Nutrient modulated structural design with application to growth and degradation
2015 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 95, no 11, 1323-1334 p.Article in journal (Refereed) Published
Phenomena such as biological growth and damage evolution can be thought of as time evolving processes, the directions of which are governed by descendent of certain goal functions. Mathematically this means using a dynamical systems approach to optimization. We extend such an approach by introducing a field quantity, representing nutrients or other non-mechanical stimuli, that modulate growth and damage evolution. The derivation of a generic model is systematic, starting from a Lyaponov-type descent condition and utilizing a Coleman-Noll strategy. A numerical algorithm for finding stationary points of the resulting dynamical system is suggested and applied to two model problems where the influence of different levels of nutrient sensitivity are observed. The paper demonstrates the use of a new modeling technique and shows its application in deriving a generic problem of growth and damage evolution. (C) 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim
Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH , 2015. Vol. 95, no 11, 1323-1334 p.
topology optimization; biological growth; structural damage; nutrient
IdentifiersURN: urn:nbn:se:liu:diva-122786DOI: 10.1002/zamm.201400008ISI: 000363885300019OAI: oai:DiVA.org:liu-122786DiVA: diva2:873327
Funding Agencies|Swedish Research Council [Dnr: 621-2012-3117]2015-11-232015-11-232015-11-23