QUANTIFICAÇÃO DA INCERTEZA DA VIDA DE PLACAS DE AÇO SOB À FADIGA VIA POLINÔMIOS DE HERMITE
DOI:
https://doi.org/10.26512/ripe.v2i16.21626Keywords:
Polinômio de Hermite Multidimensional. Fadiga. Quantificação da incerteza. Metodologia deformação-vida.Abstract
O objetivo deste trabalho é quantificar a incerteza no número de ciclos para falha por fadiga de componentes entalhados por meio do uso de polinômios de Hermite multidimensionais. A metodologia deformação-vida de estimativa de vida à fadiga é adotada e considera-se como variáveis aleatórias as propriedades do material e os níveis do carregamento aplicado. O uso de séries de polinômios de Hermite multidimensionais permitiu a predição da aleatoriedade do vetor de saída (número de ciclos para falha). Demonstra-se que um polinômio de Hermite multidimensional é capaz de estimar de forma adequada a propagação das incertezas associadas à s variáveis de entrada. Os resultados sugerem que incertezas nas propriedades do material e no carregamento podem resultar em variações significativas no número de ciclos para falha de componentes sujeitos à falha por fadiga.
References
Adomian, G. (1980). Applied Stochastic Processes. First. Vol. 1. New York: Academic Press.
Bannantine, J., J. Comer e J. Handrock (1989). Fundamentals of metal fatigue analysis. New York, State United: Prentice Hall.
Berveiller, M., B. Sudret e M. Lemaire (2006). “Stochastic finite elements a non-intrusive approach by regression”. Em: European Journal of Computational Mechanics 15.1-3, pp. 81”“92.
Blatman, G. (2009). “Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis”. Mestrado em Engenharia Civil. Clermont-Ferrand: Universite Blaise Pascal, p. 222.
Blatman, G. e B. Sudret (2008). “Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach”. Em: Comptes Rendus MÃl’canique 336.6, pp. 518”“523.
”” (2010). “An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis”. Em: Probabilistic Engineering Mechanics 25.2, pp. 183”“197.
”” (2011). “Adaptive sparse polynomial chaos expansions based on Least Angle Regression”. Em: Journal Computational Physics 230.6, pp. 2345”“2367.
Doll, J. e D. Freeman (1986). “Randomly Exact Methods”. Em: Science 234.4782, pp. 1356”“ 1360.
Ghanem, R.G. e P.D. Spanos (2003). Stochastic Finite Elements: A Spectral Approach. United State: Dover Publications.
Ghiocel, D. e R. Ghanem (2002). “Stochastic Finite Element Analysis of Seismic Soil Structure Interaction”. Em: Journal Eng. Mechanics 128.1, pp. 66”“77.
Hosder, S. e R.Walters (2010). “Non-Intrusive polynomial chaos methods for uncertainty quantification influid dynamics”. Em: 48th AIAA Aerospace sciences meeting including the new horizons forum e aerospace exposition. Orlando, USA.
Huang, S., B. Liang e K. Phoon (2009). “Geotechnical probabilistic analysis by collocation based stochastic response surface method an EXCEL add in implementation”. Em: Georisk 3.2, pp. 75”“86.
Iman, R. e W. Conover (1980). “Small Sample Sensitivity Analysis Techniques for Computer Models, with an Application to Risk Assessment”. Em: Communications in Statistics-Theory and Methods 9.17, 1749â˘A ¸S1842.
Isukapalli, S. S. (1999). “Uncertainty Analysis of Transport Transformation Models”. PhD thesis. New Jersey, United State: The State University of New Jersey, p. 141.
Keese, A. e H. Matthies (2005). “Hierarchical parallelisation for the solution of stochastic finite element equations”. Em: Journal Computers and Structures 83.14.
Le-Maitre, O.P. e O.M. Knio (2010). Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. London, UK: Springer.
Maitre, O. et al. (2001). “A stochastic projection method for fluid flow I basic formulation”. Em: Journal of Computational Physics 173.3, pp. 481”“511.
Morrow, J. (1965). “Cyclic plastic strain energy and fatigue of metals”. Em: ASTM STP 378.1.1, p. 45.
Neuber, H. (1961). “Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress-strain law”. Em: Journal of applied mechanics 28.1, pp. 544”“550.
Papoulis, A. (1991). Probability, Random Variables, and Stochastic Processes. First. Vol. 1. New York: McGraw-Hill.
Phoon, K.K. e S.P. Huang (2007). “Uncertainty Quantification Using Multi-Dimensional Hermite Polynomials, ASCE 2007, pp. 1?10.” Em: J. ASCE 1.1, pp. 1”“10.
S-K. Choi, R. Grandhi e R. Canfield (2007). Reliability-based structural design. London: Springer.
Socie, D., N. Dowling e P. Kuranth (1984). “Fatigue life estimation of notched members”. Em: ASTM STP 833 833.1, pp. 284”“299.
Sudret, B. (2007). “Uncertainty propagation and sensitivity analysis in mechanical models : Contributions to structural reliability and stochastic spectral methods”. PhD thesis. Clermont Ferrand, France: UniversitÃl’ Blaise Pascal, p. 173.
Sudret, B. e A. Der-Kiureghian (2000). Stochastic Finite Elements and Reliability: A State of the Art Report. Rel. téc. University of California, Berkeley.
Tatang, M. (1995). “Direct Incorporation of Uncertainty in Chemical and Environmental Engineering Systems”. PhD thesis. Cambridge, MA: Massachusetts Institute of Technology, p. 141.
Villadsen, J. e M. Michelsen (1978). Solution of differential equation models by polinomial approximation. Englewood Cliffs, NJ.: Prentice-Hall.
Webster, M., M. Tatang e G. McRae (1996). Application of the Probabilistic Collocation Method for an Uncertainty Analysis of a Simple Ocean Model. Rel. téc. MIT Joint Program on the Science e Policy of Global Change Reports Series No. 4, Massachusetts institute of Technology.
Xiu, D. (2009). “Fast Numerical Methods for Stochastic Computations A Review”. Em: Communications in Computational Physics 5.2-4, pp. 242”“272.
”” (2010). Numerical Methods for Stochastic Computations. New Jersey: Princeton University Press.
Xiu, D e J S Hesthaven (2005). “High Order Collocation Methods for Differential Equations with Random Inputs”. Em: SIAM J. Sci. Comput. 27.3, pp. 1118”“1139.
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