An adaptive algorithm for topology optimization with goal-oriented error control

27/2010

An adaptive algorithm for topology optimization with goal-oriented error control

Tuesday 2nd November 2010

Bruggi, Matteo; Verani, Marco

We present an adaptive scheme, named ATOPT algorithm, to address volume–constrained compliance minimization, a benchmark problem in topology optimization. The algorithm performs a set of optimization loops on an underlying grid that is iteratively adapted to improve the description quality of the topology of the structure and the accuracy of the finite element compliance approximation of the evolving solution. Two suitable error estimators are defined in order to address both the issues. Numerical simulations show that ATOPT algorithm achieves optimal layouts that are in full agreement with standard results obtained by employing large scale uniformly refined grids. However, the ATOPT algorithm turns out to be more accurate in terms of the approximation of both the elastic behavior and the topology, while the computational cost spent in the minimization algorithm is remarkably reduced. Keywords: topology optimization, minimum compliance, adaptive mesh refinement. 2000 Mathematics Subject Classification. 65N30, 93B40