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Theoretical aspects of the internal element connectivity parameterization approach for topology optimization
Author(s) -
Yoon Gil Ho,
Kim Yoon Young,
Langelaar Matthijs,
van Keulen Fred
Publication year - 2008
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.2342
Subject(s) - discretization , stiffness , link (geometry) , interpolation (computer graphics) , convergence (economics) , direct stiffness method , topology (electrical circuits) , mathematics , topology optimization , finite element method , state variable , mathematical optimization , element (criminal law) , stiffness matrix , computer science , mathematical analysis , structural engineering , engineering , physics , animation , computer graphics (images) , combinatorics , law , political science , economics , thermodynamics , economic growth
The internal element connectivity parameterization (I‐ECP) method is an alternative approach to overcome numerical instabilities associated with low‐stiffness element states in non‐linear problems. In I‐ECP, elements are connected by zero‐length links while their link stiffness values are varied. Therefore, it is important to interpolate link stiffness properly to obtain stably converging results. The main objective of this work is two‐fold (1) the investigation of the relationship between the link stiffness and the stiffness of a domain‐discretizing patch by using a discrete model and a homogenized model and (2) the suggestion of link stiffness interpolation functions. The effects of link stiffness penalization on solution convergence are then tested with several numerical examples. The developed homogenized I‐ECP model can also be used to physically interpret an intermediate design variable state. Copyright © 2008 John Wiley & Sons, Ltd.