A two-pronged approach for springback variability assessment using sparse polynomial chaos expansion and multi-level simulations
Source abstract
Abstract
In this study, we show that stochastic analysis of metal forming process requires both a high precision and low cost numerical models in order to take into account very small perturbations on inputs (physical as well as process parameters) and to allow for numerous repeated analysis in a reasonable time. To this end, an original semi-analytical model dedicated to plain strain deep drawing based on a Bending-Under-Tension numerical model (B-U-T model) is used to accurately predict the influence of small random perturbations around a nominal solution estimated with a full scale Finite Element Model (FEM). We introduce a custom sparse variant of the Polynomial Chaos Expansion (PCE) to model the propagation of uncertainties through this model at low computational cost. Next, we apply this methodology to the deep drawing process of U-shaped metal sheet considering up to 8 random variables.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Probabilistic and Robust Engineering Design · Structural Response to Dynamic Loads · High-Velocity Impact and Material Behavior
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References (24)
Show source-provided references
1. Papeleux L, Ponthot J (2002) Finite element simulation of springback in sheet metal forming. J Mater Process Technol 125–126:785–79110.1016/S0924-0136(02)00393-X ↗
2. Kleiber M, Rojek J, Stochi R (2002) Reliability assessment for sheet metal forming operations. Comput Methods Appl Mech Eng 191:4511–453210.1016/S0045-7825(02)00394-8 ↗
3. de Souza T, Rolfe B (2008) Multivariate modelling of variability in sheet metal forming. J Mater Process Technol 203:1–1210.1016/j.jmatprotec.2007.09.075 ↗
4. Naceur H, Delaméziere A, Batoz J, Guo C, Knopf–Lenoir C (2004) Some improvement on the optimum process design in deep drawing using the inverse approach. J Mater Process Technol 146:250–26210.1016/j.jmatprotec.2003.11.015 ↗
5. Breitkopf P, Naceur H, Villon P (2005) Moving least squares response surface approximation: formulation and metal forming applications. Comput Struct 83:1411–142810.1016/j.compstruc.2004.07.011 ↗
6. Kleiber M, Breitkopf P (1993) Finite elements in structural mechanics: an introduction with Pascal programs for micro-computers. Ellis Horwood
7. Meinders T, Burchitz I, Bonte M, Lingbeek R (2008) Numerical product design: Springback prediction, compensation and optimization. Int J Mach Tools Manuf 48(5):499–51410.1016/j.ijmachtools.2007.08.006 ↗
8. Radi B, El Hami A (2007) Reliability analysis of the metal forming process. Math Comput Model 45:431–43910.1016/j.mcm.2006.05.013 ↗
9. Jansson T, Nilsson L, Moshfegh R (2008) Reliability analysis of a sheet metal forming process using monte carlo analysis and metamodels. J Mater Process Technol 202:255–26810.1016/j.jmatprotec.2007.09.005 ↗
10. Donglai W, Zhenshan C, Jun C (2007) Optimization and tolerance prediction of sheet metal forming process using response surface model. Comput Mater Sci 42:228–23310.1007/s10853-006-1056-x ↗
11. Blatman G, Sudret B (2011) Adaptive sparse polynomial chaso expansion based on least angle regression. J Comput Phys 230:2345–236710.1016/j.jcp.2010.12.021 ↗
12. Ghanem R, Spanos PD (1991) Spectral stochastic finite-element formulation for reliability analysis. J Eng Mech 117(10):2351–237210.1061/(ASCE)0733-9399(1991)117:10(2351) ↗
13. Sudret B, Der Kiureghian A (2000) Stochastic finite elements methods and reliability- a state of the art. tech. rep. Department of civil and environmental engineering
14. Ghanem R, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer-Verlag, New York10.1007/978-1-4612-3094-6 ↗
15. Cameron R, Martin W (1944) Transformations of wiener integrals under translations. Ann Math 45(2):386–39610.2307/1969276 ↗
16. Xiu D (2009) Fast numerical methods for stochastic computations: a review. Commun Comput Phys 5:242–272
17. Berveiller M, Sudret B, Lemaire M (2006) Stochastic finite element: a non intrusive approach by regression. Rev Eur Méc Numér 15:81–92
18. Makinouchi A, Nakamachi E, Onate E, Wagoner R (eds) (1993) Numisheet’93 2nd international conference, numerical simulation of 3-D sheet metal forming process-verification of simulation with experiment, Riken Tokyo
19. Hibbit D, Karlsson B, Sorensen P. ABAQUS Example problems, vol 1, version 6.7. Dassault Système
20. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. In: Proc R London, vol 193, pp 281–297
21. Le Quilliec G, Breitkopf P, Roelandt J, Juillard P (2013) Semi-analytical approach for plane strain sheet metal forming using a bending-under-tension numerical model. Int J Mater Form. doi: 10.1007/s12289-012-1122-7
22. Hastie RT, Tibshirani J, Friedman G (2009) The elements of statistical learning, data mining, inference and prediction, Springer10.1007/978-0-387-84858-7 ↗
23. Hesterberg T, Choi N, Meier L, Fraley C (2008) Least angle and l 1 penalized regression: a review. Stat Surv 2:61–9310.1214/08-SS035 ↗
24. Efron B, Hastie T, Johnstone I, Tibsirani T (2004) Least angle regression. Ann Stat 32(2):407–45110.1214/009053604000000067 ↗