Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure
Keywords:
crack simulation, probability analysis, irregular truss structure model, failure criteria, Monte Carlo simulationAbstract
The problems related to agricultural structure engineering for crack simulation and reliability analysis are complicated because its variables contain wide ranges of mean and standard deviation. This paper describes an integrated model to perform crack simulation and reliability analysis of a continuum structure. The structure is assumed to be under a two-dimensional plane stress and the deformation is infinitesimal. A truss structure model that has the same behaviour as a continuum structure was developed using irregular triangle truss components where each element consists of two hinges with an axial degree of freedom at both of their ends. A Monte-Carlo simulation (MCS) was adopted for the reliability analysis. If the length of one side of the irregular triangle mesh is shorter than the thickness of the structure, the slenderness associated with compressive failure needs to be examined only for the short column. For that reason, the failure criterion suitable for the equivalent truss structure model was established by checking only axial stresses acting on truss members. Since nodes of the equivalent truss structure model for the structural analysis in this study consist of hinges, development of plastic hinges that occurred during crack propagation were not considered in this model. To simulate the development of crack, truss members over allowable stresses of tension or compression among truss members with the largest amount of stress at each completed structural analysis time step were sequentially removed. Since irregular triangle meshes have an uncertainty in themselves to compare with regular meshes, the equivalent truss structure model could describe crack propagation more realistically. The failure probabilities of structures under various loads and boundary conditions had good agreement with the analytical solutions directly solved from the limit state equations expressed in the form of moments. Keywords: crack simulation, probability analysis, irregular truss structure model, failure criteria, Monte Carlo simulation DOI: 10.3965/j.ijabe.20171001.2024 Citation: Choi W, Yoon S, Lee J. Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure. Int J Agric & Biol Eng, 2017; 10(1): 234–247.References
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[36] Corotis R B, Nafday A M. Structural system reliability using linear programming and simulation. J. Struct. Eng., ASCE, 1989; 115(10): 2435–2447.
[37] Kim D. Matrix-based system reliability analysis using the dominant failure mode search method. PhD dissertation. Seoul, South Korea: Seoul National University, 2009, 2.
[38] Melchers R E. Structural reliability, analysis and prediction. West Suxess, England: Ellis Horwood, 1987.
[39] Box G E P, Muller M E. A note on the generation of random normal deviates. Ann. Math. Stat., 1958; 29(2): 610–611.
[40] Gálvez J C, Elices M, Guinea G V, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. Int. J. Fracture, 1998; 94(3): 267–284.
[41] Griffith A A. The phenomena of rupture and flow in solids. Philos. T. R. Soc. Lond., 1920; 221: 163–198.
[42] Griffith A A. The Theory of rupture. Proc. 1th Intl. Congr. Applied Mechanics. New York, NY: John Wiley & Sons, Inc, 1924.
[43] Irwin G R. Fracture mechanics. Proc. the 1th Sym. Naval Structural Mechanics. Elmsford, NY: Pergamon Press, 1956.
[2] Park R, Paulay T. Reinforced concrete structures. New York, NY: John Wiley and Sons, 1975.
[3] Corotis R B. Probability-based design codes. Concr. Int., 1985; 7(4): 42–49.
[4] Hasofer A M, Lind N C. Exact and invariant second-moment code format. J. Eng. Mech. Div., ASCE, 1974; 100(1): 111–121.
[5] Cornell C A. Bounds on the reliability of structural systems. J. Struct. Div., ASCE, 1967; 93(1): 171–00.
[6] Freudenthal A M. Safety and the probability of structural failure. T. ASCE, 1956; 121(1): 1337–1397.
[7] Shinozuka M. Basic analysis of structural safety. J. Struct. Div., ASCE, 1983; 109(3): 721–740.
[8] Rackwitz R, Fiessler B. Note on discrete safety checking when using non-normal stochastic models for basic variables. Loads Project Working Session. Cambridge, MA: MIT. 1976.
[9] Rackwitz R, Fiessler B. Structural reliability under combined random load sequences. Comput. Struct., 1978; 9(5): 489–494.
[10] Hohenbichler M, Rackwitz R. Non-normal dependent vectors in structural safety. J. Eng. Mech. Div., ASCE, 1981; 107(6): 1227–1238.
[11] Rosenblatt M. Remarks on a multivariate transformation. Ann. Math. Stat., 1952; 23(3): 470–472.
[12] Fiessler B, Rackwitz R, Neumann H J. Quadratic limit states in structural reliability. J. Eng. Mech. Div., ASCE, 1979; 105(4): 661–676.
[13] Breitung K. Asymptotic approximations for multinormal integrals. J. Eng. Mech. Div., ASCE, 1984; 110(3): 357–366.
[14] Madsen H O, Krenk S, Lind N C. Methods of structural safety. Englewood Cliffs, NJ: Prentice-Hall, Inc. 1986.
[15] Tvedt L. Two second-order approximations to the failure probability. Section on Structural Reliability. Hovik, Norway: A/S Vertas Research. 1984.
[16] Tvedt L. On the probability content of a parabolic failure set in a space of independent standard normally distributed random variables. Section on Structural Reliability. Hovik, Norway: A/S Vertas Research. 1985.
[17] Kiureghian A D, Lin H Z, Hwang S J. Second-order reliability approximations. J. Eng. Mech. Div., ASCE, 1986; 113(8): 1208–1225.
[18] Lee J. Reliability analysis modeling of frame structures based on discretized ideal plastic method. PhD dissertation. Seoul, South Korea: Seoul National University, 1991, 2.
[19] Park S. System reliability analysis of reinforced concrete frames. PhD dissertation. Seoul, South Korea: Seoul National University, 1992, 2.
[20] Yang Y, Kim J. Probabilistic finite element analysis of plane frame. J. Comput. Struct. Eng. Inst. Korea, 1989; 2(4): 89–98.
[21] Handa K, Anderson K. Application of finite element methods in stochastic analysis of structures. Proc. 3rd Intl. Conf. Structural Safety and Reliability. New York, NY: IASAR. 1981.
[22] Ang A H-S, Amin M. Studies of probabilistic safety analysis of structures and structural systems. Urbana, IL: University of Illinois. 1967.
[23] Ishizawa J. On the reliability of indeterminate structural systems. PhD dissertation. Urbana, IL: University of Illinois, 1968.
[24] Stevenson J, Moses F. Reliability analysis of frame structures. J. Struct. Div., ASCE, 1970; 96(11): 2409–2427.
[25] Gorman M. Automatic generation of collapse mode equation. J. Struct. Div., 1981; 107(7): 1350–1354.
[26] Ma H-F, Ang A H-S. Reliability analysis of redundant ductile structural systems. Urbana, IL: University of Illinois. 1981.
[27] Moses F. System reliability developments in structural engineering. Struct. Saf., 1982; 1(1): 3–13.
[28] Moses F, Stahl B. Reliability analysis format for offshore structures. Proc. the 10th Ann. Offshore Technology Conference. Houston, TX: OTC. 1978.
[29] Murotsu Y, Okada H, Taguchi K, Grimmelt M, Yonezawa M. Automatic generation of stochastically dominant failure modes of frame structures. Struct. Saf., 1984; 2(1): 17–25.
[30] Thoft-Christensen P, Murotsu Y. Application of structural systems reliability theory. New York, NY: Springer-Verlag. 1986.
[31] Ditlevsen O, Bjerager P. Reliability of highly redundant plastic structures. J. Eng. Mech., ASCE, 1984; 110(5): 671–693.
[32] Grimmelt M, Schueller G I. Benchmark study on methods to determine collapse failure probabilities of redundant structures. Struct. Saf., 1982; 1(2): 93–106.
[33] Melchers R E. Structural system reliability assessment using directional simulation. Struct. Saf., 1994; 16(1-2): 23–37.
[34] Moses F, Fu G. Important sampling in structural system reliability. Proc. the 5th ASCE-EMD/GTD/STD Specialty Conf. Probabilistic Mechanics. Reston, VA: ASCE. 1988.
[35] Rashedi M R. Studies on reliability of structural systems. PhD dissertation. Cleveland, OH: Case Western Reserve University, 1984.
[36] Corotis R B, Nafday A M. Structural system reliability using linear programming and simulation. J. Struct. Eng., ASCE, 1989; 115(10): 2435–2447.
[37] Kim D. Matrix-based system reliability analysis using the dominant failure mode search method. PhD dissertation. Seoul, South Korea: Seoul National University, 2009, 2.
[38] Melchers R E. Structural reliability, analysis and prediction. West Suxess, England: Ellis Horwood, 1987.
[39] Box G E P, Muller M E. A note on the generation of random normal deviates. Ann. Math. Stat., 1958; 29(2): 610–611.
[40] Gálvez J C, Elices M, Guinea G V, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. Int. J. Fracture, 1998; 94(3): 267–284.
[41] Griffith A A. The phenomena of rupture and flow in solids. Philos. T. R. Soc. Lond., 1920; 221: 163–198.
[42] Griffith A A. The Theory of rupture. Proc. 1th Intl. Congr. Applied Mechanics. New York, NY: John Wiley & Sons, Inc, 1924.
[43] Irwin G R. Fracture mechanics. Proc. the 1th Sym. Naval Structural Mechanics. Elmsford, NY: Pergamon Press, 1956.
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2017-01-23
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Choi, W., Yoon, S., & Lee, J. (2017). Crack simulation and probability analysis using irregular truss structure modeling equivalent to a continuum structure. International Journal of Agricultural and Biological Engineering, 10(1), 234–247. Retrieved from https://ijabe.migration.pkpps03.publicknowledgeproject.org/index.php/ijabe/article/view/2024
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Structures and Bio-environmental Engineering
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