Determination of the Effective Parameters for Perforated Functionally Graded Plates with Polygonal Cutout by Analytical Solution
الموضوعات :M Jafari 1 , M. H Bayati Chaleshtari 2 , H Abdolalian 3
1 - Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran
2 - School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran
3 - Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran
الکلمات المفتاحية: Polygonal cutout, Functionally graded plate, Stress resultants and moments, Analytical solution, Complex-variable method,
ملخص المقالة :
This paper investigates the moments and stress resultants from infinite FG laminates with different polygonal cutouts subject to uniaxial tensile load. The analytical solution used for the calculation of stress resultants and moments is the basis of the complex-variable method and conformal mapping function. The impact of various factors, namely cutout orientation angle, cutout aspect ratio as well as the cutout corner curve on stress distribution and moment resultants is studied. The effect of the aforementioned parameters around triangular, square, pentagonal and hexagonal cutout is analyzed. The mechanical characteristics of the graded plates are hypothesized to vary throughout the thickness exponentially. Finite element numerical solution is employed to examine the results of the present analytical solution. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes.
[1] Muskhelishvili N.,1954, Some Basic Problems of the Mathematical Theory of Elasticity, Dordrecht, Springer, Netherlands.
[2] Savin G.N.,1961, Stress Concentration Around Holes, Pregamon Press.
[3] Lekhnitskiy S.G.,1969, Anperforated Plates, New York, Gordon-Breach Science.
[4] Sharma D. S., 2012, Stress distribution around polygonal cutouts, International Journal of Mechanical Sciences 65(1): 115-124.
[5] Sharma D.S., 2014, Moment distribution around polygonal cutouts in infinite plate, International Journal of Mechanical Sciences 78: 177-182.
[6] Rezaeepazhand J., Jafari M.,2010, Stress concentration in metallic plates with special shaped cutout, International Journal of Mechanical Sciences 52(1): 96-102.
[7] Ukadgaonker V.G., Rao D.K.N., 2000, A general solution for stress resultants and moments around cutouts in unsymmetric laminates, Composite Structures 49(1): 27-39.
[8] Bayati Chaleshtari M.H., Jafari M., 2017, Optimization of finite plates with polygonal cutout under in-plane loading by gray wolf optimizer, The Journal of Strain Analysis for Engineering Design 52(6): 365-379.
[9] Jafari M., Bayati Chaleshtari M.H., 2017, Optimum design of effective parameters for orthotropic plates with polygonal cut-out, Latin American Journal of Solid and Structure 14(5): 906-929.
[10] Jafari M., Moussavian H., Bayati Chaleshtari M.H., 2018, Optimum design of perforated orthotropic and laminated composite plates under in-plane loading by genetic algorithm, Structural and Multidisciplinary Optimization 57(1): 341-357.
[11] Yang Q., Gao C.-F., Chen W., 2012, Stress concentration in a finite functionally graded material plate, Science China Physics, Mechanics and Astronomy 55(7): 1263-1271.
[12] Sharma D.S., 2011, Stress concentration around circular / elliptical / triangular cutouts in infinite composite plate, Proceedings of the World Congress on Engineering.
[13] Pan E., 2003, Exact solution for functionally graded anisotropic elastic composite laminates, Journal of Composite Materials 37(21): 1903-1920.
[14] Reid R., Paskaramoorthy R., 2011, An extension to classical lamination theory for use with functionally graded plates, Composite Structures 93(2): 639-648.
[15] Uymaz B., Aydogdu M., 2013, Three dimensional mechanical buckling of FG plates with general boundary conditions, Composite Structures 96:174-193.
[16] Batra R.C., Nie G.J., 2010, A analytical solutions for functionally graded incompressible eccentric and non-axisymmetrically loaded circular cylinders, Composite Structures 92(5): 1229-1245.
[17] Dave J.M., Sharma D.S., 2016, Stresses and moments in through-thickness functionally graded plate weakened by circular/elliptical cut-out, International Journal of Mechanical Sciences 105: 146-157.
[18] Chien R.D., Lin C.Y., Chen C.S., 2011, Thermally induced buckling of functionally graded hybrid composite plates, International Journal of Mechanical Sciences 53: 51-58.
[19] Joshi P.V., Gupta A., Jain N.K., Salhotra R., Rawani A.M., Ramtekkar G.D., 2017, Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff’s plate theory: An analytical approach, International Journal of Mechanical Sciences 132: 155-170.
[20] Jafari M., Ashoori H.S., 2015, Studying the effect of different parameters on stress resultant and moments distribution around non-circular cutouts in unsymmetric laminates, ZAMM - Journal of Applied Mathematics and Mechanics 97(10): 1317-1330.
[21] Jafari M., Bayati Chaleshtari M.H., Ardalani E., 2018, Determination of optimal parameters for finite plates with a quasi-square hole , Journal of Solid Mechanics 10(2): 300-314.
[22] Bayati Chaleshtari M.H., Jafari M., 2017, Using dragonfly algorithm for optimization of orthotropic infinite plates with a quasi-triangular cut-out, European Journal of Mechanics A/Solids 66(1): 1-14.
[23] Nirwal S., Sahu S.A., Baroi J., Singh A., 2019, Analysis of different boundary types on wave velocity in bedded piezo-structure with flexoelectric effect, Composites Part B: Engineering 167: 434-447.
[24] Sahu S.A., Singhal A., Chaudhary S., 2017, Surface wave propagation in functionally graded piezoelectric material: An analytical solution, Journal of Intelligent Material Systems and Structures 29(3): 423-437.
[25] Singhal A., Sahu S.A., Chaudhary S., 2018, Approximation of surface wave frequencyin piezo-composite structure, Composites Part B: Engineering 144: 19-28.
[26] Singhal A., Sahu S.A., Chaudhary S., 2017, Liouville-green approximation: an analytical approach to study the elastic waves vibrations in composite structure of piezo material, Composite Structures 184: 714-727.
[27] Chaudhary S., Sahu S.A., Singhal A., 2017, Analytic model for Rayleigh wave propagation in piezoelectric layer overlaid orthotropic substratum, Acta Mechanica 228(2): 495-529.
[28] Singh M.K., Sahu S.A., Singhal A., Chaudhary S., 2018, Approximation of surface wave velocity in smart composite structure using Wentzel–Kramers–Brillouin method, Journal of Intelligent Material Systems and Structures 29(18): 3582-3597.
[29] Chaudhary S., Sahu S.A., Dewangan N., Singhal A., 2018, Stresses produced due to moving load in a prestressed piezoelectric substrate, Mechanics of Advanced Materials and Structures 26(12): 1028-1041.
[30] Chaudhary S., Sahu S.A., Singhal A., 2018, On secular equation of SH waves propagating in pre-stressed and rotating piezo-composite structure with imperfect interface, Journal of Intelligent Material Systems and Structures 29(10): 2223-2235.