Introduction to Shape Optimization

Haslinger, Jaroslav; Mäkinen, Raino A. E.

doi:10.1137/1.9780898718690

Cited by 274 publications

(105 citation statements)

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“…The state variables are supposed to satisfy the underlying fluid mechanical equations, and there are typically further constraints, e.g., bilateral constraints on the design variables which restrict the shape of the fluid filled domain. Shape optimization problems have been extensively studied and are well documented in the literature (cf., e.g., the monographs [1,16,31,33,58,59,81,87,94] ). The traditional approach relies on a separate treatment of the design objective and the state equation by an iterative cycle that starts from a given design, computes an approximate solution of the state equation for that design, invokes some sensitivity analysis for an update of the design, and continues this way until convergence is achieved.…”

Section: Path-following Barrier Methodsmentioning

confidence: 99%

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Antil¹,

Hoppe²,

Linsenmann³

et al. 2012

Progress in Computational Physics (PiCP) Vol: 2 Coupled Fluid Flow in Energy, Biology and Environmental Research

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Microfluidic biochips are devices that are designed for high throughput screening and hybridization in genomics, protein profiling in proteomics, and cell analysis in cytometry. They are used in clinical diagnostics, pharmaceutics and forensics. The biochips consist of a lithographically produced network of channels and reservoirs on top of a glass or plastic plate. The idea is to transport the injected DNA or protein probes in the amount of nanoliters along the network to a reservoir where the chemical analysis is performed. Conventional biochips use external pumps to generate the fluid flow within the network. A more precise control of the fluid flow can be achieved by piezoelectrically agitated surface acoustic waves (SAW) generated by interdigital transducers on top of the chip, traveling across the surface and entering the fluid filled channels. The fluid and SAW interaction can be described by a mathematical model which consists of a coupling of the piezoelectric equations and the compressible Navier-Stokes equations featuring processes that occur on vastly different time scales. In this contribution, we follow a homogenization approach in order to cope with the multiscale behavior of the coupled system that enables a separate treatment of the fast and slowly varying processes. The resulting model equations are the basis for the numerical simulation which is taken care of by implicit time stepping and finite element discretizations in space. Finally, the need for a better efficiency and cost effectiveness of the SAW driven biochips in the sense of a significant speed-up and more favorable reliability of the hybridization process requires an improved design which will also be addressed in this contribution. In particular, the challenge to deal with the resulting large scale optimal control and optimization problems can be met by the application of projection based model reduction techniques.

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Section: Path-following Barrier Methodsmentioning

confidence: 99%

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Antil¹,

Hoppe²,

Linsenmann³

et al. 2012

Progress in Computational Physics (PiCP) Vol: 2 Coupled Fluid Flow in Energy, Biology and Environmental Research

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“…Furthermore, a mathematical overview concerning sizing and shape optimization is presented by Haslinger and Mäkinen [19].…”

Section: Shape Optimizationmentioning

confidence: 99%

On gradient‐based optimization strategies for inverse problems in metal forming

Landkamer¹,

Söhngen²,

Steinmann³

et al. 2017

GAMM-Mitteilungen

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In the context of metal forming, optimization issues typically lead to inverse problems with a least-squares minimization as the objective. Due to the nonlinearities in forming simulations, iterative optimization approaches have to be considered. Gradient-based solution strategies for two inverse problems are proposed and compared to each other. Firstly, the identification of elasto-plastic material parameters is regarded. Secondly, a recently developed approach for the determination of an optimal workpiece design is investigated. As a special feature, both approaches can be coupled in a non-invasive fashion to arbitrary external finite element software via subroutines.

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“…For an overview, the interested reader is referred to the monographs. 25,26 Typically, the goal in structural optimization is to find a design which is as light as possible and can simultaneously withstand a specified load. In this work, the objective is different: here, a deformation associated with a certain load is prescribed.…”

Section: Numericalmentioning

confidence: 99%

Material parameter computation for multi-layered vocal fold models

Schmidt

Stingl

Leugering

et al. 2011

The Journal of the Acoustical Society of America

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Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.

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Introduction to Shape Optimization

Cited by 274 publications

References 0 publications

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

On gradient‐based optimization strategies for inverse problems in metal forming

Material parameter computation for multi-layered vocal fold models

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