An Elasticity Solution for the Global Buckling of Sandwich Beams/Wide Panels With Orthotropic Phases

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
George A. Kardomateas
Keyword(s):  
Compressive Loading ◽  
Beam Model ◽  
Elasticity Solution ◽  
Short Side ◽  
Single Wave ◽  
The Core ◽  
Sandwich Construction ◽  
Geometric Configurations ◽  
The Face ◽  
Global Buckling

There exist several formulas for the global buckling of sandwich plates, each based on a specific set of assumptions and a specific plate or beam model. It is not easy to determine the accuracy and range of validity of these rather simple formulas unless an elasticity solution exists. In this paper, we present an elasticity solution to the problem of global buckling of wide sandwich panels (equivalent to sandwich columns) subjected to axially compressive loading (along the short side). The emphasis on this study is on the global (single-wave) rather than the wrinkling (multiwave) mode. The sandwich section is symmetric, and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. The buckling problem is formulated as an eigenboundary-value problem for differential equations, with the axial load being the eigenvalue. The complication in the sandwich construction arises due to the existence of additional “internal” conditions at the face-sheet/core interfaces. Results are produced for a range of geometric configurations, and these are compared with the different global buckling formulas in the literature.

Wrinkling of Wide Sandwich Panels∕Beams With Orthotropic Phases by an Elasticity Approach

2004 ◽  
Vol 72 (6) ◽  
pp. 818-825 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Compressive Loading ◽  
Sandwich Panels ◽  
Wave Mode ◽  
Buckling Load ◽  
Face Sheet ◽  
Beam Model ◽  
Elasticity Solution ◽  
Short Side ◽  
Euler Buckling ◽  
Sandwich Construction

There exist many formulas for the critical compression of sandwich plates, each based on a specific set of assumptions and a specific plate or beam model. It is not easy to determine the accuracy and range of validity of these rather simple formulas unless an elasticity solution exists. In this paper, we present an elasticity solution to the problem of buckling of sandwich beams or wide sandwich panels subjected to axially compressive loading (along the short side). The emphasis on this study is on the wrinkling (multi-wave) mode. The sandwich section is symmetric and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. First, the pre-buckling elasticity solution for the compressed sandwich structure is derived. Subsequently, the buckling problem is formulated as an eigen-boundary-value problem for differential equations, with the axial load being the eigenvalue. For a given configuration, two cases, namely symmetric and anti-symmetric buckling, are considered separately, and the one that dominates is accordingly determined. The complication in the sandwich construction arises due to the existence of additional “internal” conditions at the face sheet∕core interfaces. Results are produced first for isotropic phases (for which the simple formulas in the literature hold) and for different ratios of face-sheet vs core modulus and face-sheet vs core thickness. The results are compared with the different wrinkling formulas in the literature, as well as with the Euler buckling load and the Euler buckling load with transverse shear correction. Subsequently, results are produced for one or both phases being orthotropic, namely a typical sandwich made of glass∕polyester or graphite∕epoxy faces and polymeric foam or glass∕phenolic honeycomb core. The solution presented herein provides a means of accurately assessing the limitations of simplifying analyses in predicting wrinkling and global buckling in wide sandwich panels∕beams.

Effect of Implanted Delamination and Core Density on the Buckling Behavior of Sandwich Composites

2000 ◽  
Author(s):  
Hassan Mahfuz ◽  
Syful Islam ◽  
Leif Carlsson ◽  
Makeba Atkins ◽  
Shaik Jeelani
Keyword(s):  
Finite Element ◽  
Local Buckling ◽  
Sandwich Composites ◽  
Core Density ◽  
Sandwich Construction ◽  
Buckling Behavior ◽  
The Face ◽  
Global Buckling ◽  
Plane Compression ◽  
Overall Buckling

Abstract Foam core sandwich composites have been fabricated using innovative co-injection resin infusion technique and tested under in-plane compression. The sandwich construction consisted of Klegcell foam as core materials and S2-Glass/Vinyl ester composites as face sheets. Tests were conducted with various foam densities and also with implanted delamination between the core and the face sheet. The intent was to investigate the effect of core density, and the effect of core-skin debonds on the overall buckling behavior of the sandwich. Analytical and finite element calculations were also performed to augment the experimental observations. It has been observed that core density has direct influence on the global buckling of the sandwich panel, while embedded delamination seem to have minimal effect on both global as well as local buckling. Detailed description of the experimental work, finite element modeling and analytical calculations are presented in this paper.

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.

Theory of Wrinkling in Sandwich Construction

1955 ◽  
Vol 59 (529) ◽  
pp. 30-36 ◽  
Author(s):  
Syed Yusuff
Keyword(s):  
Marginal Zone ◽  
Infinite Medium ◽  
Square Root ◽  
Test Results ◽  
The Core ◽  
Young’S Moduli ◽  
Sandwich Construction ◽  
Wide Range ◽  
The Face ◽  
Selection Of

SummaryIn this paper a theory of wrinkling in Sandwich Construction is presented in two parts. In the first part, the thickness of the core is regarded as finite. The wrinkling stress is given by a simple square root formula consisting of the Young's moduli of the materials and the ratio of the thickness of the face and core. In the second part of the theory the same procedure is followed, with the main difference that shearing stresses in the core are also considered, and the analysis is extended to the case where the face is supported by a sufficiently thick or a semi-infinite medium. The result for the wrinkling stress is a cubic root formula which consists of the moduli of the materials but indirectly depends upon the geometry of the structure; this formula is valid only if the ratio of the thickness of the core and the face is greater than or at least equal to the ratio of the width of the marginal zone of distortions in the core, and the thickness of the face. The width of the zone is also useful as the criterion which discriminates between the two cases of buckling as envisaged in this paper. The theory is compared with the previous works, and also with the test results already available. The selection of the experimental data comprises steel, aluminium alloy and Papreg (laminated paper plastic) as the face; and onazote, cellular cellulose acetate, granulated cork, sponge rubber and expanded formvar as the core materials over a wide range of core-face thickness ratio. The agreement between the theory and the tests is satisfactory.

Material Selection for CFRP-Aluminium-Foam-Sandwiches Manufactured by a PUR Spraying Process

2017 ◽  
Vol 742 ◽  
pp. 317-324
Author(s):  
Peter Rupp ◽  
Peter Elsner ◽  
Kay André Weidenmann
Keyword(s):  
Manufacturing Process ◽  
Sandwich Structures ◽  
Bending Stiffness ◽  
Effective Density ◽  
Sandwich Composites ◽  
Open Cell ◽  
The Core ◽  
Bending Modulus ◽  
The Face ◽  
Spraying Process

Sandwich structures are ideal for planar parts which require a high bending stiffness ata low weight. Usually, sandwich structures are manufactured using a joining step, connecting theface sheets with the core. The PUR spraying process allows to include the infiltration of the facesheet fibres, the curing of the matrix and the joining of the face sheets to the core within one processstep. Furthermore, this manufacturing process allows for the use of open cell core structures withoutinfiltrating the core, which enables a comparison of different material configurations, assembled bythe same manufacturing process. The selection of these materials, with the aim of the lowest possiblemass of the sandwich composite at a constant bending stiffness, is displayed systematically within thiswork.It could be shown that the bending modulus calculated from the component properties matched theexperimentally achieved values well, with only few exceptions. The optimum of the bending modulus,the face sheet thickness and the resulting effective density could be calculated and also matched theexperimental values well. The mass-specific bending stiffness of the sandwich composites with corestructures of open cell aluminium foams was higher than with closed cell aluminium foams, but wasexceeded by sandwich composites with Nomex honeycomb cores.

Devolution processes and the theory of historical development by S. Sanderson

2021 ◽  
pp. 72-77
Author(s):  
A.V. Verkhoturov ◽  
◽  
A.A. Obukhov
Keyword(s):  
Historical Development ◽  
World System ◽  
Human Society ◽  
Evolutionary Trend ◽  
The Core ◽  
The World ◽  
The Face ◽  
American Historian ◽  
Immanuel Wallerstein ◽  
Main Ideas

Analyzed is one of the most comprehensive modern approaches to the problem of the existence of evolution of human society as such and of specific human communities, i.e. “General Theory of Historical Development” by American historian and sociologist Stephen Sanderson. While agreeing, in general, with its main ideas, we believe that it is important to note that the issue of existence of individual communities demonstrating devolution (regression to an earlier historical state), stagnation or degeneration at certain historical stages is practically ignored in the framework of the theory under consideration. This creates its vulnerability in the face of specific empirical data, indicating a deviation from the evolutionary trend. We believe that overcoming this theoretical difficulty is possible in the process of comprehending the theory of S. Sanderson in the context of ideas of the world-system approach of Immanuel Wallerstein. We want to show that examples of devolution, stagnation and degeneration of societies do not deny general progressive evolutionary tendencies, characteristic for the world-system as a whole, but only indicate the transition of a particular society to a lower level within the world-system (from the core to the semi-periphery, or from the semi-periphery to the periphery).

scholarly journals Public Space as a Venue for Peacebuilding in Lebanon? The Role of Civic Movements in Reclaiming Public Space in Beirut and Tripoli

2021 ◽  
pp. 25-46
Author(s):  
Aseel Naamani ◽  
Ruth Simpson
Keyword(s):  
Public Space ◽  
Public Life ◽  
Public Spaces ◽  
Urban Spaces ◽  
Building Relationships ◽  
The Core ◽  
The Face ◽  
History Of ◽  
Post War

The issue of public spaces is increasingly at the core of civic movements and discourse of reform in Lebanon, coming to the fore most recently in the mass protests of October 2019. Yet, these most recent movements build on years of activism and contestation, seeking to reclaim rights to access and engage with public spaces in the face of encroachments, mainly by the private sector. Urban spaces, including the country’s two biggest cities – Beirut and Tripoli – have been largely privatised and the preserve of an elite few, and post-war development has been marred with criticism of corruption and exclusivity. This article explores the history of public spaces in Beirut and Tripoli and the successive civic movements, which have sought to realise rights to public space. The article argues that reclaiming public space is central to reform and re-building relationships across divides after years of conflict. First, the article describes the evolution of Lebanon’s two main urban centres. Second, it moves to discuss the role of the consociational system in the partition and regulation of public space. Then it describes the various civic movements related to public space and examines the opportunities created by the October 2019 movement. Penultimately it interrogates the limits imposed by COVID-19 and recent crises. Lastly, it explores how placemaking and public space can contribute to peacebuilding and concludes that public spaces are essential to citizen relationships and inclusive participation in public life and affairs.

Face Wrinkling and Core Strength in Sandwich Construction

1960 ◽  
Vol 64 (591) ◽  
pp. 164-167 ◽  
Author(s):  
S. Yusuff
Keyword(s):  
High Stress ◽  
Core Layer ◽  
High Strength ◽  
Bending Rigidity ◽  
Core Strength ◽  
Surface Smoothness ◽  
Lightweight Material ◽  
The Core ◽  
Sandwich Construction ◽  
Strength Material

The effect of initial waviness on the wrinkling of faces in sandwich construction is studied. Formulae are derived to determine the failing stress when the faces wrinkle due to failure of the core in tension, compression or shear. The importance of core strength requirements in maintaining surface smoothness is noted. A comparison of theory with experiments is made, and the agreement between the two is found to be reasonably good.A sandwich construction consists of two thin face layers of high-strength material and a thick core layer of lightweight material. The function of the core is twofold. Firstly, it increases the bending rigidity of the faces and second, it stabilises them so that they will not wrinkle until high stress is reached.

Effect of Core Plasticity on the Post-Buckling Behavior of Debonded Sandwich Beams

2000 ◽  
Author(s):  
Bhavani V. Sankar ◽  
Manickam Narayanan ◽  
Abhinav Sharma
Keyword(s):  
Plastic Material ◽  
Maximum Load ◽  
Face Sheet ◽  
Compression Tests ◽  
Element Analysis ◽  
The Core ◽  
Perfectly Plastic ◽  
The Face ◽  
Post Buckling ◽  
Elastic Perfectly Plastic

Abstract Nonlinear finite element analysis was used to simulate compression tests on sandwich composites containing debonded face sheets. The core was modeled as an elastic-perfectly-plastic material, and the face-sheet as elastic isotropic. The effects of core plasticity, face-sheet and core thickness, and debond length on the maximum load the beam can carry were studied. The results indicate that the core plasticity is an important factor that determines the maximum load.

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.

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