Optimal topological design through insertion and configuration of finite-sized heterogeneities

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:50

Article

Lin, Hung-Yun¹  Subbarayan, Ganesh¹ 

[1] Purdue Univ, Sch Mech Engn, W Lafayette, IN 47907 USA

关键词: Topology optimization;    Shape optimization;    Configuration optimization;    Configurational derivative;   

DOI  :  10.1016/j.ijsolstr.2012.10.006

来源: Elsevier

【 摘 要 】

In this paper, we develop a procedure for optimal topological design by sequentially inserting finite-sized non-spherical inclusions or holes within a homogeneous domain. We propose a new criterion for topology change that results in a trade-off problem to achieve the greatest/least change in the objective for the least/greatest change in the size of the inclusion/hole respectively. We derive the material derivative of the proposed objective, termed as the configurational derivative, that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion/hole as well as the domain boundaries. We specifically utilize the sensitivity to position, orientation and scaling of finite-sized heterogeneities to effect topological design. We simplify the configurational derivative to the special case of infinitesimally small spherical inclusions or holes and show that the developed derivative is a generalization of the classical topological derivative. The computational implementation relies on B-spline isogeometric approximations. We demonstrate, through a series of examples, optimal topology achieved through sequential insertion of a heterogeneity of fixed shape and optimization of its configuration (location, orientation and scale). (C) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free