Experimental and Parametric Study on Uncertainty Quantification within Topology Optimization utilizing Non-Intrusive Polynomial Chaos Theory

[1]  Junpeng Zhao,et al.  Truss topology optimization under uncertain nodal locations with proportional topology optimization method , 2017 .

[2]  Sondipon Adhikari,et al.  Eigenvalue density of linear stochastic dynamical systems: A random matrix approach , 2012 .

[3]  Qing Li,et al.  Evolutionary topology and shape design for general physical field problems , 2000 .

[4]  Geoffrey T. Parks,et al.  Robust Aerodynamic Design Optimization Using Polynomial Chaos , 2009 .

[5]  Grant P. Steven,et al.  Evolutionary structural optimization for dynamic problems , 1996 .

[6]  E. Sturler,et al.  Stochastic sampling for deterministic structural topology optimization with many load cases: Density-based and ground structure approaches , 2016, 1609.03099.

[7]  Zhan Kang,et al.  Robust shape and topology optimization considering geometric uncertainties with stochastic level set perturbation , 2017 .

[8]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[9]  D. Tortorelli,et al.  Component and system reliability-based topology optimization using a single-loop method , 2010 .

[10]  Roger Ghanem,et al.  Ingredients for a general purpose stochastic finite elements implementation , 1999 .

[11]  James K. Guest,et al.  Robust topology optimization of structures with uncertainties in stiffness - Application to truss structures , 2011 .

[12]  M. Papadrakakis,et al.  Advanced solution methods in topology optimization and shape sensitivity analysis , 1996 .

[13]  Dan M. Frangopol,et al.  Reliability-based design of MEMS mechanisms by topology optimization , 2003 .

[14]  Nestor V. Queipo,et al.  Efficient Shape Optimization Under Uncertainty Using Polynomial Chaos Expansions and Local Sensitivities , 2006 .

[15]  M. Eldred,et al.  A reduced-order stochastic finite element approach for design optimization under uncertainty , 2009 .

[16]  Kurt Maute,et al.  Reliability-based shape optimization of structures undergoing fluid-structure interaction phenomena , 2005 .

[17]  Dongbin Xiu,et al.  High-Order Collocation Methods for Differential Equations with Random Inputs , 2005, SIAM J. Sci. Comput..

[18]  Michael C. Fu,et al.  Feature Article: Optimization for simulation: Theory vs. Practice , 2002, INFORMS J. Comput..

[19]  Yi Min Xie,et al.  Evolutionary structural optimisation (ESO) using a bidirectional algorithm , 1998 .

[20]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[21]  N. Wiener.  The Homogeneous Chaos , 1938 .

[22]  Y. Xie,et al.  Evolutionary structural optimization for problems with stiffness constraints , 1996 .

[23]  Francesco Contino,et al.  A robust and efficient stepwise regression method for building sparse polynomial chaos expansions , 2017, J. Comput. Phys..

[25]  Mattias Schevenels,et al.  Robust design of large-displacement compliant mechanisms , 2011 .

[26]  Y. Xie,et al.  Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method , 2007 .

[27]  Kurt Maute,et al.  Topology Optimization under Uncertainty , 2014 .

[28]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[29]  Junpeng Zhao,et al.  Robust topology optimization under loading uncertainty based on linear elastic theory and orthogonal diagonalization of symmetric matrices , 2014 .

[30]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .

[31]  Y. Xie,et al.  Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials , 2009 .

[32]  G. Steven,et al.  Topology and shape optimization methods using evolutionary algorithms: a review , 2015 .

[33]  Geert Lombaert,et al.  Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis , 2015 .

[34]  James K. Guest,et al.  Topology optimization of continuum structures under uncertainty – A Polynomial Chaos approach , 2012 .

[35]  K. Maute,et al.  Analytical and numerical solutions for a reliability-based benchmark example , 2011 .

[36]  Gareth A. Vio,et al.  Multi-particle swarm optimization used to study material degradation in aeroelastic composites including probabalistic uncertainties , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[37]  Daniel A. Tortorelli,et al.  Topology optimization under uncertainty via non-intrusive polynomial chaos expansion , 2017 .

[38]  D. Tortorelli,et al.  Gradient based design optimization under uncertainty via stochastic expansion methods , 2016 .

[39]  Gerhart I. Schuëller,et al.  A survey on approaches for reliability-based optimization , 2010 .

[40]  Gareth A. Vio,et al.  Numerical and experimental assessment of random matrix theory to quantify uncertainty in aerospace structures , 2019, Mechanical Systems and Signal Processing.

[41]  T. Cruse,et al.  Advanced probabilistic structural analysis method for implicit performance functions , 1990 .

[42]  E. Wigner.  On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[43]  Michael D. McKay,et al.  Latin hypercube sampling as a tool in uncertainty analysis of computer models , 1992, WSC '92.

[44]  S. Adhikari.  Uncertainty Propagation in Linear Systems: An Exact Solution Using random Matrix Theory , 2007 .

[45]  Mattias Schevenels,et al.  Topology optimization with geometric uncertainties by perturbation techniques , 2012 .

[46]  Pierre Sagaut,et al.  Stochastic design optimization: Application to reacting flows , 2007 .