A Newmark space-time formulation in structural dynamics

Computational Mechanics, vol. 67, pp. 1331–1348

Abstract

Abstract In this contribution, we present a space-time formulation of the Newmark integration scheme for linear damped structures under both harmonic and transient excitations. The incremental set of equations of motion and the Newmark approximations are transformed into their corresponding space-time equivalents. The dynamic system is then represented by one algebraic space-time equation only. This equation is projected into a coupled pair of space-time equations, which is solved via the fixed point algorithm. The solution is iteratively assembled by enrichments, each of which is decomposed by a dyadic product of spatial and temporal enrichment vectors. The evolution of the spatial enrichment vectors is investigated during convergence and interpreted by comparing them to the set of linear modes of vibration. The new method is demonstrated by means of four numerical examples, presenting not only the excellent convergence behavior and the numerical efficiency but also the limits of the proposed approach.

Authors 7

1. Franz Bamer corresponding Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52062, Aachen, Germany

2. Nima Shirafkan Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52062, Aachen, Germany

3. Xiaodan Cao

   Centre National de la Recherche Scientifique · Université de Lille · Laboratoire de Mécanique, Multiphysique, Multiéchelle · Centrale Lille Institut

   Affiliation as printed

   Univ. Lille, CNRS, Centrale Lille, UMR 9013 - LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle, F-59000, Lille, France

4. Abdelbacet Oueslati

   Centre National de la Recherche Scientifique · Université de Lille · Laboratoire de Mécanique, Multiphysique, Multiéchelle · Centrale Lille Institut

   Affiliation as printed

   Univ. Lille, CNRS, Centrale Lille, UMR 9013 - LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle, F-59000, Lille, France

5. Marcus Stoffel Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52062, Aachen, Germany

6. Géry de Saxcé

   Centre National de la Recherche Scientifique · Université de Lille · Laboratoire de Mécanique, Multiphysique, Multiéchelle · Centrale Lille Institut

   Affiliation as printed

   Univ. Lille, CNRS, Centrale Lille, UMR 9013 - LaMcube - Laboratoire de Mécanique, Multiphysique, Multiéchelle, F-59000, Lille, France

7. Bernd A. Markert Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52062, Aachen, Germany