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Title: Adaptive mesh refinement in stress-constrained topology optimization

Journal Article · · Structural and Multidisciplinary Optimization
ORCiD logo [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of Illinois, Urbana-Champaign, IL (United States)
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We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1481053
Report Number(s):
LLNL-JRNL-748566; 933663
Journal Information:
Structural and Multidisciplinary Optimization, Vol. 58, Issue 6; ISSN 1615-147X
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 56 works
Citation information provided by
Web of Science

References (56)

Goal-oriented error estimation and adaptivity for the finite element method journal March 2001
Combined shape and topology optimization for minimization of maximal von Mises stress journal January 2017
On singular topologies in optimum structural design journal September 1990
Optimal topology design of continuum structures with stress concentration alleviation via level set method: TOPOLOGY DESIGN WITH STRESS CONCENTRATION ALLEVIATION journal October 2012
Stress-based topology optimization journal October 1996
Adaptive topology optimization journal October 1995
Improvements in the treatment of stress constraints in structural topology optimization problems journal August 2010
A level set solution to the stress-based structural shape and topology optimization journal January 2012
Adaptive topology optimization with independent error control for separated displacement and density fields journal April 2014
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization journal January 2011
libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations journal November 2006
A Convergent Adaptive Algorithm for Poisson’s Equation journal June 1996
An optimal control approach to a posteriori error estimation in finite element methods journal May 2001
Filters in topology optimization based on Helmholtz-type differential equations journal December 2010
Topology optimization of continuum structures with local stress constraints journal December 1998
Stress constrained topology optimization journal February 2013
Towards adaptive topology optimization journal October 2016
A review of a posteriori error estimation techniques for elasticity problems journal July 1999
Filters in topology optimization journal January 2001
Stress-based topology optimization for continua journal October 2009
A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations journal January 2002
Material interpolation schemes in topology optimization journal November 1999
Solving stress and compliance constrained volume minimization using anisotropic mesh adaptation, the method of moving asymptotes and a global p-norm journal April 2016
Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework journal August 2014
Topology optimization of non-linear elastic structures and compliant mechanisms journal March 2001
Topological optimization of structures subject to Von Mises stress constraints journal August 2009
Stress-related topology optimization via level set approach journal November 2011
Moreau–Yosida Regularization in State Constrained Elliptic Control Problems: Error Estimates and Parameter Adjustment journal January 2009
A fully adaptive topology optimization algorithm with goal-oriented error control journal August 2011
The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique journal May 1992
The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity journal May 1992
?-relaxed approach in structural topology optimization journal June 1997
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities journal September 2009
A polytree-based adaptive polygonal finite element method for topology optimization: ON AN ADAPTIVE POLYTREE MESH STRUCTURE FOR TOPOLOGY OPTIMIZATION journal December 2016
A critical comparative assessment of differential equation-driven methods for structural topology optimization journal July 2013
Hierarchical remeshing strategies with mesh mapping for topology optimisation: Hierarchical remeshing strategies with mesh mapping for topology optimisation journal February 2017
Shape optimization with a level set based mesh evolution method journal December 2014
On an alternative approach to stress constraints relaxation in topology optimization journal January 2008
Optimal topologies derived from a phase-field method journal August 2011
On projection methods, convergence and robust formulations in topology optimization journal December 2010
Stress-constrained topology optimization for compliant mechanism design journal July 2015
On singular topologies in exact layout optimization journal December 1994
Stress-related topology optimization of continuum structures involving multi-phase materials journal January 2014
Slope constrained topology optimization journal April 1998
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries book January 1997
Stress-based topology optimization using spatial gradient stabilized XFEM journal October 2017
An adaptive multilevel approach to the minimal compliance problem in topology optimization journal September 2005
An alternative interpolation scheme for minimum compliance topology optimization journal September 2001
Study on Topology Optimization with Stress Constraints journal November 1992
Structural optimization under multiple loading journal October 1968
The method of moving asymptotes—a new method for structural optimization journal February 1987
The FEniCS Project Version 1.5 text January 2015
A new approach to variable-topology shape design using a constraint on perimeter journal February 1996
Interior value extrapolation: a new method for stress evaluation during topology optimization journal September 2014
Improved ZZ a posteriori error estimators for diffusion problems: Conforming linear elements journal January 2017
Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability journal February 2021

Cited By (1)

A dual mesh method with adaptivity for stress-constrained topology optimization journal November 2019

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