Using Topology Optimization to Reduce Stress Concentration Factor in a Plate with a Hole

Document Type : Original Research Paper

Authors

Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran.

Abstract

This paper focuses on reducing stress concentration in a plate with a hole. For this purpose, a novel Reliever Topological Material Elimination (RTME) approach was introduced which uses the topology optimization technique to specify the best areas to remove material in order to refine flow of stress and reduce the Stress Concentration Factor (SCF), consequently. Using the Solid Isotropic Material with Penalization (SIMP) method, topology optimization was formulated. Three major elimination areas were determined from material elimination patterns observed in topology optimization. Two possible RTME cases were proposed numerically. To evaluate the efficiency of the method, finite element analyses were conducted for one previous technique and the results werediscussed. In addition, the results of finite element analysis were validated by some experimental tests. According to the final results, RTME approach gives up to 35.5% stress reduction, 44% SCF mitigation, and decrease about 28% of the initial volume. In comparison with the previous technique, using RTME is more effective in decreasing the SCF and weight of the plate, simultaneously. 

Keywords

References

[1] S. Nagpal, N. Jain, S. Sanyal, Stress concentration and its mitigation techniques in flat plate with singularities-a critical review, Eng. J., 16(1) (2012) 1-15.
[2] G.S. Giare, R. Shabahang, The reduction of stress concentration around the hole in an isotropic plate using composite materials, Eng. Fract. Mech., 32(5) (1989) 757-766.
[3] R. Sburlati, S.R. Atashipour, S.A. Atashipour, Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer, Compos. Part B: Eng., 61 (2014) 99-109.
[4] Q. Yang, C.F. Gao, Reduction of the stress concentration around an elliptic hole by using a functionally graded layer, Acta Mech., 227(9) (2016)2427-2437.
[5] A. Francavilla, C.V. Ramakrishnan, O. Zienkiewicz, Optimization of shape to minimize stress concentration, J. Strain Anal., 10(2) (1975) 63-70.
[6] Z. Wu, Optimal hole shape for minimum stress concentration using parameterized geometry models, Struct. Multidiscip. Optim., 37(6) (2009) 625-634.
[7] D.R. Shah, S.P. Joshi, W. Chan, Stress concentration reduction in a plate with a hole using piezoceramic layers, Smart Mater. Struct., 3(3) (1994) 302-308.
[8] D.R. Shah, S.P. Joshi, W. Chan, Static structural response of plates with piezoceramic layers, Smart Mater. Struct., 2(3) (1993) 172-180.
[9] J. Jafari Fesharaki, S.i. Golabi, Optimum pattern of piezoelectric actuator placement for stress concentration reduction in a plate with a hole using particle swarm optimization algorithm, Proceedings of the Institution of Mechanical Engineers,
Part C: J. Mech. Eng. Sci., 229(4) (2015) 614-628.
[10] P.E. Erickson, W.F. Riley, Minimizing stress concentrations around circular holes in uniaxially loaded plates, Exp. Mech., 18(3) (1978) 97-100.
[11] S.A. Meguid, Finite element analysis of defence hole systems for the reduction of stress concentration in a uniaxially-loaded plate with two coaxial holes, Eng. Fract. Mech., 25(4) (1986) 403-413.
[12] A.R. Othman, K.J. Jadee, M.Z. Ismadi, Mitigating stress concentration through defense hole system for improvement in bearing strength of composite bolted joint, Part 1: Numerical analysis, J. Compos. Mater., 51(26) (2017) 3685-3699.
[13] S. Nagpal, S. Sanyal, N. Jain, Mitigation curves for determination of relief holes to mitigate stress concentration factor in thin plates loaded axially for different discontinuities, Int. J. Eng. Innovative Technol., 2(3) (2012) 1-7.
[14] W.D. Pilkey, D.F. Pilkey, Peterson’s Stress Concentration Factors, John Wiley & Sons Publisher, Inc. (2007).
[15] W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, Seventh Edition McGraw-Hill Publisher, (2002).
[16] G.I.N. Rozvany, T. Lewiński, Topology Optimization in Structural and Continuum Mechanics, Springer Publisher, (2014).
[17] M.P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Compu. Methods Appl. Mech. Eng., 71(2) (1988) 197-224.
[18] M.P. Bendsoe, O. Sigmund, Topology Optimization: Theory, Methods, and Aplications, Springer Science and Business Media Publisher, (2013).
[19] M.H. Sadd, Elasticity: Theory, Applications, and Numerics, Academic Press, (2009).
[20] E. Lee, A Strain Based Topology Optimization Method, Rutgers University-Graduate SchoolNew Brunswick Publisher, (2011).
[21] M.P. Bendsoe, Optimal shape design as a material distribution problem, Struct. Optim., 1(4) (1989) 193-202.
[22] M. Zhou, G.I.N. Rozvany, The COC algorithm, Part II: Topological, geometrical and generalized shape optimization, Comput. Methods Appl. Mech. Eng., 89(1-3) (1991) 309-336.
[23] O. Sigmund, On the design of compliant mechanisms using topology optimization, J. Mech. Struct. Mech., 25(4) (1997) 493-524.
[24] A. Rietz, Sufficiency of a finite exponent in SIMP (power law) methods, Struct. Multidiscip. Optim., 21(2) (2001) 159-163.
[25] E. Lee, H.C. Gea, A strain based topology optimization method for compliant mechanism design, Struct. Multidiscip. Optim., 49(2) (2014) 199-207.
[26] S. Sanyal, P. Yadav, Relief holes for stress mitigation in infinite thin plates with single circular hole loaded axially, in ASME 2005 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, (2005).
[27] A. Standard, E8/E8M, 2009. Standard Test Methods for Tension Testing of Metallic Materials, ASTM international, West Conshohocken PA Publisher, (2009).
Journal of Stress Analysis
Volume 3, Issue 2
March 2019
Pages 109-116

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