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Multiphase topology design with optimal material selection using an inverse p ‐norm function
Author(s) -
James Kai A.
Publication year - 2018
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.5774
Subject(s) - parameterized complexity , inverse , topology optimization , mathematical optimization , norm (philosophy) , finite element method , topology (electrical circuits) , computer science , mathematics , algorithm , structural engineering , engineering , geometry , combinatorics , law , political science
Summary We present an original mathematical formulation for optimizing structural topology while simultaneously identifying an optimal set of design materials that are selected from a larger set of candidate materials. This design task is analogous to that, which is commonly encountered in additive manufacturing applications in which the 3D printer can print parts containing up to 3 distinct materials that can be selected from a larger suite of usable materials. The material distribution is parameterized via the shape functions with penalization formulation in which a set of activation functions, which are derived from a partition of the unit hypercube, is used to determine the effective local elasticity modulus within a single finite element. Additionally, we introduce an inverse p ‐norm function, which is used to ensure that the optimized material properties converge to a set of discrete values corresponding to the available candidate materials. The algorithm has been implemented on a set of 2D benchmark problems. Numerical results show that the formulation combining the inverse p ‐norm function with the activation functions successfully produces optimized multimaterial solutions containing no more than the prescribed number of distinct materials.