Topology optimization using a level set method with an arbitrary structured mesh

Kai A. James, Joaquim R.R.A. Martins

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Two approaches to three-dimensional structural topology optimization using level set parameterization with arbitrary finite-element meshes are presented. In both approaches the structural elasticity problem is solved on a fixed finite-element mesh. The shape sensitivities obtained from the solution of the structural problem are mapped to the orthogonal mesh in order to generate the corresponding advection velocities. The first approach superimposes a background Cartesian grid onto the finite element mesh. The level set function is defined on this Cartesian mesh with the advection velocities being taken as a weighted sum of the sensitivities at all nearby structural nodes within a prescribed radius. The second approach defines the level set function on a skewed structured mesh which is coincident with the finite element mesh. The Hamilton-Jacobi equation is then solved in this transformed mesh space and a Jacobian transformation is used create a one-to-one mapping between the structural elements and the nodes of the level set mesh. The two methods are evaluated and compared based upon the results of a benchmark problem involving three-dimensional topology optimization of an aircraft wing structure. The results indicate that the Jabobian mapping method offers a significant advantage over the superposition method, both in terms of convergence time as well as the objective value of the converged solution.

Original languageEnglish (US)
Title of host publication51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781600867422
DOIs
StatePublished - 2010
Externally publishedYes

Publication series

NameCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
ISSN (Print)0273-4508

ASJC Scopus subject areas

  • Architecture
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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