are derived through the introduction of longitudinal normal stresses in the core along with high-order distribution functions for the displacements through its depth. The mathematical formulation is based on variational principles along with moderate type of deformations for the kinematic relations. The results of the various structural quantities in the form of curves along the panel, equilibrium curves and deformed shapes for a particular sandwich panel are presented. The study discusses the effects of the transfer of the compressive load from the core to the face sheets, either directly through an edge beam or without it. Conclusions are drawn and presented.

Analysis and Optimization of Foam Core Mid-Plane Asymmetric Sandwich Beams Under Lateral Loads

2000 ◽  
Author(s):  
Jack R. Vinson ◽  
Nihar R. Satapathy
Keyword(s):  
Minimum Weight ◽  
Sandwich Beams ◽  
Lateral Loads ◽  
Honeycomb Core ◽  
The Core ◽  
Structure Factors ◽  
Honeycomb Sandwich ◽  
The Face ◽  
Weight Structure ◽  
Core Depth

Abstract The equations with which to analyze, design and optimize honeycomb sandwich beams subjected to laterally distributed loads are presented. They apply to beams using composite materials and for isotropic materials. Specifically they account for mid-plane asymmetry in order to maximize the structural efficiency, thus providing for differing face materials, ply sequencing and/or thicknesses. Explicit solutions are given for the beam subjected to a uniform lateral load for several boundary conditions. To attain minimum weight, the means to select each face thickness, the core depth and the honeycomb core wall thickness and cell size are given. Localized face dimpling and face wrinkling, using and comparing the results of Heath equation and the Hoff-Mautner equation are included. The effects of transverse shear deformation are also shown. In order to choose the face material and core materials to achieve a minimum weight structure, Factors of Merit are defined for the faces and the core. Various face materials are then compared.

The load-carrying capacity of sandwich beams in different collapse mechanisms

2020 ◽  
pp. 109963622092011
Author(s):  
Lu Guo ◽  
Renwei Mao ◽  
Shiqiang Li ◽  
Zhifang Liu ◽  
Guoxing Lu ◽  
...  
Keyword(s):  
Carrying Capacity ◽  
Sandwich Beam ◽  
Sandwich Beams ◽  
Load Carrying Capacity ◽  
The Core ◽  
Shear Mechanism ◽  
Collapse Mechanisms ◽  
Continuity Equations ◽  
Load Carrying ◽  
The Face

The load-carrying capacity of the symmetrical and asymmetrical sandwich beams, under a quasi-static central load, is investigated in this paper. Three collapse mechanisms such as face yield, core shear and indentation are considered for symmetrical sandwich beams. Core shear mechanism is taken into account for fully clamped asymmetrical sandwich beams. Continuity equations are established by simple ‘equal area’ method for the postyield behavior of the sandwich beams in face yield and core shear mechanisms at different boundary conditions. In indentation mechanism theoretical model, the effect of the local denting on the large deflection of the sandwich beam is taken into account. Then, finite element simulations are carried out to verify the validity of the proposed analysis, and a good agreement is presented. It is shown that in the core shear mechanism under fully clamped condition, no plateau phase is presented. The effect of the core thickness on the response of the symmetrical beams is discussed in detail. For asymmetry beams in core shear mechanism under fully clamped condition, the effect of the asymmetric factor (strength or thickness) for face-sheets on the load–deflection behavior of the postyield beams can be neglected, if the sum of the strength or thickness of the face sheets is constant.

Fabrication and characterization of microscale sandwich beams

2001 ◽  
Vol 16 (2) ◽  
pp. 597-605 ◽  
Author(s):  
Francisco Arias ◽  
Paul J.A. Kenis ◽  
Bing Xu ◽  
Tao Deng ◽  
Olivier J.A. Schueller ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Beam Theory ◽  
Shear Stiffness ◽  
Sandwich Beams ◽  
The Core ◽  
The Face ◽  
Polymer Metal ◽  
Fabrication And Characterization ◽  
Bending Response

Microscale sandwich beams with cell diameters and wall widths down to 150 and 15 μm, respectively, and having both metallic and polymer/metal cores were produced through fabrication methods that combined photolithography and electrodeposition. Various core structures were used, including some with negative Poisson's ratio. The bending response was investigated and compared with beam-theory predictions. Most of the cores evaluated had sufficient shear stiffness that the bending compliance was relatively high and dominated by the face sheets. Two of the core configurations were “soft” and exhibited behavior governed by core shear. The relative dimensions of the cores evaluated in this study were far from those that minimize the weight, because of fabrication constraints. The development of an ability to make high-aspect ratio cores is an essential next step toward producing structurally efficient, lightweight microscale beams and panels.

A critical evaluation of mechanical models for sandwich beams

2012 ◽  
Vol 14 (6) ◽  
pp. 629-654 ◽  
Author(s):  
Daniele Tonelli ◽  
Lorenzo Bardella ◽  
Michele Minelli
Keyword(s):  
Critical Evaluation ◽  
Sandwich Beam ◽  
Order Theory ◽  
Limited Range ◽  
Geometrical Parameters ◽  
Sandwich Beams ◽  
The Core ◽  
Mechanical Models ◽  
Higher Order Theory ◽  
Definition Of

We focus on the description of the stress state of sandwich beams under bending and shear, a non-trivial task if Saint-Venant's principle does not hold, as it is the case if the skins are somewhat stiffer than the core. Each of the analytical structural models available in literature turns out to be accurate for a limited range of relative stiffness between core and skins, or sandwich heterogeneity. For a simply supported sandwich beam subject to uniform transversal load, we evaluate the stress by means of (a) the classical theory relying on the linear cross-section kinematics, appropriate if Saint-Venant's principle holds, (b) the structural theory based on the zig-zag warping (e.g. Krajcinovic D. Sandwich beam analysis. J Appl Mech, Trans ASME 1972; 39(3): 773–778), and (c) the higher-order theory of Frostig et al. (Frostig Y, Baruch M, Vilnay O, et al. High-order theory for sandwich-beam behavior with transversely flexible core. J Eng Mech, Trans ASCE 1992; 118(5): 1026–1043), the latter usually appropriate when the core is much softer than the skins. The results are compared, for several combinations of material and geometrical parameters, with those of finite element simulations in which the sandwich is modelled as a plane stress continuum. This comparison allows us to provide some graphs which can help in selecting the model appropriate for each sandwich heterogeneity. This is accomplished in terms of non-dimensional material and geometrical parameters the sandwich heterogeneity depends on. We identify and discuss two levels of heterogeneity at which one should switch analytical model: one level is related to the validity of Saint-Venant's principle, while the other level is concerned with the definition of antiplane sandwich.

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