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Meshfree Approach for the Torsional Analysis of Orthotropic and FGM Thin-Walled Open Sections | ||
| Mechanics of Advanced Composite Structures | ||
| مقاله 13، دوره 12، شماره 3 - شماره پیاپی 26، بهمن 2025، صفحه 629-644 اصل مقاله (4.67 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22075/macs.2025.34565.1692 | ||
| نویسندگان | ||
| Ram Bilas Prasad* 1؛ Rahul Kumar2؛ Jeeoot Singh1 | ||
| 1Department of Mechanical Engineering, Madan Mohan Malaviya University of Technology, Gorakhpur, U.P., 273010, India | ||
| 2Department of Mechanical Engineering, DDU Gorakhpur University, India | ||
| تاریخ دریافت: 05 تیر 1403، تاریخ بازنگری: 16 دی 1403، تاریخ پذیرش: 19 بهمن 1403 | ||
| چکیده | ||
| The torsional study of different engineering sections made up of orthotropic and functionally graded material is presented in this paper. Prandtl’s stress function approach is used for the formulation of governing differential equations. Thin plate spline (TPS) radial basis function-based collocation meshfree method is utilized for discretization and solution of the governing differential equations. A classical power law is considered for the modeling of FGM material. A computer program is developed for the solution of the discretized partial differential equations. To assess the efficacy and accuracy of the present mesh-free approach, a numerical example of an equilateral triangle is considered to conduct a convergence and accuracy test. Finally, the torsional stiffness and shear stress for the orthotropic and FGM sections of the equilateral triangle, L-section, and T-sections are computed. The novelty in the present meshfree methodology lies in the handling of the singular behavior of re-entrant corners. The effect of stress concentration can be seen at the re-entrant corners. The proposed methodology shows excellent performance in solving these types of torsion problems. | ||
| کلیدواژه‌ها | ||
| Torsion؛ RBF؛ FGM؛ Orthotropic؛ T-Shape؛ Triangular؛ L-Shape | ||
| مراجع | ||
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[1] Timoshenko S, Goodier JN., 1970. Theory of Elasticity. 3rd ed. McGraw-Hill Book Company. [2] Muskhelishvili NI., 1977. Some basic problems of the mathematical theory of Elasticity. 2nd ed. Springer-Science+ Business Media, B.V. [3] Boresi AP, Schmidt RJ., 2003. Advanced Mechanics of Materials. 6th ed. John Wiley & Sons, Inc. [4] Sadd MH., 2014. Elasticity. 3rd ed. Elsevier Academic Press. [5] Chen Y., 1964. Torsion of nonhomogeneous bars. J Franklin Inst, 277, pp 50–4. [6] Ely JF., Zienkiewicz OC., 1960. Torsion of Compound Bars- A Relaxation Solution. Int J Mech Sci,1, pp. 356–365. [7] Franců J, Nováčková P, Janíček P, 2012. Torsion of a Non-Circular Bar. Eng Mech;19, pp. 45–60. [8] Angelo Danao LM., Cabrera RM., 2007. Torsion of a rectangular prismatic bar: Solution using a power fit model. Philipp Eng J., 28, pp. 77–98. [9] Tarn JQ, Chang HH., 2008. Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects. Int J. Solids Struct, 45, pp. 303–319. [10] Rooney FJ, Ferrari M., 1995. Torsion and flexure of inhomogeneous elements. Compos Eng., 5, pp. 901–911. [11] Swanson SR., 1998. Torsion of laminated rectangular rods. Compos Struct., 42, pp. 23–31. [12] Savoia M., Tullini N., 1993. Torsional response of inhomogeneous and multilayered composite beams. Compos Struct., 25, pp. 587–594. [13] Rongqiao X, Jiansheng H, Weiqiu C., 2010. Saint-Venant torsion of orthotropic bars with inhomogeneous rectangular cross section. Compos Struct., 92, pp. 1449–1457. [14] Arghavan S., Hematiyan MR., 2009. Torsion of functionally graded hollow tubes. Eur J. Mech A/Solids, 28, pp. 551–559. [15] Ecsedi I., 2009. Some analytical solutions for Saint-Venant torsion of non-homogeneous cylindrical bars. Eur J Mech A/Solids, 28, pp. 985–990. [16] Krahula J.L., Lauterbach G.F., 1969. Finite Element Solution for Saint-Venant Torsion. AIAA J., 7, pp. 2200–2203. [17] Li Z, Ko JM, Ni YQ., 2000. Torsional rigidity of reinforced concrete bars with arbitrary sectional shape. Finite Elem. Anal. Des., 35, pp. 349–361. [18] Saygun A., Omurtag MH, Orakdogen E., Girgin K., Kucukarslan S., Darilmaz K., 2007. A simplified solution of the torsional rigidity of the composite beams by using FEM. Adv. Struct. Eng., 10, pp. 467–473. [19] Jog CS., Mokashi IS., 2014. A finite element method for the Saint-Venant torsion and bending problems for prismatic beams. Comput. Struct., 135, pp. 62–72. [20] Abdelkader K., Toufik Z., Mohamed BJ., 2015. Torsional stress in non-circular cross sections by the finite element method. Adv. Mech. Eng., 7, pp. 1–20. [21] Beheshti A., 2018. A numerical analysis of Saint-Venant torsion in strain-gradient bars. Eur. J. Mech. A/Solids, 70, pp. 181–190. [22] Tsiatas GC., Babouskos NG., 2017. Elastic-plastic analysis of functionally graded bars under torsional loading. Compos. Struct., 176, pp. 254–267. [23] Darılmaz K., Orakdö E. and Girgin, K., 2018. Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach. Acta Mechanica, 229, pp. 1387–1398. [24] Ecsedi I., Baksa A., 2019. Saint-Venant torsion of cylindrical orthotropic elliptical cross section. Mech. Res. Commun.,99, pp. 42–46. [25] Horgan CO., Chan AM., 1998. Torsion of functionally graded isotropic linearly elastic bars. J. Elast., 52, pp. 181–199. [26] Horgan C.O., 2007. On the torsion of functionally graded anisotropic linearly elastic bars. IMA Journal of Applied Mathematics, 72(5), pp. 556–562. [27] Sapountzakis EJ., 2001. Nonuniform torsion of multi-material composite bars by the boundary element method. Comput. Struct., 79, pp. 2805–2816. [28] Katsikadelis JT., Tsiatas GC., 2016. Saint - Venant Torsion of Non - homogeneous Anisotropic Bars. J. Appl. Comput. Mech., 2, pp. 42–53. [29] Nikmehr O., Lashkarbolok M., 2019. A Numerical Investigation on the Torsional Rigidity of Bars with Functionally Graded Material (FGM) Cross Sections Weakened by Cracks. Iran. J. Sci. Technol. – Trans. Civ. Eng., 43, pp. 117–123. [30] Gorzelańczyk P., 2010. Method of fundamental solutions and random numbers for the torsion of bars with multiply connected cross sections. Computer Assisted Methods in Engineering and Science, 17(2/3/4), pp. 99–112. [31] Hassenpflug W.C., 2003. Torsion of Uniform Bars with Polygon Cross-Section. Comput. Math. with Appl., 46, pp 313–392. [32] Kołodziej J.A., Gorzelańczyk P., 2012. Application of method of fundamental solutions for elasto-plastic torsion of prismatic rods. Eng. Anal. Bound. Elem., 36, pp 81–86. [33] Chen H., Gomez J., Pindera M.J., 2020. Saint Venant’s torsion of homogeneous and composite bars by the finite volume method. Compos. Struct. ,242, pp. 112–128. [34] Ferreira AJM., 2004. Polyharmonic (thin-plate) splines in the analysis of composite plates. Int. J. Mech. Sci.,46, pp. 1549–1569. [35] Liu G.R., 2009. Mesh Free Methods: Moving beyond the finite element method. 2nd ed. CRC Press. [36] Hardy RL., 1971. Multiquadric Equations of Topography and Other Irregular Surfaces. J. Geophys. Res.,76, pp. 1905–1915. [37] Bui T.Q., Nguyen M.N., Zhang C., 2011. An efficient meshfree method for vibration analysis of laminated composite plates. Comput. Mech. ,48(2), pp. 175–193. [38] Bui T.Q., Nguyen M.N., 2013. Meshfree Galerkin Kriging model for bending and buckling analysis of simply supported laminated composite plates. Int. J. Comput. Methods., 10, pp. 1350011. [39] Bui T.Q., Khosravifard A., Zhang C., Hematiyan M.R., Golub M.V., 2013. Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method. Eng. Struct., 47, pp. 90–104. [40] Mukhtar FM, Al-Gahtani HJ., 2016. Application of radial basis functions to the problem of elasto-plastic torsion of prismatic bars. Appl Math Model,40, pp 436–50. [41] Solanki M.K., Mishra S.K., Singh J., 2016. Meshfree approach for linear and nonlinear analysis of sandwich plates: A critical review of twenty plate theories. Eng. Anal. Bound. Elem., 69, pp. 93–103. [42] Liew K.M., Zhao X., Ferreira A.J.M., 2011. A review of meshless methods for laminated and functionally graded plates and shells. Compos. Struct., 93, pp. 2031–2041. [43] Ferreira A.J.M., 2005. Free Vibration Analysis of Timoshenko Beams and Mindlin Plates by Radial Basis Functions. Int. J. Comput. Methods, 02, pp. 15–31. [44] Ferreira A.J.M., Roque C.M.C., Jorge R.M.N., 2005. Analysis of composite plates by trigonometric shear deformation theory and multiquadrics. Comput. Struct., 83, pp. 2225–2237. [45] Fasshauer G.E., 1997. Solving Partial Di erential Equations by Collocation with Radial Basis Functions. Construction, 93, pp. 1–8. [46] Fasshauer G.E., 1999. Solving differential equations with radial basis functions: Multilevel methods and smoothing. Adv. Comput. Math., 11, pp. 139–159. [47] Franke C., Schaback R., 1998. Solving partial differential equations by collocation using radial basis functions. Appl. Math. Comput.,93, pp. 73–82. [48] Singh J., Shukla K.K., 2012. Nonlinear flexural analysis of laminated composite plates using RBF based meshless method. Compos. Struct., 94, pp. 1714–1720. [49] Singh J., Shukla K.K., 2012. Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method. Engineering Analysis with Boundary Elements, 36(12), pp. 1819–1827. [50] Shukla V., Singh J., 2020. Modeling and analysis of cross-ply and angle-ply laminated plates under patch loads using RBF based meshfree method and new HSDT. Comput. Math. with Appl., 79, pp. 2240–2257. [51] Shukla V., Singh J., 2020. Buckling behavior of rectangular angle-ply laminated composite plates subjected to thermal and mechanical loads using the meshfree method. Int. J. Comput. Mater. Sci. Eng., 09, pp. 2050021. [52] Skyciv Section Builder Software, 2021. Skyciv Platform. | ||
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