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periodic solid

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Design of Frame-Like Periodic Solids for Isotropic Symmetry by Member Sizing
K. Theerakittayakorn, P. Suttakul, P. Sam, P. Nanakorn
Journal:

Journal of Mechanics / Volume 33 / Issue 1 / February 2017

Published online by Cambridge University Press:

11 July 2016, pp. 41-54

Print publication:

February 2017
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In this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.