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The Discrete Topology Optimization of Structures Using the Modified Quadrilateral Discretization Model

[+] Author Affiliations
Hong Zhou, Ravinder G. Malela

Texas A&M University-Kingsville, Kingsville, TX

Paper No. DETC2012-70422, pp. 1303-1312; 10 pages
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 32nd Computers and Information in Engineering Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4501-1
  • Copyright © 2012 by ASME


The modified quadrilateral discretization model is introduced for the discrete topology optimization of structures in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is eradicated. In the proposed discrete topology optimization method of structures, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the optimized structure safe. The binary bit-array genetic algorithm is used to search for the optimal topology to circumvent the geometrical bias against the vertical design cells. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented discrete topology optimization procedure is illustrated by two topology optimization examples of structures.

Copyright © 2012 by ASME



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