Characterization of Stress Concentration in Thin Cylindrical Shells with Rectangular Cutout Under Axial Pressure

ADMT Journal

مقاله 13، دوره 10، شماره 2، شهریور 2017، صفحه 133-141   

نوع مقاله: Original Article

نویسندگان

O. Sam Daliri¹؛ M. Farahani^{* 2}

¹School of Mechanical Engineering, College of engineering, University of Tehran, Tehran, Iran

²School of Mechanical Engineering, College of engineering, University of Tehran, Tehran, Iran

چکیده

In this paper, stress concentration in the thin cylindrical shell with rectangular cutout subjected to uniform axial pressure was investigated using a parametric finite element model. Design of experiments techniques and statistical analysis was used to provide a model for characterizing the critical stress in these components. The influences of the geometrical parameters and their combinations were studied in detail. It was observed that the length to width ratio of the cutout, the length and the radius to thickness ratio of the cylinder were significant parameters for describing the stress concentration around the cutout, respectively. By increasing the length to width ratio as a main effective geometrical factor in the stress concentration, the stress around the cutout was increased significantly. Based on the statistical analysis conducted in this study, a formula was derived which can predict the stress concentration around the cutout of the cylinder with the accuracy more than 84% (R2 = 88.7%, R2pred = 84.6%, R2adj= 86.7%).

کلیدواژه‌ها

Finite Element Method؛ Statistical Analysis؛ Stress concentration؛ Thin cylindrical shell؛ Rectangular Cut-out

مراجع

[1]     Ghanbari Ghazijahani, T., Jiao, H., and Holloway, D., “Structural behavior of Shells with Different Cut-outs under Compression: An Experimental Study”, Journal of Constructional Steel Research, Vol. 105, 2015, pp. 129-137.

[2]     Han, H., Cheng, J., Taheri, F., and Pegg, N., “Numerical and Experimental Investigations of the Response of Aluminum Cylinders with a Cut-out Subject to Axial Compression”, Thin-Walled Structures, Vol. 44, 2006, pp. 254-270.

[3]     Naghdi, A. K.. Gersting, J. M., Jr., “The Effect of a Transverse Shear Acting on the Edge of a Circular Cut-out in a Simply Supported Circular Cylindrical Shell”, Ingenieur-Archiv, Vol. 42, 1973, pp. 141-150.

[4]     Aliabadi, M., Rooke, D., and Cartwright, D., “An Improved Boundary Element Formulation for Calculating Stress Intensity Factors: Application to Aerospace Structures”, The Journal of Strain Analysis for Engineering Design, Vol. 22, 1987, pp. 203-207.

[5]     Theocaris, P., Petrou, L., “From the Rectangular Hole to the Ideal Crack”, International journal of Solids and Structures, Vol. 25, 1989, pp. 213-233.

[6]     Folias, E., Wang, J.-J., “On the Three-Dimensional Stress Field Around a Circular Hole in a Plate of Arbitrary Thickness”, Computational Mechanics, Vol. 6, 1990, pp. 379-391.

[7]     Lasko, G., Deryugin, Y., Schmauder, S., and Saraev, D., “Determination of Stresses Near Multiple Pores and Rigid Inclusion by Relaxation Elements”, Theoretical and Applied Fracture Mechanics, Vol. 34, 2000, pp. 93-100.

[8]     Singh, A., Paul, U., “Finite Displacement Static Analysis of thin Plate with an Opening-a Variational Approach”, International Journal of Solids and Structures, Vol. 40, 2003, pp. 4135-4151.

[9]     Paik, J. K., “Ultimate Strength of Perforated Steel Plates under Edge Shear Loading”, Thin-Walled Structures, Vol. 45, 2007, pp. 301-306.

[10]  Rezaeepazhand, J., Jafari, M., “Stress Concentration in Metallic Plates with Special Shaped Cut-out”, International Journal of Mechanical Sciences, Vol. 52, 2010, pp. 96-102.

[11]  Woo, J.-H., Na, W.-B., “Effect of Cut-out Orientation on Stress Concentration of Perforated Plates with Various Cut-outs and Bluntness”, International Journal of Ocean System Engineering, Vol. 1, 2011, pp. 95-101.

[12] Rezaeepazhand, J., Jafari, M., “Stress Analysis of Composite Plates with a Quasi-square Cut-out Subjected to Uniaxial Tension”, Journal of Reinforced Plastics and Composites, 2009.

[13]  Pan, Z., Cheng, Y., and Liu, J., “Stress Analysis of a Finite Plate with a Rectangular Hole Subjected to Uniaxial Tension using Modified Stress Functions”, International Journal of Mechanical Sciences, Vol. 75, 2013, pp. 265-277.

[14] Rahimi, G., Alashti, R., “Plastic Limit Loads of Cylinders with a Circular Opening under Combined Axial Force and Bending Moment”, The Journal of Strain Analysis for Engineering Design, Vol. 42, 2007, pp. 55-66.

[15] Kalita, K., Shinde, D., and Haldar, S., “Analysis on Transverse Bending of Rectangular Plate”, Materials Today: Proceedings, Vol. 2, 2015, pp. 2146-2154.

[16] Thirumump, M., Kalita, K., Ramachandran, M., and Ghadai, R., “A numerical Study of SCF Convergence using ANSYS”, ARPN Journal of Engineering and Applied Sciences, Vol. 10, 2015.

[17] Kalita, K., Shinde, D., and Thomas, T. T., “Non-Dimensional Stress Analysis of an Orthotropic Plate”, Materials Today: Proceedings, Vol. 2, 2015, pp. 3527-3533.

[18] Santos, A., “Determination of Stress Concentration Factors on Flat Plates of Structural Steel”, in Journal of Physics: Conference Series, 2013, pp. 012035.

[19] Verri, F. R., Junior, J. F. S., de Faria Almeida, D. A., de Oliveira, G. B. B., de Souza Batista, V. E., Honório, H. M., et al., “Biomechanical Influence of Crown-to-Implant Ratio on Stress Distribution over Internal Hexagon Short Implant: 3-D finite Element Analysis with Statistical Test”, Journal of biomechanics,Vol. 48, 2015, pp. 138-145.

[20] Cerik, B. C., “Ultimate Strength of Locally Damaged Steel Stiffened Cylinders under Axial Compression”, Thin-Walled Structures, Vol. 95, 2015, pp. 138-151.

[21] Guoliang, J., Lin, C., and Jiamei, D., “Monte Carlo Finite Element Method of Structure Reliability Analysis”, Reliability Engineering & System Safety, Vol. 40, 1993, pp. 77-83.

[22] Narayana, A. L., Rao, K., and Kumar, R. V., “FEM Buckling Analysis of Quasi-Isotropic Symmetrically Laminated Rectangular Composite Plates with a Square/Rectangular Cut-out”, Journal of Mechanical Science and Technology, Vol. 27, 2013, pp. 1427-1435.

[23]  Vartdal, B., Al-Hassani, S., and Burley, S., “A Tube with a Rectangular Cut-out. Part 1: Subject to Pure Bending”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 220, 2006, pp. 625-643.

[24]  Lubarda, V. A., “On the Circumferential Shear Stress Around Circular and Elliptical Holes”, Archive of Applied Mechanics, Vol. 85, 2015, pp. 223-235.

[25]   Dimopoulos, C. A., Gantes, C. J., “Numerical Methods for the Design of Cylindrical Steel Shells with Unreinforced or Reinforced Cut-outs”, Thin-Walled Structures, Vol. 96, 2015, pp. 11-28.

[26]   Mazraehshahi, H. T., Zakeri, A., “Influence of Material and Geometrical Parameters on Stress Field of Composite Plates with Insert”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2011, pp. 1573-1582.

[27]  Kumar, A., Agrawal, A., Ghadai, R., and Kalita, K., “Analysis of Stress Concentration in Orthotropic Laminates”, Procedia Technology, Vol. 23, 2016, pp. 156-162.

[28]  Kalita, K., Halder, S., “Static Analysis of Transversely Loaded Isotropic and Orthotropic Plates with Central Cut-out”, Journal of the Institution of Engineers (India): Series C, Vol. 95, 2014, pp. 347-358.

[29]  ABAQUS 6.4 PR11 user’s manual.

[30] Fereidoon, A., Kolasangiani, K., Akbarpour, A., and Shariati, M., “Study on Buckling of Steel Cylindrical Shells with an Elliptical Cut-out under Combined Loading”, Journal of Computational & Applied Research in Mechanical Engineering (JCARME), Vol. 3, 2013, pp. 13-25.

[31] Jadvani, N., Dhiraj, V. S., Joshi, S., and Kalita, K., “Non-Dimensional Stress Analysis of Orthotropic Laminates”, Materials Focus, Vol. 6, 2017, pp. 63-71.

[32] Chaloner, K., Verdinelli, I., “Bayesian Experimental Design: A Review”, Statistical Science, 1995, pp. 273-304.

[33] Atkinson, A. C., “Optimal Experimental Design”, in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), J. D. Wright, Ed., ed Oxford: Elsevier, 2015, pp. 256-262.

[34] Graciano, C., Mendes, J., “Elastic Buckling of Longitudinally Stiffened Patch Loaded Plate Girders using Factorial Design”, Journal of Constructional Steel Research, Vol. 100, 2014, pp. 229-236.

[35]  Mason, R. L., Gunst, R. F., and Hess, J. L., “Statistical Design and Analysis of Experiments: with Applications to Engineering and Science”, Vol. 474, John Wiley & Sons, 2003.