Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
http://www.sciepub.com/author/signin

To unsubscribe from our mailing list, please click on the following link: unsubscribe

I am looking forward to hearing from you.

Kind regards,

David Rain
Email:join@sciepub.com
Science and Education Publishing (http://www.sciepub.com)

Analysis of Stress Mitigation through Defence Hole System in GFRP Composite Bolted Joint

Khudhayer J. Jadee*, A.R. Othman

Technical Engineering College-Baghdad, Middle Technical University, Baghdad, Iraq

Abstract: The effect of the defence hole system (DHS) on the stress distribution around the bolt-hole in glass fibre reinforced polymer (GFRP) composite bolted joint has been investigated using a finite element method. The analyses have been carried out on a double-lap composite bolted joint with various geometric parameters for two cases of without and with DHS. The analyses have taken into account a 3D stress plane condition, in which the circumferential and radial stresses at the bearing region, shear-out and net tension regions of the bolt-hole have been determined. Results showed that adding auxiliary hole near the bolt-hole has contributed in reducing the stresses in the vicinity of the bolt-hole.

Keywords: defence hole system, bolted joint, GFRP, finite element analysis

Received July 28, 2015; Revised August 10, 2015; Accepted August 17, 2015

Citation: Khudhayer J. Jadee, A.R. Othman, Analysis of Stress Mitigation through Defence Hole System in GFRP Composite Bolted Joint. American Journal of Mechanical Engineering, 3 (4). 126-134. January 2015. doi:10.12691/ajme-3-4-4

1. Introduction

Several methods are available for the use in the assembly between the composite parts, including adhesively bonded joint, mechanical fastening joint, or combination of them. Bolted joint is one of the mechanical fastening methods, which is preferred due to low cost, free from surface treatment [1,2], and the simplicity in repair and maintenance [3]. The stress concentration around the bolt-hole is critical in the design of the bolted joint. These stresses affect the failure load as well as the bearing strength that a structure could sustain, thus the focus should consider on how the stress concentration around the bolt-hole could be reduced to avoid undesirable catastrophic failure.

Various techniques are available from the literatures in reducing the stresses in the vicinity of the hole in the composite plate, such as by increasing the thickness of the plates [4], reinforcement of the hole [5,6], applying trajectorial fiber steering aligned with the stress vectors [7] and optimization the hole shape [8,9,10,11,12]. The latter technique, however could not be applied in the case of bolted joints due to the hole shape being related to the bolt.

One of the methods known as a defence hole system (DHS), has been used to redistribute the stresses around the main hole by introducing an auxiliary holes in the low stress area near the main hole. The method allows the flow of the stress trajectories to be smoothened around the main hole. The previous studies have investigated the use of DHS in the isotropic plates with hole by optimizing the shape, size, and distance of the auxiliary hole to achieve maximum stress reduction, with some results have successfully reported the reduction of 30% [13-23]. However, only limited studies have considered the DHS for the use in orthotropic plates [24,25,26,27] to achieve reduction of the stress concentration around the main hole. The work has proven that the maximum stress could be well reduced up to 31.7% [27].

Several investigations on the DHS in isotropic and/or orthotropic plates with main central hole have been analysed using finite element method to examine the effect of the configuration in mitigating the stresses around the primary hole [17,18,21,24,25,26,28,29,30]. However, the question remains on how the DHS could improve the stress distribution and reduction, hence increasing the bearing capacity of the composite bolted joints. Therefore, this study presents the numerical investigation on the effect of introducing auxiliary hole near the bolt-hole on the improvement of the stress distribution around the bolt-hole in single-bolt, double-lap composite bolted joint.

2. Finite Element Analysis

The performance of composite bolted joint with single-bolt, double-lab joint as in Figure 1, subjected to tensile loading was analysed using the finite element method (FEM) based on ANSYS code. The analysis was carried out on the two different configurations of without the DHS and with the DHS.

Figure 1. Single-bolt, double-lab joint configuration of composite plate

2.1. Geometry and Material Properties

The configuration of the coupons for the cases of without DHS and with DHS was illustrated in Figure 2. The different in width to bolt-hole diameter ratio (W/D) as well as the edge distance to bolt-hole diameter ratio (E/D) were studied in both cases. The effects of W/D ratios at 2, 3, 4 and 5 and the E/D ratios at 1, 2, 3, 4 and 5 on the stress distribution were examined. For the coupons with the DHS, two additional parameters were further investigated, the first was the defence hole diameter (DHD), while the second parameter involved the defence hole distance from the bolt-hole (DS). Both DHD and DS were selected relative to the bolt-hole diameter (D), in which the values of DHD were 0.625D and 0.75D, while the DS values were varied as 1.5D, 2D, and 2.5D. As a result, 20 models have been evaluated for the laminates without the DHS, and 120 models for the DHS counterparts.

Figure 2. The geometry of composite coupons with and without the DHS

The composite plate was made of plain weave 800g/m² glass fibre reinforced polymer (GFRP) consisted of eight plies oriented in the load direction as [0]₈. In general, the balanced plain weave structure composes of two fibre directions (weft and warp), assuming one direction was aligned parallel to the applied load and the other was perpendicular to it. The mechanical properties of the 800g/m² plain weave GFRP lamina were determined experimentally, and listed in Table 1.

Table 1. Mechanical properties of 800g/m² plain weave GFRP laminate

SOLID185 elements were utilized to model the laminate. This element is a 3-D layered structural solid element defined by eight nodes with three degrees of freedom at each node, translated in the nodal x, y, and z directions. It is available in two options; a homogeneous structural solid (KEYOPT K3=0) and a layered structural solid (KEYOPT K3=1) which usually used to simulate the layered thick shells or solids. Higher concentration of the elements around the holes has been set to provide the superior accuracy in the high stresses region.

2.2. Boundary Conditions

Due to the symmetrical condition of the model with respect to x-z plane, only half of the model has been constructed for the analysis. The boundary conditions for the laminates for both cases were shown in Figure 3. A uniform distributed tensile load was applied to the nodes at the far end of the composite edge. In order to simulate the condition of rigid bolt, a radial boundary condition was applied at all nodes in the area that in contact with the bolt; these nodes are constrained in the radial direction and free in the circumferential direction [2,31,32,33,34]. Finger tight torque was applied to the bolt; the torque restrained the nodes on the surface under the washers in the z-direction. In the symmetry axis, the displacement of the nodes was constrained in the y-direction.

Figure 3. Finite element model of laminate with and without DHS

2.3. Model Verification

In order to verify the herein model, a previous work on the stress distribution around the bolted-hole of the [0/45/90/-45]s carbon fibre epoxy laminate was selected for the verification [35]. The laminate consisted of large values of W/D and E/D (equal to 5), with the geometry of the bolted-hole specimen is illustrated in Figure 4.

In those work, the authors have applied a full 3-D contact problem using ABAQUS program where three-dimensional solid brick elements (C8D3) were used for this purpose, assuming the bolt joint as a pinned joint. The stress distribution around the bolt-hole was examined as a polar stresses (radial and circumferential) normalized by the bearing stress (σb), as computed using the following Equation 1:

[picture] | (1)

where, F is the applied load (N), D is the bolt-hole diameter (mm), and t is the laminate thickness (mm).

Figure 4. The geometry of the test specimen for pinned-loaded joint

2.4. Stress Analysis

Since the bolt-hole provides the critical region in the joints, the state of the stresses around the bolt-hole requires to be considered extensively. A plane stress condition was assumed for the model, in which only the in-plane stresses were considered in the stress analysis (i.e. τ₁₃, τ₂₃, σ₃=0). A tensile load of 2000N was applied to the model; this value was chosen to be less than the minimum experimental yield failure load for the weakest geometry (W/D=2 with E/D=1), to ensure that the analysis was completed before the failure initiation. For the laminates without the DHS, the effect of the geometric parameters (W/D and E/D) on the stress distribution around the bolt-hole was also investigated. The effect the DHS on the stress distribution was also analysed extensively.

3. Results and Discussion

3.1. Model Verification Results

Figure 5 shows the comparisons of circumferential and radial stresses distribution around the bolt-hole between the current model and the previous work. The results verified similar tendency of the stress distribution obtained between the comparative results, with some variations were observed in the stress values. The maximum disparity between those two models was computed as 19% for the circumferential stress (σθθ/σb) at ply 1 of θ=90o, while up to 13.7% variation was observed for radial stress (σrr/σb) at ply 4 of θ=-45o. These variations were attributed to the differences of the types of elements used and the differences in the modelling techniques of the pin hole contact simulation.

Figure 5. (a) Circumferential and (b) radial stresses distribution around the bolt-hole of the [0/45/90/-45]s laminates at an applied load of F = 1.2 kN

3.2. Laminated Bolted Joint without the DHS

The distribution of stresses around the hole at applied load F=2000N were examined as shown in Figure 6, in which the effects of W/D and E/D were evaluated. It was clear that the maximum value of the normalized circumferential stress (σθθ/σb) was observed at θ=90o for all W/D and E/D ratios, indicating a region of high stress concentration at the hole boundary in the net-tension plane.

The maximum value of the normalized radial stresses (σrr/σb) for the laminates with short edge distance (E/D=1) was located at θ=52.5o for all W/D ratios, whilst for the laminates with E/D=2, the (σrr/σb)max was observed at θ=22.5o for W/D=2 to 3 and θ=30o for W/D≥4. These results indicated that all laminates experienced a shear-out failure mode around the bolted joint. However, for E/D≥3 at all the tested W/D ratios, the value of the (σrr/σb)max was found at θ=15o, indicating a high stress concentration at the bearing region. The behavior of the above results was found to completely agree with the results of stress distribution presented in the previous technical paper [36].

To further illustrate the effects of the geometrical dimension on the stress distribution of the bolted joint, the normalized circumferential stresses at θ=90o for all E/D and W/D ranges at an applied load of 2000N was plotted as in Figure 7. From the analysis, it was apparent that a large decline in the (σθθ/σb) has taken place for the laminates with the edge distance ratio of E/D=1 to 3 (Figure 7a) and width ratio of W/D=2 and 3 (Figure 7b). Within the range of the ratio of 1≤ E/D ≤2, the joint were subjected to high stresses, thus causing shear out failure mode. Beyond the values, a small decline in the circumferential stress was observed and the specimens have experienced less stress concentration, which was expected to reduce the probability of failure in shear-out or net-tension. Except for the joint with W/D=2, all the laminates have suffered from the bearing mode; a desirable failure for the bolted joint configuration.

Similar phenomena were observed when the stress profile was plotted as a function of W/D. For smaller configurations of W/D=2 and 3, the joint with the ratio of 1≤E/D≤2 experienced a shear-out mode, whilst for larger ratio of E/D≥3, the laminates suffered net tension mode for W/D<3. But beyond these values, the failure has changed to the bearing mode due to the reduce stress values around the main hole. It was also apparent that the (σθθ/σb) has decreased by increasing the width and edge ratios. Interestingly, for those smaller geometries of E/D, the reduction in the circumferential stress was very minimal with the failure remained as the shear-out mode.

Figure 6. Normalized stresses in laminate at F=2000N for (a) W/D=2; (b) W/D=3; (c) W/D=4 and (d) W/D=5

Figure 7. Normalized circumferential stresses (at θ=90o) as a function of (a) E/D and (b) W/D at F=2000N

Figure 8 summarizes the normalized shear stresses (τxy/σb) at θ=90⁰ for all E/D and W/D ratios subjected to loading of F=2000N. For the plot of (τxy/σb) versus E/D, the shear stress was found to drop abruptly for E/D=1 and E/D=2. Higher stress was observed for that range of smaller edge ratios, contributing to the shear out failure mode. As the E/D was increased to 3, a less accentuated inclination was observed, and beyond that the inclination was barely recognized. The failure has changed as the E/D was increased beyond E/D>2, to the bearing mode for all the joints, except for the laminates with W/D=2 (i.e. net-tension).

It has also been pointed out that the maximum shear stresses was propagated in the laminates with short edge distance (i.e. E/D=1), contributing to the occurrence of the shear-out failure mode. The reduction of about 50% in the normalized shear stresses was computed for the laminates with E/D=2 in comparison to that with E/D=1. This reduction percentage has increased slightly as the edge ratio increased beyond E/D≥3. As a result, the effect of W/D on shear stress was found small or barely noticeable.

Figure 8. Normalized shear stresses as a function of (a) E/D and (b) W/D subjected to load of F=2000N for shear-out plane (Y=R)

3.3. Laminated Bolted Joint with the DHS

In the defense hole system, an auxiliary hole is introduced in the low stress region near the main hole to redistribute the stresses or to smoothen the stress flow lines around the main hole. The examples of stress distribution (σx, σy, and σxy) of laminated composite bolted holes without and with the DHS at 2000N applied load are shown in Figure 9 - Figure 11. It was apparent that the stress contours highlighted the high and low stress regions. The maximum tensile stress (+σx) was observed in the area between the hole boundary and the width edge (net-tension plane) and the maximum compression stress (-σx) was obtained in the area opposite to the bolt shank (bearing area). Whilst, for the shear stress (σxy), the maximum concentration was clearly found in the area between the hole boundary and the end edge (shear-out plane). The introduction of the auxiliary hole in the bolted joint configuration has helped to redirect the stress profiles to wider area around the main and defense holes. This then contributed to the reduction in the maximum stress contours especially at the bearing region, hence improving the loading capacity of the joint before failure. As a result, lower stress distribution could be observed around the auxiliary hole as well as in the area behind the bolt shank, but then, it did not posses as a critical region in the joint.

Figure 9. Stress distribution (σx) around the bolt hole for laminates with W/D=5 and E/D=5 at F=2000N;(a) Laminate without the DHS (b) Laminate with the DHS

Figure 10. Stress distribution (σy) around the bolt hole for laminates with W/D=5 and E/D=5 at F=2000N;(a) Laminate without the DHS (b) Laminate with the DHS

Figure 11. Stress distribution (σxy) around the bolt hole for laminates with W/D=5 and E/D=5 at F=2000N;(a) Laminate without the DHS (b) Laminate with the DHS

Figure 12. Main failure planes in the composite specimen

In order to further analyze the effect of the DHS on the stress distribution around the bolt-hole, the Cartesian tensile stresses in the x-direction (σx) within the critical region of the net-tension plane (point A in Figure 12) was evaluated. For all specimens, a comprehensive comparison of the stress with respect to laminates without the DHS was attained for all the geometric parameters of W/D and E/D, and the DHS parameters of DHD and DS, as shown in Figure 13 and Figure 14.

Figure 13. Tensile stresses (σx) at 2000N applied load of laminates with (a) W/D=2, (b) W/D=3, (c) W/D=4 and (d) W/D=5

It was found that the general trend of the results revealed that the stresses have decreased with the edge distance ratio (E/D). All the laminates have demonstrated the minimum stresses (σx) when the DHS of diameter of DHD=0.625D was introduced at a distance of DS=2.5D, except for those narrow laminates with W/D=2, in which the minimum stresses occurred at DS=2D and DHD=0.75D. For the laminates with the defence hole distances of 1.5D and 2D, more stress reduction could be achieved by increasing the DHD. Moreover, similar behaviour was observed for those of the narrow laminates (i.e. W/D=2) with a defence hole distance of 2.5D. However, for wide laminates (i.e. W/D≥3) with the defence hole distance of 2.5D, the maximum stress reduction was achieved when the DHD decreased from 0.75D to 0.625D.

In contrast, Figure 14 shows that the narrow laminates of W/D=2 could retain high stresses, and the effect of the DHS on the stress reduction was found insignificant. But when the laminate width has increased, these stresses have shown a remarkable decrease. For most of the cases, the maximum tensile stress reduction was observed when the DS=2.5D and DHD=0.625D. The configuration has enabled the stress to be effectively re-distributed at the area behind the bolt shank. In contrast, when the DHD has been increased to 0.75D, the stress value on the net tension region has increased again, diminishing the benefits of the DHS in controlling the maximum bearing capacity of the bolted joint. However, it was noticed that for the narrow laminates (W/D=2), the minimum stresses has occurred at DS=2D and DHD=0.75D.

Table 2. σx reduction (%) at 2000N applied load

Table 2 has further distinguished the percentage in the stress reduction at 2000N applied load for the tested composite bolted joints with the DHS, in comparison with those of without the DHS. For the narrow laminates of W/D=2, the stress reduction ranged from 2.3% (for the laminates with small edge distance of E/D=1) to 6.1% (for the laminates with large edge distance of E/D=5). Within the range of E/D ratios, the benefits of the auxiliary hole was clearly marked at DS=2D and DHD=0.75.

Figure 14. Tensile stresses (σx) at 2000N applied load of laminates with (a) E/D=1, (b) E/D=2, (c) E/D=3, (d) E/D=4 and (e) E/D=5

In contrast, for those of wide laminates (i.e. W/D≥3) the stress reduction has ranged from 1.9% (for laminates with small edge distance of E/D=1 at W/D=4 and 5) to remarkably 18.6% (for the laminates with large edge distance of E/D=5 at W/D=4). It was clear that by introducing the DHS in the design of composite bolted joint, the maximum stress around the main hole (especially at the net-tension region) has been successfully reduced with the benefits of the auxiliary hole was more apparent for large geometries of W/D and E/D configurations.

4. Conclusions

Finite element analysis on double-lap single-bolt joint in GFRP composite structure for laminates with and without the DHS was carried out to study the stress distribution around the bolt-hole. The effect of introducing auxiliary hole in the low stress region near the bolt-hole on the stress concentration has been investigated using ANSYS program. The results have shown that the auxiliary hole contributed in reducing the stress concentration in the vicinity of the bolt-hole; this reduction related to the geometric parameters of the laminate (W/D and E/D) and the size and position of the auxiliary hole (DHD and DS). Optimum stress mitigation was obtained for the wide laminates (W/D >2) with the DHS of auxiliary hole diameter of DHD=0.625D at a distance of DS=2.5D from the bolt-hole, which obtained a maximum stress reduction of 18.6% than those of the counterparts without the DHS.

References

[1]   | Choi JH, Ban CS, Kweon JH, Failure load prediction of a mechanically fastened composite joint subjected to a clamping force, Journal of Composite Materials, 42(14). 1415-1428. July 2008.
[2]   | Ryu CO, Choi JH, Kweon JH, Failure load prediction of composite joints using linear analysis, Journal of Composite Materials, 41.865-878. April 2007.
[3]   | Goswami S. A finite element investigation on progressive failure analysis of composite bolted joints under thermal environment, Journal of Reinforced Plastics and Composites, 24. 161-171. January 2005.
[4]   | Tenchev TR, K. Nygard M, Echtermeyer A, Design procedure for reducing the stress concentration around circular holes in laminated composites, Composites, 26 (12). 815-828. December 1995.
[5]   | Giare GS, Shabahang R, The reduction of stress concentration around the hole in an isotropic plate using composite materials, Engineering Fracture Mechanics,32(5). 757-766. 1989.
[6]   | Muc A, Ulatowska A, Local fibre reinforcement of holes in composite multilayered plates, Composite Structures, 94(4). 1413-1419. March 2012.
[7]   | Tosh MW, Kelly DW, On the design, manufacture and testing of trajectorial fibre steering for carbon fibre composite laminates, Composites Part A: Applied Science and Manufacturing, 31(10). 1047-1060. October2000.
[8]   | Dhir SK, Optimization in a class of hole shapes in plate structures, Journal of Applied Mechanics, 48(4). 905-908. January 1981.
[9]   | Wu Z. Optimal hole shape for minimum stress concentration using parameterized geometry models, Structural and Multidisciplinary Optimization, 37(6). 625-634. February 2009.
[10]   | Wu H-C, Mu B, On stress concentrations for isotropic/orthotropic plates and cylinders with a circular hole, Composites Part B: Engineering, 34(2). 127-134. March 2003.
[11]   | William LK, Stress concentration around a small circular hole in the HiMAT composite plate. NASA technical memorandum 86038, 1-16. December 1985.
[12]   | Toubal L, Karama M, Lorrain B, Stress concentration in a circular hole in composite plate, Composite Structures, 68(1). 31-36. April 2005.
[13]   | Durelli AJ, Rajaiah K, Optimum hole shapes in finite plates under uniaxial load, Journal of Applied Mechanics, 46(3). 691-695. 1979.
[14]   | Rajaiah K, Naik NK, Hole-shape optimization in a finite plate in the presence of auxiliary holes, Experimental Mechanics, 24(2). 157-161. June 1984.
[15]   | Erickson PE, Riley WF, Minimizing stress concentrations around circular holes in uniaxially loaded plates, Experimental Mechanics, 18(3). 97-100. March 1978.
[16]   | Naik NK, Photoelastic investigation of finite plates with multi-holes, Mechanics Research Communications, 15(3). 141-146. May 1988.
[17]   | Akour SN, Nayfeh JF, Nicholson DW, Defense hole design for a shear dominant loaded plate, International Journal of Applied Mechanics, 2(2). 381-398. June 2010.
[18]   | Sanyal S, Yadav P, Relief holes for stress mitigation in infinite thin plates with single circular hole loaded axially, ASME 2005 International Mechanical Engineering Congress and Exposition, ASME . 717-720.
[19]   | Providakis CP, Sotiropoulos DA, A BEM approach to the stress concentration reduction in visco-plastic plates by multiple holes, Computers and Structures, 64(1). 313-317. July 1997.
[20]   | Nagpal S, Optimization of rectangular plate with central square hole subjected to in-plane static loading for mitigation of SCF, International Journal of Engineering Research and Technology, 1(6). 1-8. August 2012.
[21]   | Nagpal S, S.Sanyal, Jain N, Mitigation curves for determination of relief holes to mitigate stress concentration factor in thin plates loaded axially for different discontinuities, International Journal of Engineering and Innovative Technology, 2(3). 1-7. September 2012.
[22]   | Ulrich TW, Moslehy FA, A boundary element method for stress reduction by optimal auxiliary holes, Engineering Analysis with Boundary Elements, 15(3). 219-223. January 1995.
[23]   | Meguid SA, Shen CL, On the elastic fields of interacting defense and main hole systems, International Journal of Mechanical Sciences, 34(1). 17-29. January 1992.
[24]   | Rhee J, Rowlands RE, Stresses around extremely large or interacting multiple holes in orthotropic composites, Computers and Structures,61(5). 935-950. December 1996.
[25]   | Rhee J, Cho H-K, Marr DJ, Rowlands RE, Local compliance, stress concentrations and strength in orthotropic materials, The Journal of Strain Analysis for Engineering Design, 47(2). 113-128. February 2012.
[26]   | Jain NK, The reduction of stress concentration in a uni-axially loaded infinite width rectangular isotropic/orthotropic plate with central circular hole by coaxial auxiliary holes, IIUM Engineering Journal, 12(6). 141-150. 2011.
[27]   | Akour SN, Al-Husban M, Nayfeh JF, Design and optimization of defense hole system for hybrid loaded laminates, Technology Engineering and Management in Aviation: Advancements and Discoveries, IGI Global, Hershey, 151-160. 2012.
[28]   | Jindal UC, Reduction of stress concentration around a hole in a uniaxially loaded plate, The Journal of Strain Analysis for Engineering Design, 18(2). 135-141. April 1983.
[29]   | Akour SN, Nayfeh JF, Nicholson DW, Design of a defence hole system for a shear-loaded plate, The Journal of Strain Analysis for Engineering Design, 38(6). 507-517. January 2003.
[30]   | Meguid SA, Gong SX, Stress concentration around interacting circular holes: a comparison between theory and experiments, Engineering Fracture Mechanics, 44(2). 247-256. January 1993
[31]   | Okutan B, The effects of geometric parameters on the failure strength for pin-loaded multi-directional fiber-glass reinforced epoxy laminate, Composites Part B: Engineering, 33(8). 567-578. November 2002.
[32]   | Karakuzu R, Çalışkan CR, Aktaş M, İçten BM, Failure behavior of laminated composite plates with two serial pin-loaded holes, Composite Structures, 82(2). 225-234. January 2008.
[33]   | Karakuzu R, Taylak N, İçten BM, Aktaş M, Effects of geometric parameters on failure behavior in laminated composite plates with two parallel pin-loaded holes, Composite Structures, 85(1). 1-9. September 2008.
[34]   | Karakuzu R, Gülem T, I ten BM, Failure analysis of woven laminated glass-vinylester composites with pin-loaded hole, Composite Structures, 72(1). 27-32. January 2006.
[35]   | Kelly G, Hallström S, Bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance, Composites Part B: Engineering, 35(4). 331-43. January 2004.
[36]   | Crews JH, Jr., Hong CS, Raju IS, Stress-concentration factors for finite orthotropic laminates with a pin-loaded hole, NASA Technical Paper 1862, 1-40. May1981.