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Please use this identifier to cite or link to this item: http://hdl.handle.net/10204/3709

Title: Effects of planar element formulation and numerical integration order on checkerboard material layouts
Authors: Long, CS
Loveday, PW
Groenwold, AA
Keywords: Planar finite element
Checkerboard
Homogenization
Reduced integration
Multidisciplinary optimization
Bilinear elements
Quadratic elements
Gauss quadrature rules
Topology optimization
Issue Date: Jan-2009
Publisher: Springer -Verlag
Citation: Long, CS, Loveday, PW and Groenwold AA. 2009. Effects of planar element formulation and numerical integration order on checkerboard material layouts. Structural and Multidisciplinary Optimization, Vol. 39(5), pp 487-501
Abstract: The effects of selected planar finite element formulations, and their associated integration schemes, on the stiffness of a checkerboard material layout are investigated. Standard 4-node bilinear elements, 8- and 9-node quadratic elements, as well as 4-node elements with drilling degrees of freedom are considered. Integration schemes evaluated include popular Gauss quadrature rules, as well as modified 5- and 8-point integration schemes. It is shown that, although checkerboarding may be slightly alleviated when using elements with drilling degrees of freedom, the homogenized checkerboard stiffness is identical to that of standard bilinear elements. This is significant since elements with drilling degrees of freedom are derived from an 8-node parent element. Researchers do however demonstrate that modified reduced integration schemes, applied to quadratic elements, effectively reduce the stiffness of a checkerboard material layout. Furthermore, the proposed schemes effectively suppress spurious zero energy modes which may occur on the element level in topology optimization.
Description: Copyright: 2009 Springer-Verlag. This is the author's version of the work. It is posted here by permission of Springer-Verlag for your personal use. Not for redistribution. The definitive version was published in the journal, Structural and Multidisciplinary Optimization, Vol. 39(5), pp 487-501
URI: http://hdl.handle.net/10204/3709
ISSN: 1615-147X
Appears in Collections:Advanced mathematical modelling and simulation
General science, engineering & technology

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