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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on November 11, 2005
The Quarterly Journal of Mechanics and Applied Mathematics 2006 59(1):139-161; doi:10.1093/qjmam/hbi035
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Q. Jl Mech. Appl. Math, Vol. 59. No. 1 © The Author 2005. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Inverse homogenization and design of microstructure for pointwise stress control

R. Lipton{dagger} and M. Stuebner

( Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA )

{dagger} lipton{at}math.lsu.edu

New higher-order homogenization results are employed in an inverse homogenization procedure to identify graded microstructures that provide desirable structural response while ensuring stress control near joints or junctions between structural elements. The methodology is illustrated for long cylindrical shafts reinforced with stiff cylindrical elastic fibres with generators parallel to the shaft. The local fibre geometry can change across the shaft cross-section. The methodology is implemented numerically for cross-sectional shapes that possesses reentrant corners typically seen in lap joints and junctions of struts. Graded locally layered microgeometries are identified that provide the required structural rigidity with respect to torsion loading while at the same time mitigating the influence of stress concentrations at the reentrant corners.


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