Concurrent shape optimization of a multiscale structure for controlling macrostructural stiffness View Full Text


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Article Info

DATE

2022-07-14

AUTHORS

Minami Fujioka, Masatoshi Shimoda, Musaddiq Al Ali

ABSTRACT

We propose a novel shape optimization method for designing a multiscale structure with the desired stiffness. The shapes of the macro- and microstructures are concurrently optimized. The squared error norm between actual and target displacements of the macrostructure is minimized as an objective function. The design variables are the shape variation fields of the outer and interface shapes of the macrostructure and the shapes of holes in the microstructures. Subdomains with independent periodic microstructures are arbitrarily defined in the macrostructure in advance. Homogenized elastic tensors are calculated and applied to the correspondent subdomains. The shape gradient functions are theoretically derived with respect to each shape variation of the macro- and microstructures, and applied to the H1 gradient method to determine the optimum shapes. The proposed method is applied to several numerical examples, including Poisson’s ratio design and deformation control designs of an L-shaped bracket and a both ends fixed beam with holes. The results of the design examples confirm that the desired stiff or compliant deformation can be achieved while obtaining clear and smooth boundaries. The influence on the final results of the initial shape of the unit cell, the connectivity of adjacent microstructures, and interface optimization is also discussed. More... »

PAGES

211

References to SciGraph publications

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