Assessment of the Buckling Behavior of Square Composite Plates with Circular Cutout Subjected to In-Plane Shear

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1 Assessment of the Buckling Behavior of Square Composite Plates with Circular Cutout Sujecte to In-Plane Shear Husam Al Qalan 1)*, Hasan Katkhua 1) an Hazim Dwairi 1) 1) Assistant Professor, Civil Engineering Department, The Hashemite University * Corresponing Author: P.O. Box , Zarqa 1115, Joran, hqalan@hotmail.com ABSTRACT This paper aims at evaluating the effect of various parameters on the uckling loa of square cross-ply laminate plates with circular cutouts. The parameters consiere in this stuy are: (1) cutout size () cutout location () fier orientation angle an (4) type of loaing. Three types of in-plane loaing were consiere; namely, uniaxial compression, iaxial compression an shear loaing. The reuction in the uckling loa ue to the increase of cutout size was significant in the case for shear loaing as compare to uniaxial an iaxial compression. For relatively small size cutouts, a etter performance was achieve if the cutout is kept close to the ege of the plate, however, for relatively large size cutouts, a higher uckling loa is achieve if the cutout is kept in the mile of the plate. Several other imperative finings ase upon the various parameters are also presente in this stuy. KEYWORDS: Buckling, Laminates, Cutouts, Finite element analysis. INTRODUCTION Composite materials have such an influence on our lives that many researches investe a great eal of time an effort for a etter unerstaning of their ehavior. Composite materials have een use for a while in many inustries such as: aerospace, automotive, marine an civil engineering applications one can say that composite materials usage is limite y the iniviual imagination. One type of composite materials is cross-ply laminate plates with cutouts, where cutouts are introuce for accessiility reasons or to just lighten the structure. Such plates are vulnerale to uckle when sujecte to various types of in-plane loaings; therefore it is of great importance to fully unerstan the effects of various parameters on its uckling loa. Accepte for Pulication on 15/4/009. Many researchers investigate this prolem over the years from ifferent perspectives; the following paragraphs summarize their work an key finings. Vanenrink an Kamat (1987) stuie the uckling loa an post-uckling ehavior of isotropic an composite plate with central holes. In their stuy, they compare the Finite Element Metho (FEM) results with experimental results an foun a goo agreement. In their work they conclue that there is a it more loss in composite plates post-uckling strength as compare to isotropic plates. They also foun that the uckling loa of composite plates with large holes egin to increase aove that of the corresponing soli plate for fier orientation angle of 60 o. Larsson (1987, 1989) investigate the uckling loa an post uckling ehavior of orthotropic laminate square an circular plates with central circular cutout. Larsson utilize the FEM to solve the prolem for JUST. All Rights Reserve.

2 uniaxial an iaxial compression for various ounary conitions. Larsson reporte a reuction in the uckling loa of square plates with central cutouts which was more pronounce in the case of uniaxial compression. Lee et al. (1989) use the FEM to stuy the uckling of orthotropic square plates with central circular hole. They oserve ifferent uckling moes in the stronger an weaker material irections an, therefore, recommene the use of full-scale configuration moel in the analysis of the uckling prolem. Hyer an Lee (1991) explore the improvement of the uckling loa of square composite plates with central holes through the use of curvilinear fier format. The stuy conclue that fier orientation far from the hole has less effect on the uckling loa as compare to the effect of fier orientation near the hole. Hu an Lin (1995) presente an optimization scheme with respect to fier orientation for the uckling loa of symmetrically laminate plates with central holes. They reporte that the optimal uckling loas of thin square composite plates with a central circular cutout, except simply supporte plates, increase with the increase of the sizes of cutouts; therefore, it is theoretically possile to come up with a cutout size an fier angle to increase the uckling loas eyon those of corresponing plates without cutouts. Kong et al. (001) investigate the uckling an post-uckling ehavior of laminate plates with central holes through comparison of progressive failure FEM an experimental results. They conclue that the ening stiffness in the axial irection has a great effect on the uckling loa an post-uckling ehavior of such plates. Akulut an Sayman (001) stuie the uckling of laminate plates with central square holes uner uniaxial an iaxial loaing. In their formulation, first orer shear theory was inclue. Angle-ply laminates with [45/-45] n orientation of plies showe the est performance uner uniaxial compression. Saha et al. (004) teste composite plates with central holes uner compression loaing. They foun that as the hole iameter increases, the plate slenerness ratio (height/with) ecomes less effective on the uckling loa. Jain an Kumar (004) an Ghannapour et al. (006) investigate the critical uckling loa an post-uckling ehavior of laminate plates with circular an elliptical cutouts uner axial compression. They foun that uckling loa ecreases as the central circular hole iameter increases. A laminate without a cutout fails near the iagonal corner, ut in the presence of a circular cutout the failure location shifts towars the cutout ege. However, with an elliptical cutout the failure takes place near the vertex of the cutout. Small cutouts can e neglecte from analysis which reuce the meshing effort. Baltaci et al. (006) analyze laminate circular plates with circular holes using finite element analysis. They conclue that the critical uckling loa ecreases as the hole gets closer to the plate center. The critical uckling loa for square notche plates was more sensitive for simply supporte plates than clampe ones. Mallela an Upahyay (006) presente a parametric stuy on laminate composite lae-stiffene panels sujecte to in-plane shear. They propose some esign charts that can e use to selecting the optimum parameters for etter stiffener proportions. Baa (007) an Baa an Baltaci (007) stuie the effect of support conitions on the uckling loa of laminate plates with circular in semicircular cutouts uner axial compression. They foun that the uckling loa of clampe-clampe plates is 75% higher than the uckling loa of simply supporte plates, an 50% for the case of clampe-pinne ounary conition. Also, an increase of the length/thickness ratio of 50% increases the uckling loa in the range of 75%. Eviently, the vast majority of the research conucte on the uckling prolem of laminate plates has pai less attention to the uckling ue to in-plane shear loaing. Thus, the current parametric stuy attempts at reinforcing the literature with the lacking information on the uckling of cross-ply laminate plates with circular cutouts ue to in-plane shear loaing. The effect of various parameters was also investigate for comparison reasons, these parameters inclues: (1) cutout size () cutout location or eccentricity () fier orientation angle an (4) type of loaing. Three types of in-plane loaing were consiere;

3 Assessment of the Buckling Husam Al Qalan, Hasan Katkhua an Hazim Dwairi namely, uniaxial compression, iaxial compression an shear loaing. FINITE ELEMENT MODEL Moeling composite laminate plates requires extra attention in efining the properties of the plate, incluing numer of layers, thickness an fier orientation of each layer, as well as mesh sizing, especially near the cutouts. In the present work, Eigen-uckling analysis is performe for the laminate composite plates which take into consieration higher-orer shear eformation theory, through the use of the finite element package name ABAQUS. The plate imension consiere is 000 mm 000 mm. The thickness of each layer of this eight-layer laminates is 1.5 mm. The material properties of the lamina are given in Tale (1). In this tale, E 1, E, E are the moulus of elasticity, G 1, G 1 are the shear moulus corresponing to the planes 1- an 1-, respectively an υ 1, υ 1, υ are the corresponing Poisson ratios. Tale (1): Material properties of the lamina. Mechanical Properties Values E.0 GPa 1 E.0 GPa E.0 GPa G = 5.0 GPa 1 G 1 ν = ν 1 ν = 0.5 ν The moel is compose of mainly four noe shell elements that have six egrees of freeom per noe. Three noe shell elements are only use in irregular zones aroun the holes. The composite laminates are ivie into sufficient numer of elements to allow for free evelopment of uckling moes an isplacements. Some trial runs were also carrie out to stuy the convergence of the results. In this stuy, three types of loaing were consiere; namely, uniaxial compression, iaxial compression an shear loaing. The plate area is locate in the xy plan. For uniaxial loaing, the compressive loas were applie in the x irection, while for iaxial an shear, the loas were applie in the x an y irections as shown in Figure (1). Series of preselecte cases are moele to verify the accuracy of the metho of analysis. The results are compare to theoretical an numerical values, as shown in Tale () an Tale (). In Tale,, h are the with an thickness of the plate, respectively, is the uckling loa an D is as follows: E h D = (1) 1 ( 1 ν ) an in Tale (), is the iameter of the cutout. From these results, it can e oserve that the present stuy an the values availale in the literature are in goo agreement. The uckling moe shapes otaine in the present stuy are similar in respect with the uckling moe shapes availale in the literature as shown in Figure (1). PLATE SUBJECTED TO UNIAXIAL LOAD The isotropic an anisotropic 000 mm 000 mm square plate mentione aove is sujecte to uniaxial loa to stuy the effect of cutout size, cutout location an fier orientation angle on the ucking ehavior. Effect of Cutout Size The ratio of the cutout iameter () to the isotropic an anisotropic plate with () is varie from 0.0 to 0.5. The location of the cutout was assume to e locate at the center an at one quarter of the plate as shown in Figure (). From this figure, it can e oserve that the uckling loa for anisotropic plate is ecrease with ifferent percentages when the cutout size is increase an the effect of cutout size on ucking loa for the isotropic plate is consiere minor as compare to that of the anisotropic. It is worth mentioning that the ecrease in uckling loa in the case of fier orientation angle [0, 90]4s is more than in the other cases where this ecrease reaches 68% when changing the (/) ratio from 0.0 to 0.5 as shown in Figure ()

4 Tale (): Comparison of uckling loa etween theoretical metho an finite element moel for isotropic plate without cutouts. Theoretical Metho Uniaxial Case 4π D = Biaxial Case π D = Shear Case 9.4π D = E (Pa) ν (m) h (m) Non-Dimensional Buckling Loa (Theoretical) Eh Non-Dimensional Buckling Loa (FE Moel) Eh Tale (): Comparison of uckling loa etween current finite element moel an results availale from Ghannapour et al. (006) for composite plate [0, 90] 4s with circular cutout sujecte to uniaxial loa. / Non-Dimensional uckling loa (Ghannapour et al [11]) E h Non-Dimensional uckling loa (FE Moel) E h Effect of Location The location of the cutout is change through the square plate in comination with the size of the cutout. The changes in location are represente y the ratio of the eccentricity (e x ), i.e. istance from the ege of the plate to the center of the cutout, to the plate with (). Uniaxial loa is sujecte to isotropic an anisotropic plates as shown in Figure (). In the case of isotropic plate an for (/) = 0.1, 0. an 0., the uckling loa is increase with small percentages when (e x /) = 0., 0.4 an 0.5, then these percentages get higher when (e x /) = 0. an 0.1. On other han, the uckling loa is ecrease for (/) = 0.4 an 0.5 when the cutout is move towar the eges

5 Assessment of the Buckling Husam Al Qalan, Hasan Katkhua an Hazim Dwairi () () Cutout (a) () y x (c) Figure (1): In-plane loaing cases an first uckling moe shape for (a) uniaxial loaing () iaxial loaing (c) shear loaing. In the case of anisotropic plate with fiers orientation ( ), the uckling loa is increase for (/) = 0.1 an 0. when the cutout is move towar the eges as shown in Figure (). However, uckling loa is ecrease for (/) = 0.4 an 0.5 when the cutout is move towar the eges. PLATE SUBJECTED TO BIAXIAL LOAD The same laminate square plate mentione aove is sujecte to iaxial loa to stuy the effect of cutout size, cutout location an fier orientation angle on the ucking ehavior. Effect of Cutout Size The uckling loa is ecrease with very small percentages for the isotropic case when the cutout size increase when it was locate at the center an one quarter of the plate as shown in Figure (4). For the case of the cutout at the center of the anisotropic plate, the uckling loa is ecrease for [0, 90]4s fiers orientation when the iameter of the cutout is increase, while this loa is ecrease with smaller percentages for the other fiers orientation until (/) = 0.4; then the uckling loa starts increasing. In the case of cutout at one quarter of the anisotropic plate, the uckling loa is ecrease when the cutout size is increase. The percentages of ecrease are higher for the fiers orientation [0, 90]4s an [0,-0]4s compare with others as shown in Figure (4)

6 5 0 Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] (a) 5 0 Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] () Figure (): Variation of uckling loa for laminate plate sujecte to uniaxial loa with ifferent sizes of cutout locate at (a) the center of the laminate plate () one quarter of the laminate plate. Effect of Location The uckling loa is increase for (/) = 0.1, 0. an 0. when the cutout is move towar the eges of the anisotropic plate with fiers orientation ( ) as shown in Figure (5). On the other han, the loa is ecrease for (/) = 0.4 an 0.5 when the cutout is move towar the eges

7 Assessment of the Buckling Husam Al Qalan, Hasan Katkhua an Hazim Dwairi 4 Nx /Eh.5.5 e x e x / [/=0.1] [/=0.] [/=0.] [/=0.4] [/=0.5] (a) 0 Nx /Eh e x 0.1 e x / [/=0.1] [/=0.] [/=0.] [/=0.4] [/=0.5] () Figure (): Variation of uckling loa with ifferent sizes of cutout for ifferent locations of (a) isotropic plate () laminate [ ] plate sujecte to uniaxial loa. PLATE SUBJECTED TO SHEAR LOAD The same square laminate plate mentione aove is sujecte to shear loa to stuy the effect of cutout size, cutout location an fier orientation angle on the ucking ehavior

8 1 Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] (a) 1 Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] () Figure (4): Variation of uckling loa for laminate plate sujecte to iaxial loa with ifferent sizes of cutout locate at (a) the center of the laminate plate () one quarter of the laminate plate

9 Assessment of the Buckling Husam Al Qalan, Hasan Katkhua an Hazim Dwairi Nx /Eh e x e x / [/=0.1] [/=0.] [/=0.] [/=0.4] [/=0.5] Figure (5): Variation of uckling loa with ifferent sizes of cutout for ifferent locations of anisotropic [ ] plate sujecte to iaxial loa Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] (a)

10 60 50 Nx /Eh / Isotropic [0,90] 4s [45,-45] 4s [0,-0] 4s [45,-45,90,0,0,90,-45,45] () Figure (6): Variation of uckling loa for laminate plate sujecte to shear loa with ifferent sizes of cutout locate at (a) the center of the laminate plate () one quarter of the laminate plate Nx /Eh e x e x / [/=0.1] [/=0.] [/=0.] [/=0.4] [/=0.5] Figure (7): Variation of uckling loa with ifferent sizes of cutout for ifferent locations of anisotropic [ ] plate sujecte to shear loa

11 Assessment of the Buckling Husam Al Qalan, Hasan Katkhua an Hazim Dwairi Effect of Cutout Size The uckling loa is ecrease in the isotropic plate when the cutout size is increase. Although this ecrease is not significant compare with the laminate plate, it is significant when compare with the same plate ut in ifferent loaing conitions such as uniaxial an iaxial. Figure (6) shows that the uckling loa is ecrease with high percentages as the cutout size is increase when it is at the center an at one quarter of the laminate plate. It is worth mentioning that the ecrease in uckling loa in the case of fier orientation angle [0, 90]4s is more than in the other cases where this ecrease reaches 75% when changing the (/) ratio from 0.0 to 0.5 as shown in Figure (6). Effect of Location The uckling loa is increase for (/) = 0.1 an 0. when the cutout is move towar the eges as shown in Figure (7), while the loa is ecrease for (/) = 0., 0.4 an 0.5 when the cutout is move towar the eges. CONCLUSIONS In this stuy, the effect of various parameters on the uckling loa of square composite plates with circular cutout was investigate. These parameters inclue: (1) cutout size () cutout location () fier orientation angle an (4) type of loaing which also inclue: uniaxial an iaxial compression, as well as, in-plane shear loaing. The following conclusions can e rawn: 1. Due to uniaxial an iaxial compression loaing cases, cutout size has a more pronounce effect on some of the fier orientation angles an less pronounce on others. The est performance was achieve y [45,-45]4s fier orientation an the worst was oserve in the [0, 90]4s fier orientation.. The reuction in the uckling loa ue to increasing the cutout size was significant in the case of shear loaing as compare to uniaxial an iaxial compression for the same fier orientation angle.. The location of the cutout was irectly relate to the cutout size. For relatively small size cutout (i.e., / < 0.), the uckling loa increases as the cutout is shifte away from the mile of the plate, ut for large size cutouts (i.e, / > 0.) it was notice that the uckling loa ecreases as the cutout is closer to the ege of the plate. REFERENCES Akulut, H. an Sayman, O An investigation on uckling of laminate plates with central square hole. Journal of Reinforce Plastics an Composites, 0 (1): Baa, B Buckling ehavior of laminate composite plates, Journal of Reinforce Plastics an Composites, 6 (16): Baa, B. an Baltaci, A Buckling characteristics of symmetrically an antisymmetrically laminate composite plates with central cutout. Applie Composite Materials, (14): Baltaci, A., Sarikanat, M. an Yiliz, H Buckling analysis of laminate composite circular plates with holes. Journal of Reinforce Plastics an Composites, 5 (7): Ghannapour, S., Najafi, A., an Mohammai, B On the uckling ehavior of cross-ply laminate composite plates ue to circular/elliptical cutouts. Composite Structures, (75): -6. Hyer, M. W. an Lee, H. H The use of curvilinear fier format to improve uckling resistance of composite plates with central circular holes. Composite Structures, (18): Hu, H. an Lin, B Buckling optimization of symmetrical laminate plates with various geometries an en conitions. Composites Science an Technology, 55 (6): Jain, P. an Kumar, A Postuckling response of

12 square laminates with a central circular/elliptical cutout. Composite Structures, (65): Kong, C., Hong, C. an Kim, C Postuckling strength of composite plate with a hole. Journal of Reinforce Plastics an Composites, (0): Larsson, P. L On uckling of orthotropic compresse plates with circular holes. Composite Structures, (7): 11. Larsson, P. L On uckling of orthotropic stretche plates with circular holes. Composite Structures, (11): Lee, Y. J., Lin, H. J. an Lin, C. C A stuy on the uckling ehavior of an orthotropic square plate with a central circular hole. Composite Structures, (1): Mallela, U. an Upahyay, A Buckling of laminate composite stiffene panels sujecte to in-plane shear: a parametric stuy. Thin-Walle Structures, (44): Saha, M., Prahakaran, R. an Waters, W Compressive ehavior of pultrue composite plates with circular holes. Composite Structures, (65): 9-6. Vanenrink, D. J. an Kamat, M.P Post-uckling response of isotropic an laminate composite square plates with circular hole. Finite Elements in Analysis an Design, ():

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