Elsevier

Composite Structures

Volume 145, 10 June 2016, Pages 129-141
Composite Structures

Experimental and numerical investigations of five-layered trapezoidal beams

https://doi.org/10.1016/j.compstruct.2016.02.079Get rights and content

Abstract

This paper is devoted to orthotropic sandwich beams that consist of five layers: two thin facings made of steel sheets and the core made of three corrugated layers. The obtained experimental results are compared for some geometrical parameters with numerical analysis (FEA) and theoretical solutions to a problem of elastic three point-bending of a beam. Laser welding was used for bonding together thin-walled corrugated and flat sheets. The small diameter of welding spot guarantees that material is not overheated and can be welded quickly. The presented results include experimental and numerical (FEA – SolidWorks) solutions and sensitivity analysis of a beam.

Introduction

Sandwich structures are developed in response to demands for lighter, but stronger structures with good thermal, electrical and acoustical properties. They consist of thin facings and much thicker core that contributes greatly to the overall strength of a sandwich panel. The core of the investigated beams is corrugated.

The theory of sandwich plates has been being developed since the mid of 20th century. That resulted in many papers published in journals and presented at scientific conferences. In the last five decades, the properties of three-layered sandwich structures composed of a light core and two thin facings have been extensively studied. In such structures only a core is subject to shear.

The theoretical study of seven-layered steel beams subjected to three-point bending is presented in [1], the main core of those beams is made of sinusoidally corrugated steel sheets and two sandwich facings have steel foam cores. A transverse shearing effect is described in [2]. There authors consider three-layered beams with sinusoidal corrugated cores subjected to three-point bending.

The theory of sandwich structures is described in many monographs, for example [3], [4]. A review of Zig-Zag theories for multi-layered plates and shells is presented in [5]. Analytical and numerical-FEM modelling of sandwich beams and plates with corrugated cores is described in [6], [7]. The new sandwich structures are presented by Magucka, Wittenbeck and Jasion in [8]. They show some analytical solutions for seven-layered beams with a corrugated, trapezoidal core that are based on the broken line hypothesis. The authors compare obtained results with numerical simulations made in ANSYS and ABAQUS in order to better understand how to use the broken line hypothesis for modelling multi-layered, orthotropic structures. Strength and buckling problems of sandwich beams and other structures with a corrugated core are presented in [9]. Kazemahvazi et al. [10] present a comparison between their theoretical model and results of strength tests of monolithic and corrugated composite cores subjected to compression and shear. In [11] Magnucki et al. consider bending and buckling problems of orthotropic sandwich beams with three-layered facings. The presented work is inspired by the results included in the paper [12]. Experimental investigations of multi-layered orthotropic structures are presented by Aboura et al. [13]. Tanner et al. [14] developed an analytical model and experimental tests for the compressive and shear response of monolithic and hierarchical corrugated composite cores. Other works on that subject are Valdevit et al. [15], Seong and al. [16] and Grygorowicz et al. [17].

The considered beams consist of five layers: two thin facings made of steel sheets and a core made of three corrugated layers. The shape of corrugation is trapezoidal. Layers of a core are perpendicular to each other. 3D model and an actual beam are shown in Fig. 1.

The experimental tests were performed in the laboratory that belongs to the Division of Strength of Materials and Structures at Poznan University of Technology. Beams were investigated using a specially designed test stand and strength test machine. The obtained results are presented in the form of plots and tables. The aim of the presented researches is to verify continuously developed analytical and numerical models.

Section snippets

Experimental investigations

At the beginning, material properties of steel sheets used for making the investigated beams were determined. The stress–strain curve of each steel sheet was obtained by tensile tests of specimens cut out of a beam. A Zwick Z100/TL3S strength test machine, with a macro extensometer, was used to perform the strength tests. The results were implemented in a numerical model (Table 1). The determined relationships between stress and elongation percentage are shown in Fig. 2.

The determined material

Numerical investigations – FEA

The presented numerical analyses were done in CAE software SolidWorks Simulation Advanced Professional 2011 based on COSMOS/M [18]. This software is integrated with popular CAD system SolidWorks. The aim of numerical investigations is to compare their results with actual experiments and check if beams are modelled properly. This comparison may be used also to check if a test stand is built correctly. The dimensions assumed in a numerical model are shown in Fig. 10(a)–(d). Because the load,

Sensitivity analysis of a beam

The conduced sensitivity analysis of a beam refers to the thickness of steel sheets (t01, t02, ts) and geometrical parameters of corrugated layers, i.e. their height (tc1, tc2) and width (bf1, bf2). All parameters were changed by ±10%. The total depth of a beam was assumed to be constant, except of slight changes caused by considering different thicknesses of steel sheets. When h1 was changed then h0 was adjusted respectively, so the total depth was the same. The maximum deflections of beams with

Analytical studies

The problem of three point bending has been analytically solved. The theoretical model and the field of displacement of the cross section of the beam have been assumed as presented in Fig. 20.

The beam consists of five layers: two facings and one main core. Each facing has a flat outer layer of thickness ts and an inner trapezoidal corrugated layer of thickness tc2. Directions of the corrugations of the main core and facing cores are perpendicular to each other. In a mathematical model the shear

Conclusions

There is a good agreement between numerical and experimental results. The difference between the measured stresses in beams is small. The difference between the numerical and experimental deflection of beams is less than 13.4% if 4 mm mesh is used and less than 12.8% in the case of 12 mm mesh. The presented numerical model is stiffer than an actual beam in spite of taken assumptions that should model it accurately.

The sensitivity analysis of beams reveals that thicker steel sheets results in

Acknowledgments

The project was funded by the National Science Centre allocated on the basis of the decision Number DEC-2013/09/B/ST8/00170.

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