Long, Craig SLoveday, Philip WGroenwold, AA2009-11-022009-11-022009-01Long, 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 487-5011615-147Xhttp://hdl.handle.net/10204/3709https://link.springer.com/content/pdf/10.1007/s00158-008-0345-1.pdfDOI 10.1007/s00158-008-0345-1Copyright: 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 487-501The 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.enPlanar finite elementCheckerboardHomogenizationReduced integrationMultidisciplinary optimizationBilinear elementsQuadratic elementsGauss quadrature rulesTopology optimizationArticleLong, C. S., Loveday, P. W., & Groenwold, A. (2009). Effects of planar element formulation and numerical integration order on checkerboard material layouts. http://hdl.handle.net/10204/3709Long, Craig S, Philip W Loveday, and AA Groenwold "Effects of planar element formulation and numerical integration order on checkerboard material layouts." (2009) http://hdl.handle.net/10204/3709Long CS, Loveday PW, Groenwold A. Effects of planar element formulation and numerical integration order on checkerboard material layouts. 2009; http://hdl.handle.net/10204/3709.TY - Article AU - Long, Craig S AU - Loveday, Philip W AU - Groenwold, AA AB - 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. DA - 2009-01 DB - ResearchSpace DP - CSIR KW - Planar finite element KW - Checkerboard KW - Homogenization KW - Reduced integration KW - Multidisciplinary optimization KW - Bilinear elements KW - Quadratic elements KW - Gauss quadrature rules KW - Topology optimization LK - https://researchspace.csir.co.za PY - 2009 SM - 1615-147X T1 - Effects of planar element formulation and numerical integration order on checkerboard material layouts TI - Effects of planar element formulation and numerical integration order on checkerboard material layouts UR - http://hdl.handle.net/10204/3709 ER -