Structural Engineering and Mechanics

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Multipoint variable generalized displacement methods: Novel nonlinear solution schemes in structural mechanics

  • Maghami, Ali (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad) ;
  • Shahabian, Farzad (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad) ;
  • Hosseini, Seyed Mahmoud (Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad)
  • Received : 2021.09.23
  • Accepted : 2022.04.28
  • Published : 2022.07.25
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Abstract

The generalized displacement method is a nonlinear solution scheme that follows the equilibrium path of the structure based on the development of the generalized displacement. This method traces the path uniformly with a constant amount of generalized displacement. In this article, we first develop higher-order generalized displacement methods based on multi-point techniques. According to the concept of generalized stiffness, a relation is proposed to adjust the generalized displacement during the path-following. This formulation provides the possibility to change the amount of generalized displacement along the path due to changes in generalized stiffness. We, then, introduce higher-order algorithms of variable generalized displacement method using multi-point methods. Finally, we demonstrate with numerical examples that the presented algorithms, including multi-point generalized displacement methods and multi-point variable generalized displacement methods, are capable of following the equilibrium path. A comparison with the arc length method, generalized displacement method, and multi-point arc-length methods illustrates that the adjustment of generalized displacement significantly reduces the number of steps during the path-following. We also demonstrate that the application of multi-point methods reduces the number of iterations.

Keywords

Acknowledgement

This work was accomplished during a postdoctoral research program of the first author (Ali Maghami) at the department of Industrial Engineering of the Ferdowsi University of Mashhad. Ali Maghami was supported by a grant from Ferdowsi University of Mashhad, Iran (No. FUM 67230).

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