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A platform for research: civil engineering, architecture and urbanism
Material-based topology optimization provides a general tool in structural design. However, since its results are usually lacking in clearness and smoothness, the optimized layouts can often only be used as conceptional design idea instead of a clearly defined form of the structure. Therefore, the application of adaptive techniques in topology optimization is discussed and a method to generate smooth and well-defined two-dimensional structures is introduced. The proposed methods are based on a division of design and analysis model. In the design model the structural layout is described by a pixel-like scanning, as usually used in material-based topology optimization. These design patches are linked to the finite elements of the analysis model. Their material parameters are the active optimization variables of the corresponding cycle. The parametrization of the analysis model is adapted to the material distribution of each design cycle. Applying a simple mesh refining technique as used in h-type adaptive finite element analysis, on the one hand, the number of optimization variables can be reduced, since void domains of the design space are meshed coarser than non-void domains. On the other hand, the optimization results still contain jagged boundaries. Therefore, a method is proposed that adapts size and orientation of the finite elements in the analysis model to the material distribution in the design model. Consequently, a smooth and clearly defined structural layout can be generated by topology optimization. In addition, since in this method void areas are neglected during the optimization step, the number of active optimization variables is considerably reduced. The features of the proposed method are demonstrated by optimizing the layout of two-dimensional elastic structures with respect to maximum stiffness by an optimality criteria method. However, since adaptive topology optimization is also embedded in a mathematical programming scheme, a broad range of design problems can be solved efficiently.
Material-based topology optimization provides a general tool in structural design. However, since its results are usually lacking in clearness and smoothness, the optimized layouts can often only be used as conceptional design idea instead of a clearly defined form of the structure. Therefore, the application of adaptive techniques in topology optimization is discussed and a method to generate smooth and well-defined two-dimensional structures is introduced. The proposed methods are based on a division of design and analysis model. In the design model the structural layout is described by a pixel-like scanning, as usually used in material-based topology optimization. These design patches are linked to the finite elements of the analysis model. Their material parameters are the active optimization variables of the corresponding cycle. The parametrization of the analysis model is adapted to the material distribution of each design cycle. Applying a simple mesh refining technique as used in h-type adaptive finite element analysis, on the one hand, the number of optimization variables can be reduced, since void domains of the design space are meshed coarser than non-void domains. On the other hand, the optimization results still contain jagged boundaries. Therefore, a method is proposed that adapts size and orientation of the finite elements in the analysis model to the material distribution in the design model. Consequently, a smooth and clearly defined structural layout can be generated by topology optimization. In addition, since in this method void areas are neglected during the optimization step, the number of active optimization variables is considerably reduced. The features of the proposed method are demonstrated by optimizing the layout of two-dimensional elastic structures with respect to maximum stiffness by an optimality criteria method. However, since adaptive topology optimization is also embedded in a mathematical programming scheme, a broad range of design problems can be solved efficiently.
Adaptive topology optimization
Adaptive Topologie-Optimierung
Structural Optimization ; 10 ; 100-112
1995
13 Seiten, 19 Bilder, 6 Tabellen, 25 Quellen
Article (Journal)
English
Optimierung , Anpassungsfähigkeit , Variable , Problemlösung , Anordnungsplanung , Auslegung (Dimension) , Gewichtsminimierung , Konstruktionsdaten , geometrische Form , Topologie , Finite-Elemente-Methode , Maschennetz , Näherungsverfahren , Formgebung , Steifigkeit , Elastizität , orthotrope Platte , Isotropie , Balken , Platte (Bauteil) , Wanddicke , Grenzwert , Rechenmodell , Iteration , Bildabtastung , Lochplatte
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