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A staggered approach to structural shape and topology optimization
Author(s) -
Riehl Stefan,
Steinmann Paul
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510277
Subject(s) - sensitivity (control systems) , boundary (topology) , topology optimization , topology (electrical circuits) , shape optimization , domain (mathematical analysis) , representation (politics) , mathematics , finite element method , mathematical optimization , computer science , algorithm , mathematical analysis , engineering , combinatorics , structural engineering , electronic engineering , politics , political science , law
This contribution is concerned with the design and evaluation of a staggered approach to computational shape and topology optimization. The main idea is to interrelate a classical boundary variation scheme based on the results from shape sensitivity analysis and an evolutionary‐type element removal procedure that relies on the topological sensitivity as a rejection criterion. The key ingredient in this perspective is to consider an advancing front algorithm that is gradually removing, from the evolving boundary of the domain, a number of finite elements based on the evaluation of the topological sensitivity. This process is repeated until the minimum topological sensitivity is no longer encountered at the boundary but in the interior of the domain, such that a topological change is to be considered for the current design layout. However, we first aim to establish a more accurate approximation of the true optimal shape of the newly established (zig‐zag representation) of the design boundary. This is achieved by the evaluation of the shape sensitivity and the accompanying boundary variations obtained by a basic descent algorithm. Only then, we create a hole in the interior of the domain by removing all cells that are adjacent to the nodal point that exhibits the minimum topological sensitivity and resume the advancing front algorithm to alter the newly established design boundary. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)