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Large strain phase‐field‐based multi‐material topology optimization
Author(s) -
Wallin Mathias,
Ivarsson Niklas,
Ristinmaa Matti
Publication year - 2015
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.4962
Subject(s) - topology optimization , finite element method , penalty method , mathematics , boundary value problem , mathematical optimization , topology (electrical circuits) , nonlinear system , optimization problem , boundary (topology) , shape optimization , displacement field , simple (philosophy) , mathematical analysis , engineering , physics , structural engineering , philosophy , epistemology , combinatorics , quantum mechanics
Summary A multi‐material topology optimization scheme is presented. The formulation includes an arbitrary number of phases with different mechanical properties. To ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions, an obstacle potential function, which introduces infinity penalty for negative densities, is utilized. The problem is formulated for nonlinear deformations, and the objective of the optimization is the end displacement. The boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method. To illustrate the possibilities of the method, it is applied to a simple boundary value problem where optimal designs using multiple phases are considered. Copyright © 2015 John Wiley & Sons, Ltd.