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Shape Optimization and Shape Identification for Transient Diffusion Problems in Textile Structures

Korycki R.

Fibres & Textiles in Eastern Europe

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2007

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Vol. 15, no. 1 (60)

43--49

EN

The equation of substance balance and the set of boundary and initial conditions determine the transient diffusion problem within the homogenized textile structure. Introducing an arbitrary behavioral functional, its first-order sensitivity expressions can be stated using the material derivative concept and both the direct and the adjoint approaches. Shape optimization and identification problems are then formulated applying the sensitivity expressions. Simple numerical examples of shape identification and optimization of textile structures are presented.

PL

Nieustalony problem dyfuzji wewnątrz homogenicznej konstrukcji włókienniczej jest określony równaniem bilansu substancji oraz układem równań warunków brzegowych i początkowych. Wprowadzając dowolny funkcjonał, określa się jego wrażliwość pierwszego rzędu przy wykorzystaniu koncepcji pochodnej materialnej oraz metod bezpośredniej i układów sprzężonych analizy wrażliwości. Problemy optymalizacji i identyfikacji kształtu są następnie sformułowane z wykorzystaniem uzyskanych wyrażeń wrażliwości. Zaprezentowano proste przykłady numeryczne identyfikacji i optymalizacji kształtu konstrukcji włókienniczych.

2

Evolutionary stress minimisation on a turbine blade shank

Grela W., Burczyński T.

Computer Assisted Mechanics and Engineering Sciences

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2005

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Vol. 12, No. 2-3

147-161

EN

The paper describes shape optimisation of a turbine blade shank. The turbine blade shank zone with a compound fillet is a critical location where a high risk of failure exists. The APDL language operating in Ansys environment is used to write a parametric turbine blade shank FEM models generator, which is a basic part of evolutionary optimisation routine. The goal of the optimisation is the 1st principal stress reduction with maximum allowable mass constraint imposed. Parameterisation routine and optimisation results are presented and discussed.

3

On stability analysis in shape optimisation : critical shapes for Neumann problem

Dambrine M., Sokolowski J., Żochowski A.

Control and Cybernetics

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2003

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Vol. 32, no 3

503-528

EN

The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then, the new estimates for the shape Hessian are derived in order to overcome the classical two norms-discrepancy well know in control problems, Malanowski (2001). In the context of shape optimization, the situation is similar compared to control problems, actually, the shape Hessian can be coercive only in the norm strictly weaker with respect to the norm of the second order differentiability of the shape functional. In addition, it is shown that an appropriate regularization makes possible the stability of critical shapes.