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Topological derivative for linear elastic plate bending problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This study concerns the application of the Topological-Shape Sensitivity Method as a systematic procedure to determine the Topological Derivative for linear elastic plate bending problems within the framework of Kirchhoff's kinematic approach. This method, based on classical Shape Sensitivity Analysis, leads to a constructive procedure to obtain the Topological Derivative. Utilising the well known terminology of structural optimization, we adopt, the total potential strain energy as the cost function and the equilibrium equation as the constraint. Variational formulation as well as the direct differentiation method are used to perform the shape derivative of the cost function. Finally, in order to obtain a uniform distribution of bending moments in several plate problems, the Topological Derivative was approximated, by the Finite Element Method, and used to find the best place to insert holes. A simple hard-kill like topology algorithm, which furnishes satisfactory qualitative results in agreement with those reported in the literature, is also shown.
Rocznik
Strony
339--361
Opis fizyczny
Bibliogr. 39 poz., rys., wykr.
Twórcy
  • Laboratorio Nacional de Computacao Cientıfica LNCC/MCT Av. Getulio Vargas 333, 25651-075 Petropolis - RJ, Brasil
autor
  • Laboratorio Nacional de Computacao Cientıfica LNCC/MCT Av. Getulio Vargas 333, 25651-075 Petropolis - RJ, Brasil
autor
  • Centro Atomico Bariloche 8400 Bariloche, Argentina
autor
  • Laboratorio Nacional de Computacao Cientıfica LNCC/MCT Av. Getulio Vargas 333, 25651-075 Petropolis - RJ, Brasil
Bibliografia
  • Amstutz S., Dominguez, N. and Samet, B. (2004) Sensitivity Analysis with Respect to the Insertion of Small Inhomogeneities. In: P. Neittaanmaki et al. (2004), Mini-symposium on Topological Sensitivity Analysis: Theory and Applications.
  • Batoz, J.L. (1982) An Explicit Formulation for an Efficient Triangular Plate-Bending Element. International Journal for Numerical Methods in Engineering 18, 1077-1089.
  • Cea, J. (1981) Problems of Shape Optimal Design. In: Haug and Cea.
  • Cea, J., Garreau, S., Guillaume, Ph. and Masmoudi, M. (2000) The Shape and Topological Optimizations Connection. Computer Methods in Applied Mechanics and Engineering 188, 713-726.
  • Eschenauer, H.A. and Olhoff, N. (2001) Topology Optimization of Continuum Structures: A Review. Applied Mechanics Review 54, 331-390.
  • Eschenauer, H.A., Kobelev, V.V. and Schumacher, A. (1994) Bubble Method for Topology and Shape Optimization of Structures. Structural Optimization 8, 42-51.
  • Eshelby, J.D. (1975) The Elastic Energy-MomentumTensor. Journal of Elasticity 5, 321-335.
  • Feijoo, G.R. (2004) On The Solution of Inverse Scattering Problems Using the Topological Derivative. In: P. Neittaanmaki et al. (2004).
  • Feijoo, R.A., Novotny, A.A., Taroco, E. and Padra, C. (2003) The Topological Derivative for the Poisson’s Problem. Mathematical Models and Methods in Applied Sciences 13-12, 1-20.
  • Feijoo, R.A., Novotny, A.A., Padra, C. and Taroco, E. (2004) The Topological-Shape Sensitivity Method and its Application in 2D Elasticity. To appear in Journal of Computational Methods in Sciences and Engineering.
  • Germain, P. and Muller, P. (1994) Introduction a la Mecanique des Milieux Continus. Masson, Paris.
  • Garreau, S., Guillaume, Ph. and Masmoudi, M. (1998) The Topological Gradient. Research Report, UFR MIG, Universite Paul Sabatier, Toulouse 3, France.
  • Garreau, S., Guillaume, Ph. and Masmoudi, M. (2001) The Topological Asymptotic for PDE Systems: The Elasticity Case. SIAM Journal on Control and Optimization 39, 1756-1778.
  • Guzina, B.B. and Chikichev, I. (2004) On the Generalized Concept of Topological Sensitivity. In: P. Neittaanmaki et al. (2004).
  • Hassine, M., Jan, S. and Masmoudi, M. (2004) From Differential Calculus to 0-1 Optimization. In: P. Neittaanmaki et al. (2004).
  • Haug, E.J., Choi, K.K. and Komkov, V. (1986) Design Sensitivity Analysis of Structural Systems. Academic Press.
  • Haug, E.J. and Cea, J. (1981) Proceedings: Optimization of Distributed Parameters Structures. Iowa, EUA.
  • Hughes, T.J.R. (1987) The Finite Element Method - Linear Static and Dynamic Finite Element Analysis. Prentice-Hall.
  • Ilin, A.M. (1992) Matching of Asymptotic Expansions of Solutions of Boundary Value Problems. Translations of Mathematical Monographs 102. AMS, Providence.
  • Lewiński, T. and Sokołowski, J.(2003) Energy change due to the appearance of cavities in elastic solids. International Journal of Solids and Structures 40, 1765-1803.
  • Liang, Q.Q. and Steven, G.P. (2002) A Performance-Based Optimization Method for Topology Design of Continuum Structures with Mean Compliance Constraints. Computer Methods in Applied Mechanics and Engineering 191, 1471-1489.
  • Murat, F. and Simon, J. (1976) Sur le Controle par un Domaine Geometrique. Thesis, Universite Pierre et Marie Curie, Paris VI.
  • Neittaanmaki, P., Rossi, T., Korotov, S., Onate, E., Periaux J. and Knorzer, D., eds. (2004) Proceedings of ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering, Jyvaskyla, 24-28 July, CD-RIM ISBN 951-39-1869-6.
  • Novotny, A.A. (2003) Analise de Sensibilidade Topologica. Ph. D. Thesis, LNCC/MCT, Petropolis - RJ, Brasil, (http://www.lncc.br/∼novotny/principal.htm).
  • Novotny, A.A., Feijoo, R.A., Padra, C. and Taroco, E. (2003) Topological Sensitivity Analysis. Computer Methods in Applied Mechanics and Engineering 192, 803-829.
  • Novotny, A.A., Felipe, T.G., Feijo, R.A., Padra, C. and Taroco, E. (2004) Topological-Shape Sensitivity Method Applied to Inverse Poisson’s Conductivity Problem. Inverse Problems, Design and Optimization - IPDO Synposium, Rio de Janeiro, Brasil.
  • Novotny, A.A., Padra, C., Feijoo, R.A. and Taroco, E. (2004) The Topological-Shape Sensitivity Method. In: P. Neittaanmaki et al. (2004).
  • Padra, C., Novotny, A.A., Feijoo, R.A. and Taroco, E. (2004) The Topological-Shape Sensitivity Method and its Applications in Topology Design and Inverse Problems. In: P. Neittaanmaki et al. (2004).
  • Pironneau, O. (1984) Optimal Shape Design for Elliptic Systems. Springer-Verlag.
  • Pironneau, O. (2004) Derivatives with Respect to Piecewise Constant Coefficients of a PDE with Application to Calibration. In: P. Neittaanmaki et al., eds., Mini-symposium on Topological Sensitivity Analysis: Theory and Applications.
  • Schumacher, A. (1995) Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungkriterien. Ph.D. Thesis, UniversitatGesamthochschule-Siegen, Siegen.
  • Sokołowski, J.(2004) Asymptotic Analysis and Shape Optimization in Elasticity. In: P. Neittaanmaki et al. (2004).
  • Sokołowski, J. and Żochowski, A. (1999) On the Topological Derivative in Shape Optimization. Research Report n. 3170, INRIA-Lorraine, France, 1997. SIAM Journal on Control and Optimization 37, 1251-1272.
  • Sokołowski, J. and Żochowski, A. (1999) Topological Derivatives for Elliptic Problems. Inverse Problems 15, 123-134.
  • Sokołowski, J. and Żochowski, A. (2004) Topological Derivatives for Contact Problems. In: P. Neittaanmaki et al. (2004).
  • Sokołowski, J. and Zolesio, J.-P. (1992) Introduction to Shape Optimization - Shape Sensitivity Analysis. Springer-Verlag.
  • Taroco, E., Buscaglia, G.C. and Feij´oo, R.A. (1998) Second-Order Shape Sensitivity Analysis for Nonlinear Problems. Structural Optimization 15, 101-113.
  • Zienkiewicz, O.C. and Taylor, R.L. (1989) The Finite Element Method. McGraw Hill.
  • Zolesio, J.-P. (1981) The Material Derivative (or Speed) Method for Shape Optimization. In: Haug and Cea (1981).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0093
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