Fracture resistance via topology optimization

Challis, Vivien J., Roberts, Anthony P. and Wilkins, Andrew H. (2008) Fracture resistance via topology optimization. Structural and Multidisciplinary Optimization, 36 3: 263-271. doi:10.1007/s00158-007-0160-0

Author Challis, Vivien J.
Roberts, Anthony P.
Wilkins, Andrew H.
Title Fracture resistance via topology optimization
Journal name Structural and Multidisciplinary Optimization   Check publisher's open access policy
ISSN 1615-147X
Publication date 2008-09
Year available 2007
Sub-type Article (original research)
DOI 10.1007/s00158-007-0160-0
Volume 36
Issue 3
Start page 263
End page 271
Total pages 9
Editor G. Rozvany
Place of publication Germany
Publisher Springer
Collection year 2008
Language eng
Subject 239999 Mathematical Sciences not elsewhere classified
780101 Mathematical sciences
Abstract The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.
Keyword topology optimisation
level set
Q-Index Code C1
Q-Index Status Confirmed Code
Additional Notes Published online: 9 August 2007

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Created: Tue, 15 Apr 2008, 10:06:36 EST by Marie Grove on behalf of School of Mathematics & Physics