Structural and Multidisciplinary Optimization

, Volume 56, Issue 2, pp 371–390 | Cite as

Topology optimization of structures with gradient elastic material



Topology optimization of structures and mechanisms with microstructural length-scale effect is investigated based on gradient elasticity theory. To meet the higher-order continuity requirement in gradient elasticity theory, Hermite finite elements are used in the finite element implementation. As an alternative to the gradient elasticity, the staggered gradient elasticity that requires C 0-continuity, is also presented. The solid isotropic material with penalization (SIMP) like material interpolation schemes are adopted to connect the element density with the constitutive parameters of the gradient elastic solid. The effectiveness of the proposed formulations is demonstrated via numerical examples, where remarkable length-scale effects can be found in the optimized topologies of gradient elastic solids as compared with linear elastic solids.


Topology optimization Gradient elasticity (GE) Staggered gradient elasticity (SGE) Length-scale effect Hermite finite elements 



The presented work is supported in part by the US National Science Foundation through Grant CMS-1055314. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Civil & Environmental Engineering & Earth SciencesUniversity of Notre DameNotre DameUSA

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