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A projection‐based method for topology optimization of structures with graded surfaces
Author(s) -
Luo Yunfeng,
Li Quhao,
Liu Shutian
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6031
Subject(s) - topology optimization , projection (relational algebra) , topology (electrical circuits) , interpolation (computer graphics) , surface (topology) , projection method , constraint (computer aided design) , mathematical optimization , minification , mathematics , function (biology) , network topology , computer science , algorithm , finite element method , dykstra's projection algorithm , geometry , structural engineering , engineering , image (mathematics) , combinatorics , artificial intelligence , evolutionary biology , biology , operating system
Summary Graded surfaces widely exist in natural structures and inspire engineers to apply functionally graded (FG) materials to cover structural surfaces for performance improvement, protection, or other special functionalities. However, how to design such structures with FG surfaces by topology optimization is a quite challenging problem due to the difficulty for determining material properties of structural surfaces with prescribed variation rule. This paper presents a novel projection‐based method for topology optimization of this class of FG structures. Firstly, a projection process is proposed for ensuring the material properties of the surfaces vary with a prescribed function. A criterion of determining the values of parameters in projection process is given by a strict theoretical derivation, and then, a new interpolation function is established, which is capable of simultaneously obtaining clear substrate topologies and realizable FG surfaces. Though such structures are actually multimaterial gradient structures, only the design variables of single‐material topology optimization problem are needed. In the current research, the classical compliance minimization problem with a mass constraint is considered and the robust formulation is used to control the length scale of substrates. Several 2D and 3D numerical examples illustrate the validity and applicability of the proposed method.