Hybrid discretization of convective terms for aeroacoustics

2013 ◽  
Author(s):  
M. G. Cojocaru
Keyword(s):  
Hybrid Discretization

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

Simulation of the insulation properties of a HVDC transformer using a hybrid discretization based on finite elements and harmonic functions

2007 ◽  
Vol 90 (5) ◽  
pp. 331-336 ◽  
Author(s):  
Stephan Koch ◽  
Herbert De Gersem ◽  
Thomas Weiland ◽  
Jens Hoppe ◽  
Peter Heinzig
Keyword(s):  
Finite Elements ◽  
Harmonic Functions ◽  
Hybrid Discretization

The Comparision of Hybrid and Quadrilateral Discretization Models for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Nitin M. Dhembare
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Search Space ◽  
Structural Members ◽  
Constraint Violation ◽  
Local Connection ◽  
Hybrid Discretization ◽  
Local Topology ◽  
Design Cell

The design domain of a synthesized compliant mechanism is discretized into quadrilateral design cells in both hybrid and quadrilateral discretization models. However, quadrilateral discretization model allows for point connection between two diagonal design cells. Hybrid discretization model completely eliminates point connection by subdividing each quadrilateral design cell into triangular analysis cells and connecting any two contiguous quadrilateral design cells using four triangular analysis cells. When point connection is detected and suppressed in quadrilateral discretization, the local topology search space is dramatically reduced and slant structural members are serrated. In hybrid discretization, all potential local connection directions are utilized for topology optimization and any structural members can be smooth whether they are in the horizontal, vertical or diagonal direction. To compare the performance of hybrid and quadrilateral discretizations, the same design and analysis cells, genetic algorithm parameters, constraint violation penalties are employed for both discretization models. The advantages of hybrid discretization over quadrilateral discretization are obvious from the results of two classical synthesis examples of compliant mechanisms.

scholarly journals Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows

2018 ◽  
Vol 77 (3) ◽  
pp. 1424-1443 ◽  
Author(s):  
Karol L. Cascavita ◽  
Jérémy Bleyer ◽  
Xavier Chateau ◽  
Alexandre Ern
Keyword(s):  
Yield Surface ◽  
Discretization Methods ◽  
Pipe Flows ◽  
Surface Detection ◽  
Hybrid Discretization

The Uncertainty Elimination in Discrete Topology Optimization of Compliant Mechanisms

2013 ◽  
Author(s):  
Hong Zhou ◽  
Satya Raviteja Kandala
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Process ◽  
Design Domain ◽  
Discrete Topology ◽  
Optimization Strategy ◽  
Hybrid Discretization ◽  
Ambiguous Point

Topology uncertainty leads to different topology solutions and makes topology optimization ambiguous. Point connection and grey cell might cause topology uncertainty. They are both eradicated when hybrid discretization model is used for discrete topology optimization. A common topology uncertainty in the current discrete topology optimization stems from mesh dependence. The topology solution of an optimized compliant mechanism might be uncertain when its design domain is discretized differently. To eliminate topology uncertainty from mesh dependence, the genus based topology optimization strategy is introduced in this paper. The topology of a compliant mechanism is defined by its genus which is the number of holes in the compliant mechanism. With this strategy, the genus of an optimized compliant mechanism is actively controlled during its topology optimization process. There is no topology uncertainty when this strategy is incorporated into discrete topology optimization. The introduced topology optimization strategy is demonstrated by examples with different degrees of genus.

scholarly journals Tomographic Image Reconstruction Based on Minimization of Symmetrized Kullback-Leibler Divergence

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Ryosuke Kasai ◽  
Yusaku Yamaguchi ◽  
Takeshi Kojima ◽  
Tetsuya Yoshinaga
Keyword(s):  
Differential Equation ◽  
High Performance ◽  
Euler Method ◽  
Tomographic Image Reconstruction ◽  
Multiplicative Calculus ◽  
Leibler Divergence ◽  
Dynamical Method ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Hybrid Discretization

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation. We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance.

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