Non-intrusive polynomial chaos expansion for topology optimization using polygonal meshes

  • Nilton Cuellar
  • Anderson PereiraEmail author
  • Ivan F. M. Menezes
  • Americo CunhaJr.
Technical Paper


This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to calculate low-order statistical moments of the mechanical–mathematical model response. This procedure, known as robust topology optimization, can optimize the mean of the compliance while simultaneously minimizing its standard deviation. In order to address possible variabilities in the loads applied to the mechanical system of interest, magnitude and direction of the external forces are assumed to be uncertain. In this probabilistic framework, forces are described as a random field or a set of random variables. Representation of the random objects and propagation of load uncertainties through the model are efficiently done through Karhunen–Loève and polynomial chaos expansions. We take advantage of using polygonal elements, which have been shown to be effective in suppressing checkerboard patterns and reducing mesh dependency in the solution of topology optimization problems. Accuracy and applicability of the proposed methodology are demonstrated by means of several topology optimization examples. The obtained results, which are in excellent agreement with reference solutions computed via Monte Carlo method, show that load uncertainties play an important role in optimal design of structural systems, so that they must be taken into account to ensure a reliable optimization process.


Topology optimization Stochastic spectral approach Polynomial chaos Karhunen–Loève expansion Robust optimization Polygonal finite element 



NC acknowledges the financial support from the Group of Technology in Computer Graphics (Tecgraf/PUC-Rio), Rio de Janeiro, Brazil. AP and IFMM acknowledge the financial support from the National Council for Scientific and Technological Development (CNPq) under projects 312280/2015-7 and 309708/2015-0, respectively. AP and ACJr are thankful for the support from Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ) under grants E-26/203.189/2016, E-26/010.002.178/2015 and E-26/010.000.805/2018. The information provided in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies..


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringPontifical Catholic University of Rio de Janeiro (PUC-Rio)Rio de JaneiroBrazil
  2. 2.Nucleus of Modeling and Experimentation with Computers (NUMERICO)Universidade do Estado do Rio de Janeiro (UERJ)Rio de JaneiroBrazil

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