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Combined gradient‐stochastic optimization with negative circular masks for large deformation topologies
Author(s) -
Saxena Anupam,
Sauer Roger.A.
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4401
Subject(s) - topology optimization , network topology , morphing , topology (electrical circuits) , gravitational singularity , mathematical optimization , smoothing , mathematics , computer science , mathematical analysis , structural engineering , finite element method , engineering , artificial intelligence , statistics , combinatorics , operating system
SUMMARY Topology optimization of large deformation two‐dimensional continua is presented using a combined gradient‐stochastic search with negative circular masks. The possibility of generating perfect black and white topologies is explored while attaining the efficiency of first‐order and second‐order search algorithms. The design region is modeled with honeycomb tessellation to thwart the known connectivity singularities such as the checkerboards and point flexures. Mask shrinkage is incorporated for ease in density transition between gradient and stochastic steps. Notches at continuum boundaries are moderated through multiple use of a simple boundary smoothing method. A neo‐Hookean elasticity model is employed to simulate the material nonlinearities in large displacement continua. With examples on stiff beams and large deformation compliant mechanisms, it is illustrated that perfectly binary, connected and smooth topologies can be obtained within a few hundred design evaluations.Copyright © 2012 John Wiley & Sons, Ltd.