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Eine effiziente Beschreibung des mechanischen Verhaltens von speziellen 3D-Körpern, deren Abmessungen in einer oder zwei Richtungen klein gegenüber den übrigen Abmessungen sind, ist durch sogenannte Platten- oder Balkenmodelle möglich.

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Publikationen

 Artikel in Referierten Journalen

  • S. Neukamm, H. Olbermann, Homogenization of the nonlinear bending theory for plates, Calculus of Variations and Partial Differential Equations, (published online on Sept. 14, 2014), DOI 10.1007/s00526-014-0765-2 .
    Abstract
    We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting functional is not simply a quadratic functional of the second fundamental form of the deformed plate as it is the case in nonlinear plate theory. It turns out that the limiting functional discriminates between whether the deformed plate is locally shaped like a "cylinder" or not. For the derivation we investigate the oscillatory behavior of sequences of second fundamental forms associated with isometric immersions, using two-scale convergence. This is a non-trivial task, since one has to treat two-scale convergence in connection with a nonlinear differential constraint.

  • R.B. Guenther, P. Krejčí, J. Sprekels, Small strain oscillations of an elastoplastic Kirchhoff plate, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 88 (2008), pp. 199--217.

  • P. Krejčí, J. Sprekels, Clamped elastic-ideally plastic beams and Prandtl--Ishlinskii hysteresis operators, Discrete and Continuous Dynamical Systems -- Series S, 1 (2008), pp. 283--292.

  • W. Dreyer, F. Duderstadt, S. Eichler, M. Jurisch, Stress analysis and bending tests for GaAs wafer, Microelectronics Reliability, 46 (2006), pp. 822--835.

  • V. Arnăutu, J. Sprekels, D. Tiba, A reduction approximation method for curved rods, Numerical Functional Analysis and Optimization. An International Journal, 26 (2005), pp. 139-155.

  • A. Ignat, J. Sprekels, D. Tiba, A model of a general elastic curved rod, Mathematical Methods in the Applied Sciences, 25 (2002), pp. 835-854.

  • J. Sprekels, D. Tiba, An analytic approach to a generalized Naghdi shell model, Advances in Mathematical Sciences and Applications, 12 (2002), pp. 175-190.

  • A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches, SIAM Journal on Control and Optimization, 40 (2001), pp. 1107-1133.

  • V. Arnăutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 337--354.

  • J. Sprekels, D. Tiba, Sur les arches lipschitziennes, Comptes Rendus Mathematique. Academie des Sciences. Paris, 331 (2000), pp. 179--184.

 Beiträge zu Sammelwerken

  • J. Sprekels, D. Tiba, Optimization problems for thin elastic structures, in: Optimal Control of Coupled Systems of Partial Differential Equations, K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., 158 of Internat. Series Numer. Math., Birkhäuser, Basel et al., 2009, pp. 255--273.

 Vorträge, Poster

  • J. Sprekels, Oscillating elastoplastic bodies: Dimensional reduction, hysteresis operators, existence results, Direct, Inverse and Control Problems for PDE's (DICOP 08), September 22 - 26, 2008, Cortona, Italy, September 22, 2008.

  • J. Sprekels, Oscillating thin elastoplastic bodies: Dimensional reduction, hysteresis operators, existence results, Seminar Partial Differential Equations: Models and Applications, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, May 20, 2008.

  • F. Duderstadt, Simulation eines Wafer-Biegetests durch Verwendung der von Kármán'schen Plattentheorie für kubisch anisotrope Materialien, Oberseminar Numerik/Analysis, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, January 9, 2007.

  • J. Sprekels, Elastic-ideally plastic beams and 1D Prandtl--Ishlinskii hysteresis operators, Workshop ``Phase Transitions'', June 3 - 9, 2007, Mathematisches Forschungsinstitut Oberwolfach, June 7, 2007.

  • F. Duderstadt, A challenge to engineers: The Babuška-Paradox, International Conference on ``Programs and Algorithms of Numerical Mathematics 13'' in honor of Ivo Babuška's 80th birthday, May 28 - 31, 2006, Academy of Sciences of the Czech Republic, Mathematical Institute, Prague, May 31, 2006.

  • J. Sprekels, Phase field models with hysteresis, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7 - 11, 2003, Sydney, Australia, July 8, 2003.

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