DIRECT STRESSES ON LAYERS OF A SANDWICH BEAM WITH FOAM CORE

Transcription

1 BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publiat de Universitatea Tehniă Gheorghe Asahi din Iaşi Tomul LX (LXIV), Fas. 3, 2014 Seţia CONSTRUCŢII. ARHITECTURĂ DIRECT STRESSES ON LAYERS OF A SANDWICH BEAM WITH FOAM CORE BY IULIANA DUPIR (HUDIŞTEANU) *, NICOLAE ŢĂRANU and CRISTINA VLĂDOIU Reeived: June 19, 2014 Aepted for publiation: July 14, 2014 Gheorghe Asahi Tehnial University of Iaşi Faulty of Civil Engineering and Building Servies Abstrat. The study investigates the variation of diret stresses on layers of a sandwih beam, onsidering the effet of inreasing the thikness and the foam ore density. The paper presents the numerial modeling of multi layered sandwih beams, with thin idential steel faes and rigid polyurethane foam ore with density of 40, 60, 80 and 100 kg/m 3, loaded in bending, in stati onditions. Assumptions like linear elasti behavior of the faes and ore and also the isotropy of the layers materials are aepted in the numerial simulations. The obtained results are entralized in table and the variation of diret stresses are illustrated with suggestive diagrams. Key words: diret stresses; sandwih elements; foam ore; numerial modeling. 1. Introdution Sandwih elements with external steel faings and polyurethane foam ore offer many advantages ompared to the elements made from traditional materials. Therefore, they are widely used as ladding and strutural elements in ivil and industrial engineering (Ţăranu, 1978). * Corresponding author: iulianahudisteanu@e.tuiasi.ro

2 100 Iuliana Dupir (Hudişteanu), Niolae Ţăranu and Cristina Vlădoiu The purpose of this analysis is to study the influene of the ore and the variation of diret stresses on layers of a sandwih beam with foam ore, by alternating the thikness and the density of the intermediate layer. Behavior of sandwih elements with foam ore subjeted to different loading ations is very omplex and it is substantially different than the lassial solutions with homogeneous materials. For this reason, it has been the fous of reent studies and numerial analysis. For example, flexural tests of sandwih elements on transverse diretion are arried out on speimens with standardized dimensions, aording to ASTM standards, having as main purpose the determination of the overall bending stiffness of the multi layered panels (Marta, 2007). The flexural behavior of sandwih panels made of polyurethane ore and glass fiber reinfored polymer skins and ribs was a theme of researh (Tarek, 2010). The load-defletion behavior of a sandwih plate under stati loading onditions has been analysed by (Feldhusen et al., 2008), using the four-point bending test. The linear elasti behavior and the different failure of sandwih plate onditions have also been investigated. 2. Distribution of Diret Stresses on the Layers of the Sandwih Beam The distribution of the diret stresses along the ross setion of the sandwih beam is based on the general theory of flexure, adapted to the multi-layered struture of the sandwih element (Allen, 1969). a - a t y max f max d h z t b Fig. 1 The distribution of diret stresses on the layers of the sandwih beam. The diret stresses on the ore thikness an be alulated with the following relation: ME D z, for f max max z, (1) 2 2

3 Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, where: σ is the diret stress in the ore, [N/mm 2 ]; E the longitudinal Young s modulus of the ore material, [N/mm 2 ]; M the bending moment, [N.mm]; D the stiffness of the sandwih beam, [N. mm 2 ]; the thikness of the ore, [mm]. The diret stresses in the faings an be alulated with the following relation: ME f f z, for D h z 2 2 h and z 2 2, (2) where: σ f is the normal stress in the faings, [N/mm 2 ]; E f the longitudinal Young s modulus in the faings, [N/mm 2 ]; h the height of the sandwih beam, [mm]. The maximum diret stresses in the ore an be omputed with the relation: ME. (3) max D 2 The maximum diret stresses in the faings an be determined with the following relation: ME h. (4) f f max D 2 3. Numerial modeling The numerial modeling enables the analysis of the variation of diret stresses on layers of the sandwih beam, depending on the thikness and the density of the ore. This analysis is realized by hanging the thikness of the intermediate layer and also by modifying the density of the polyurethane foam ore. The numerial simulations assumptions are based on stati loading onditions, on linear elasti behavior of the faes and ore and on the isotropy of the materials. 3.1 Geometry desription A simply supported sandwih beam of span L, ated by a onentrated load P at the mid span is onsidered (Fig. 2). The sandwih element is omposed by two idential thin external layers made of steel, of thikness t, and an internal thik layer of polyurethane foam, of thikness. The ross setion a-a of the sandwih beam is shown in Fig. 1. The width of the ross setion is b, while the height of the setion is h. The distane between the neutral axes of the faes is d.

4 102 Iuliana Dupir (Hudişteanu), Niolae Ţăranu and Cristina Vlădoiu Fig. 2 The stati sheme and the loading onditions of the sandwih beam. a) Geometrial harateristis The geometrial harateristis of the sandwih beam used in the numerial modeling have onstant values, exept for the thikness of rigid polyurethane foam ore and impliitly the distane between the neutral axes of the faes. The geometrial harateristis are presented below: L = 1440 mm; b = 200 mm; t = 1 mm; = 40 mm; 60 mm; 80 mm; 100 mm; d = 41 mm; 61 mm; 81 mm; 101 mm. b) Flexural rigidity Aording to the presented geometrial harateristis, the sandwih beam with d << b is onsidered a wide beam, therefore the elasti modulus of the materials will be omputed with the following relation: E E', (5) 2 1 where: E is the longitudinal Young s modulus of the material, [N/mm 2 ]; and ν the Poisson s ratio. Therefore, the flexural rigidity of the sandwih beam is defined aording to the relation: ' bt btd b D 2E f E ', (6) where: D is the flexural rigidity of the sandwih beam, [N. mm 2 ]; longitudinal Young s modulus in the faings, [N/mm 2 ]; Young s modulus of the ore material, [N/mm 2 ]. ' E f the ' E the longitudinal

5 Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, ) Materials The sandwih element is omposed of two thin steel faings and a ontinuous polyurethane foam ore. The numerial modeling of the layered sandwih beam is realized by seleting the polyurethane foam densities, with values from 40 to 100 kg/m 3, that also modifies the elasti moduli of the layers materials and impliitly the flexural rigidity of the sandwih beam. A major influene on the stiffness of the multi-layered element has the thikness of the ore, beause while inreasing the distane between the faings, the flexural rigidity of the beam is also inreased. Table 1 The Charateristis of the Materials Used in the Numerial Modeling Materials for sandwih layers ν E E N/mm 2 N/mm 2 kg/m 3 Steel Polyurethane Polyurethane Polyurethane Polyurethane d) Loads The sandwih beam is subjeted to bending, ated at the mid span, by a onentrated load equal with 3,000 N, in the vertial diretion, perpendiular to the longitudinal axis of the beam (Fig. 2). e) The geometry and the mesh of the model The geometry and the mesh of the model presented in the Figs. 3 and 4 are realized using the speialised software ANSYS Design Modeler and ANSYS Meshing. Fig. 3 presents the geometry of the sandwih beam, with respet to the geometrial harateristis and the materials desribed before. The mesh of the model is realized with a fine retangular grid: 123,019 nodes and 23,040 ells (Fig. 4) The Analysis of the Numerial Results The numerial results present the values for the diret stresses, for the 16 numerial models. The sandwih beam with the thikness of 60 mm and the density of the polyurethane ore of 80 kg/m 3, shown in Fig. 5, is representative to ilustrate the deformed shape.

6 104 Iuliana Dupir (Hudişteanu), Niolae Ţăranu and Cristina Vlădoiu Fig. 3 The geometry of the sandwih beam. Fig. 4 The mesh of the omputing model. Fig. 5 Numerial results for the diret stresses of the beam.

7 Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, Aording to the loading onditions and supports (Fig. 2), the distribution of diret stresses on layers of a sandwih beam is realisti, with maximum values in faes and redued in the intermediate layer, with a zero value at the neutral axis level. The superior fae of the sandwih element generates diret ompressive stresses, while the inferior fae presents diret tensile stresses. Moreover, the maximum diret stresses our at the midspan of the element, where the bending moment is maximum, suggesting that the numerial model follows the studied theories of strength of materials. The values for the maximum diret stresses of the sandwih beams resulted from the numerial modeling are entralised in Table 2. Thikness of the ore, [mm] Table 2 Maximum Diret Stresses of the Sandwih Beams, σ max MPa Density, [kg/m 3 ] The values presented in Table 2 show a derease of the maximum diret stresses, while inreasing the thikness and the density of the ore. This aspet is ilustrated also in the following diagrams. Fig. 6 presents the variation of the maximum diret stresses of the sandwih element, depending on the thikness of the ore, for different densities of the polyurethane foam, while Fig. 7 illustrate the variation of the maximum normal stresses for different thiknesses of the intermediate layer. Fig. 6 The variation of the maximum diret stresses, funtion of the thikness of the ore, for different densities of the polyurethane foams. For the thiknesses and the densities adopted, it is notied that the thikness of the ore influene more than density the dereasing of the diret stresses.

8 106 Iuliana Dupir (Hudişteanu), Niolae Ţăranu and Cristina Vlădoiu Fig. 7 The variation of the maximum diret stresses, funtion of the density of the polyurethane foam, for different thiknesses of the ore. 4. Conlusions The results reveal a signifiant derease of the diret stresses, while inreasing the thikness and the density of the polyurethane foam. This study indiates that the thikness of the ore influene more than density the dereasing of the diret stresses on the layers of the sandwih beam. The variation of density of the polyurethane foam ore modifies the elasti moduli of the layers materials and impliitly the flexural rigidity of the sandwih beam. Moreover, the thikness of the ore has a major influene on the flexural rigidity of the multi-layered element, following the priniples of the I-beam analogy. As a onsequene of inreasing the foam ore density, a brittle behaviour regarding failure and frature of the sandwih beams is sustained by the speialized literature (Nasirzadeh, 2014). Reent appropriate studies of the authors (Dupir, 2014) mention the omparative analysis of sandwih beams with different harateristis of the intermediate layer, foused on the influene of the ore upon the rigidity and the weight of the sandwih elements. Further researhes an take into onsideration the non linear harateristis and the anisotropy of the materials, to obtain more aurate results. REFERENCES Allen H.G., Analysis and Design of Strutural Sandwih Panels. Pergamon Press, Oxford, 1969.

9 Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, Dupir I., Elemente de înhidere stratifiate de tip sandviş u miez ontinuu. Master degree diploma, Gh. Asahi Tehnial Univ., Iaşi, Feldhusen J., Torsakul S., Brezing A., Krishnamoorthy S., Numerial Modeling and Experimental Investigation of the Failure Modes of the Cellular Foam Sandwih Strutures. J. of Metals, Materials and Minerals, 18, 2, (2008). Marta C., Optimizarea multiriterială a elementelor de înhidere pentru onstruţii industrial. Ph.D. Diss., Gh. Asahi Tehnial Univ., Iaşi, Nasirzadeh R., Sabet A.R., Study of Foam Density Variations in Composite Sandwih Panels under High Veloity Impat Loading. Internat. J. of Impat Engng., 63, (2014). Tarek A. Sharaf, Flexural Behavior of Sandwih Panels Composed of Polyurethane Core and GFRP Skins and Ribs. Ph.D. Diss., Queen s Univ., Kingston, Ontario, Canada, August Ţăranu N., Elemente portante din materiale plasti. Ph.D. Diss., Gh. Asahi Tehnial Univ., Iaşi, 1978 TENSIUNI NORMALE IN STRATURILE UNEI GRINZI SANDVIŞ CU MIEZ CONTINUU (Rezumat) Sopul studiului este de a investiga variaţia tensiunilor normale în straturile unei grinzi sandviş, sub efetul reşterii grosimii şi densităţii miezului. Se prezintă formularea teoretiă şi modelarea numeriă pentru evaluarea tensiunilor normale ale unei grinzi stratifiate de tip sandviş, u feţe exterioare subţiri din oţel şi miez din spumă rigidă poliuretaniă, u densitatea de 40, 60, 80 şi 100 kg/m 3, soliitată la înovoiere, în ondiţii de înărare statiă. Rezultatele numerie obţinute sunt entralizate în tabel, iar variaţia tensiunilor normale este ilustrată prin diagrame.

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