An Uncoupling Strategy in the Newmark Method for Dynamic Problems

  • Jonathan Esteban Arroyo Silva
  • Michelli Marlane Silva LoureiroEmail author
  • Webe Joao Mansur
  • Felipe dos Santos Loureiro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)


When the semidiscrete formulation of the finite element method (FEM) is employed in traditional elastodynamic problems, a system of ordinary differential equations (ODEs) is obtained. The present paper focuses on the development of a numerical strategy to decouple the resulting system by means of the implicit unconditionally stable Newmark method, allowing the parts to be solved independently, and through an iterative procedure, managing to preserve the stability and accuracy properties of the original method. It is observed that only one iteration is sufficient to achieve the same level of accuracy of the solution of the fully coupled system, rendering a very efficient algorithm. The accuracy and potentialities of the proposed decoupling strategy will be studied through the solution of two 2D structural dynamic problems that present materials with functionally graded properties.


Structural dynamics Newmark FEM FGM 



The financial support of CNPQ, FAPEMIG, UFSJ and UFJF is greatly acknowledged.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jonathan Esteban Arroyo Silva
    • 1
  • Michelli Marlane Silva Loureiro
    • 2
    Email author
  • Webe Joao Mansur
    • 3
  • Felipe dos Santos Loureiro
    • 4
  1. 1.Postgraduate Program in Computational ModelingFederal University of Juiz de ForaJuiz de ForaBrazil
  2. 2.Department of Computer ScienceFederal University of São João del-ReiSão João del-ReiBrazil
  3. 3.Department of Civil Engineering, COPPEFederal University of Rio de JaneiroRio de JaneiroBrazil
  4. 4.Department of Thermal and Fluid SciencesFederal University of São João del-ReiSão João del-ReiBrazil

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