BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Optimization of bodies with locally periodic microstructure

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

Summary
This article describes a numerical study of the optimization of elastic bodies featuring a locally periodic microscopic pattern. The authors’ approach makes the link between the microscopic level and the macroscopic one. Two-dimensional linearly elastic bodies are considered; the same techniques can be applied to three-dimensional bodies. Homogenization theory is used to describe the macroscopic (effective) elastic properties of the body. The macroscopic domain is divided in (rectangular) finite elements and in each of them the microstructure is supposed to be periodic; the periodic pattern is allowed to vary from element to element. Each periodic microstructure is discretized using a finite element mesh on the periodicity cell, by identifying the opposite sides of the cell in order to handle the periodicity conditions in the cellular problem. Shape optimization and topology optimization are used at the microscopic level, following an alternate directions algorithm. Numerical examples are presented, in which a cantilever is optimized for different load cases, one of them being multi-load. The problem is numerically heavy, since the optimization of the macroscopic problem is performed by optimizing in simultaneous hundreds or even thousands of periodic structures, each one using its own finite element mesh on the periodicity cell. Parallel computation is used in order to alleviate the computational burden.


Where published
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES

Publication Identifiers
ISSN - 1537-6494



Document Identifiers
URL - http://dx.doi.org/10.1080/15376494.2011.642939
DOI - https://doi.org/10.1080/15376494.2011.642939

Keywords
shape optimization topology optimization alternate directions algorithm locally periodic homogenization cellular problem parallel computation