General purpose software for efficient uncertainty management of large finite element models

The aim of this paper is to demonstrate that stochastic analyses can be performed on large and complex models within affordable costs. Stochastic analyses offer a much more realistic approach for analysis and design of components and systems although generally computationally demanding. Hence, resorting to efficient approaches and high performance computing is required in order to reduce the execution time. A general purpose software that provides an integration between deterministic solvers (i.e. finite element solvers), efficient algorithms for uncertainty management and high performance computing is presented. The software is intended for a wide range of applications, which includes optimization analysis, life-cycle management, reliability and risk analysis, fatigue and fractures simulation, robust design. The applicability of the proposed tools for practical applications is demonstrated by means of a number of case studies of industrial interest involving detailed models.

[1]  Michał Kleiber,et al.  The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation , 1993 .

[2]  M. F. Pellissetti,et al.  Efficient component-wise and solver-based intrusive SFEM analysis of complex structures , 2010 .

[3]  Pol D. Spanos,et al.  Computational Stochastic Mechanics , 2011 .

[4]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[5]  Dimitri Kececioglu,et al.  Reliability engineering handbook , 1991 .

[6]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[7]  H. M. Panayirci,et al.  Efficient solution for Galerkin-based polynomial chaos expansion systems , 2010, Adv. Eng. Softw..

[8]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[9]  Edoardo Patelli,et al.  Global sensitivity of structural variability by random sampling , 2010, Comput. Phys. Commun..

[10]  G. Schuëller,et al.  Chair of Engineering Mechanics Ifm-publication 2-374 a Critical Appraisal of Reliability Estimation Procedures for High Dimensions , 2022 .

[11]  G. Stefanou The stochastic finite element method: Past, present and future , 2009 .

[12]  Kevin N. Gurney,et al.  An introduction to neural networks , 2018 .

[13]  Gerhart I. Schuëller,et al.  Efficient stochastic structural analysis using Guyan reduction , 2011, Adv. Eng. Softw..

[14]  Kari Karhunen,et al.  Über lineare Methoden in der Wahrscheinlichkeitsrechnung , 1947 .

[15]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[16]  Helmut J. Pradlwarter,et al.  Robust model updating with insufficient data , 2009 .

[17]  Nicholas Zabaras,et al.  A stochastic variational multiscale method for diffusion in heterogeneous random media , 2006, J. Comput. Phys..

[18]  H. Pradlwarter,et al.  Reliability of Structures in High Dimensions , 2003 .

[19]  Gerhart I. Schuëller,et al.  Computational methods in optimization considering uncertainties – An overview , 2008 .

[20]  G. Schuëller A state-of-the-art report on computational stochastic mechanics , 1997 .

[21]  Bruce R. Ellingwood Structural safety special issue: General-purpose software for structural reliability analysis , 2006 .

[22]  O. Hasançebi,et al.  Adaptive evolution strategies in structural optimization: Enhancing their computational performance with applications to large-scale structures , 2008 .

[23]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[24]  J. Arbocz,et al.  The initial imperfection data bank at the Delft University of Technology: Part I , 1979 .

[25]  Christian Soize A nonparametric model of random uncertainties for reduced matrix models in structural dynamics , 2000 .

[26]  Michel Loève,et al.  Probability Theory I , 1977 .

[27]  Wilhelm Cauer,et al.  Theorie der linearen Wechselstromschaltungen , 1940 .

[28]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[29]  Gerhart I. Schuëller,et al.  Scalable uncertainty and reliability analysis by integration of advanced Monte Carlo simulation and generic finite element solvers , 2009 .

[30]  Edoardo Patelli,et al.  On multinormal integrals by Importance Sampling for parallel system reliability , 2011 .

[31]  A. Saltelli,et al.  Tackling quantitatively large dimensionality problems , 1999 .

[32]  I. J. Myung,et al.  Tutorial on maximum likelihood estimation , 2003 .

[33]  Raúl Tempone,et al.  Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations , 2004, SIAM J. Numer. Anal..

[34]  A. Kiureghian,et al.  Multivariate distribution models with prescribed marginals and covariances , 1986 .

[35]  M. F. Pellissetti,et al.  Parallel processing in structural reliability , 2009 .

[36]  M. Beer,et al.  Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics , 2004 .

[37]  Jasbir S. Arora,et al.  Optimization of structural and mechanical systems , 2007 .

[38]  Helmut J. Pradlwarter RELATIVE IMPORTANCE OF UNCERTAIN STRUCTURAL PARAMETERS , 2005 .

[39]  H. Pradlwarter Relative importance of uncertain structural parameters. Part I: algorithm , 2007 .

[40]  Jie Pan,et al.  Introduction to Grid Computing , 2009 .

[41]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[42]  Kai Yang,et al.  Design for Six Sigma , 2005 .

[43]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[44]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[45]  Christian A. Schenk,et al.  Uncertainty assessment of large finite element systems , 2005 .

[46]  G. Schuëller,et al.  A critical appraisal of methods to determine failure probabilities , 1987 .

[47]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[48]  Stefano Tarantola,et al.  Random balance designs for the estimation of first order global sensitivity indices , 2006, Reliab. Eng. Syst. Saf..

[49]  G. Schuëller,et al.  Uncertainty analysis of complex structural systems , 2009 .

[50]  Gerhart I. Schuëller,et al.  On the treatment of finite element structures in stochastic linear dynamics using a mode-based meta-model , 2011 .

[51]  Steven J. M. Jones,et al.  Sun Grid Engine Package for OSCAR - A Google Summer Of Code 2005 Project , 2006, 20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment (HPCS'06).

[52]  George Em Karniadakis,et al.  Generalized polynomial chaos and random oscillators , 2004 .

[53]  Masanobu Shinozuka,et al.  Neumann Expansion for Stochastic Finite Element Analysis , 1988 .