NDLI: Relaxed representations and improving stability in time-stepping analysis of three-dimensional structural nonlinear dynamics

Content Provider	Springer Nature Link
Author	Lopez, Salvatore
Copyright Year	2011
Abstract	In the present paper, we propose a representation of the discrete motion equations in structural nonlinear dynamics to obtain an improvement in the stability of time numerical integrations. A geometrically nonlinear total Lagrangian formulation for three-dimensional beam elements in the hypotheses of large rotations and small strains is presented. In this formulation, slopes are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. Such representations of the internal strains—rotations compatibility are then imposed in their time derivatives version. The results, related to Newmark approximations for the variations in the displacement and velocity vectors, show a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration steps. The numerical tests, furthermore, show that the variation in the total energy in the time steps has bounded oscillations about the zero value.
Starting Page	705
Ending Page	720
Page Count	16
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	69
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-12-22
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Numerical stability Time relaxed representation Structural three-dimensional nonlinear dynamics Automotive Engineering Mechanics Mechanical Engineering Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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