Abstract
A robust design method based on fatigue for stochastic problems is proposed. In most cases, fatigue analyses of structures are performed by assuming the nominal values of their parameters in a deterministic way. However, since the systems are frequently subject to parametric uncertainty and random forces simultaneously, it does not provide a representative fatigue index. Thus, it becomes essential to consider these uncertainties on the fatigue models. Here, a plate stochastic finite element is used to formulate the probabilistic Sines’ index in frequency-domain, where the random fields are discretized using Karhunen-Loève expansion with hypercube sampling as stochastic solver. To maximize fatigue performance, a robust optimization combined with a robust reduction is proposed to increase the efficiency of the method. The envelopes of stresses and the Sines’ coefficients for optimized solutions confirm the importance of considering uncertainty on fatigue models for more realistic situations.
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Abbreviations
- M̅ :
-
Parameterized mass matrix
- K̅ :
-
Parameterized stiffness matrix
- K̅ m/b :
-
Stiffness matrix related to the membrane (m) or bending (b) effects
- B(x, y):
-
Strain-displacement differential operators
- C :
-
Isotropic material properties matrix
- h(x, y, θ):
-
Bidimensional random thickness
- ξ r (θ):
-
Set of random variables
- E[•]:
-
Mathematical expectation
- M(θ):
-
Stochastic mass matrix
- K(θ):
-
Stochastic stiffness matrix
- G(ω, θ):
-
Frequency response function of the stochastic system
- ε(x, y, t, θ):
-
Time-domain random strains
- s(x, y, t, θ):
-
Time-domain random stresses
- s̅ (x, y, t, θ):
-
Mean value of the random stresses
- Φ s(ω, θ):
-
Stress response function (SRF) of the stochastic system
- Φ f(ω):
-
PSD of random loading
- s (t,θ):
-
Time-domain random stresses
- D s :
-
Sines’ index
- R i :
-
Semi-axes of the prismatic hull
- J 2a (θ):
-
Second invariant of the random
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Acknowledgments
The authors are grateful to the FAPEMIG for the support to their research activities through the re-search grant PPM-0058-18 (A.M.G. de Lima). It is also important to acknowledge CNPq, especially for the research grant 306138/2019-0 (A.M.G. de Lima).
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U. L. Rosa received his Ph.D. in Mechanical Engineering from Federal University of Uberlândia. He is interested in fatigue damage analyses of engineering structures subjected to uncertainties, especially structures from automobiles and aeronautical industries. He is also interested in vibration control techniques, stochastic modelling, robust multiobjective optimization and reduction methods.
A. M. G. de Lima is a Full Professor of Mechanical Engineering at Federal University of Uberlândia in Brazil. He received his Ph.D. in Sciences pour l’Ingénieur from University of Franche-Comté in Besançon, France, and his Ph.D. in Mechanical Engineering from Federal University of Uberlândia. His research interests include vibration control techniques using passive and active methods, uncertainty quantification and stochastic modeling, reliability of structures, aeroelasticity control techniques in super- and subsonic regimes, reduction methods and optimization.
L. K. S. Gonçalves lectures at School of Civil Engineering at Federal University of Uberlândia — Brazil. She received her Ph.D. in Mechanical Engineering in 2018 from the same university. Her field of research includes fatigue damage analyses of composite materials, robust optimization and uncertainty propagation.
M. H. Belonsi is an Associate Professor of Mathematics at Goiás State University in Brazil. He received his Ph.D. in Mechanical Engineering at Federal University of Uberlândia in Structural Dynamics. His research interests include passive and active vibration control techniques, machining learning, data mining, nonlinear vibrations, uncertainty propagation, reduction methods and probabilistic structural analysis.
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Rosa, U.L., de Lima, A.M.G., Gonçalves, L.K.S. et al. A robust-based fatigue optimization method for systems subject to uncertainty. J Mech Sci Technol 36, 4571–4581 (2022). https://doi.org/10.1007/s12206-022-0820-4
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DOI: https://doi.org/10.1007/s12206-022-0820-4