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Application of an anisotropic growth formulation to computational structural design
Author(s) -
Waffenschmidt Tobias,
Menzel Andreas
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210132
Subject(s) - benchmark (surveying) , topology optimization , mathematical optimization , computer science , boundary value problem , boundary (topology) , mathematics , engineering , structural engineering , mathematical analysis , finite element method , geodesy , geography
Abstract Common structural optimisation problems consist of problem‐specific objective functions which have to be minimised mathematically with respect to design and state variables taking into account particular constraints. In contrast to this, we adopt a conceptually different approach for the design of a structure which is not based on a topology‐optimisation technique. Instead, we apply a one‐dimensional energy‐driven constitutive evolution equation for the referential density–originally proposed for the simulation of remodelling effects in bones–and embed this into the micro‐sphere‐concept to end up with a three‐dimensional anisotropic growth formulation. The objective of this contribution is to investigate this approach with emphasis on its application to structural design problems by means of two three‐dimensional benchmark‐type boundary value problems. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)