Topology optimization analysis based on the direct coupling of the boundary element method and the level set method

The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies’ dimensions, materials strength and structural system configuration. In this regard, topolog...

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Bibliographic Details
Published in:International journal of advanced structural engineering 2017-12, Vol.9 (4), p.397-407
Main Authors: Vitório, Paulo Cezar, Leonel, Edson Denner
Format: Article
Language:English
Subjects:
Boundary element method
Building Construction and Design
Civil Engineering
Control
Coupling
Dynamical Systems
Engineering
Engineering Design
Finite element method
Geometry
Iterative methods
Mathematical analysis
Nonlinear programming
Original Research
Reconstruction
Solid Mechanics
Structural design
Topology optimization
Vibration
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Summary:The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies’ dimensions, materials strength and structural system configuration. In this regard, topology optimization aims for achieving the optimal structural geometry, i.e. the shape that leads to the minimum requirement of material, respecting constraints related to the stress state at each material point. The present study applies an evolutionary approach for determining the optimal geometry of 2D structures using the coupling of the boundary element method (BEM) and the level set method (LSM). The proposed algorithm consists of mechanical modelling, topology optimization approach and structural reconstruction. The mechanical model is composed of singular and hyper-singular BEM algebraic equations. The topology optimization is performed through the LSM. Internal and external geometries are evolved by the LS function evaluated at its zero level. The reconstruction process concerns the remeshing. Because the structural boundary moves at each iteration, the body’s geometry change and, consequently, a new mesh has to be defined. The proposed algorithm, which is based on the direct coupling of such approaches, introduces internal cavities automatically during the optimization process, according to the intensity of Von Mises stress. The developed optimization model was applied in two benchmarks available in the literature. Good agreement was observed among the results, which demonstrates its efficiency and accuracy.
ISSN:2008-3556
2008-6695
DOI:10.1007/s40091-017-0175-8