BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Shape and Topology Optimization for Periodic Problems Part II: optimization algorithm and numerical examples

Participants in the publication
C. Barbarosie (Author)
Dep. Matemática
CMAFcIO
A.-M. Toader (Author)
Dep. Matemática
CMAFcIO

Summary
The present paper deals with the implementation of an optimization algorithm for periodic problems which alternates shape and topology optimization; the theoretical background about shape and topological derivatives was developed in Part I (Barbarosie and Toader, Struct Multidiscipl Optim, 2009). The proposed numerical code relies on a special implementation of the periodicity conditions based on differential geometry concepts: periodic functions are viewed as functions defined on a torus. Moreover the notion of periodicity is extended and cases where the periodicity cell is a general parallelogram are admissible. This approach can be adapted to other frameworks (e.g. Bloch waves or fluid dynamics). The numerical method was tested for the design of periodic microstructures. Several examples of optimal microstructures are given for bulk modulus maximization, maximization of rigidity for shear response, maximization of rigidity in a prescribed direction, minimization of the Poisson coefficient.


Where published
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION

Publication Identifiers
ISSN - 1615-147X

Document Identifiers
DOI - https://doi.org/10.1007/s00158-009-0377-1
URL - https://link.springer.com/article/10.1007/s00158-009-0377-1

Keywords
optimization of microstructures finite element method on a periodic mesh mesh regeneration shape optimization topology optimization auxetic materials