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On the advantages of using the first-order generalised-alpha scheme for structural dynamic problems / Djordje, Peric; Wulf, Dettmer; Chennakesava, Kadapa

Computers & Structures, Volume: 193, Pages: 226 - 238

Swansesa University Authors: Djordje, Peric, Wulf, Dettmer, Chennakesava, Kadapa

Abstract

The advantages of using the generalised-alpha scheme for first-order systems for computing the numerical solutions of second-order equations encountered in structural dynamics are presented. The governing equations are rewritten so that the second-order equations can be solved directly without havin...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: 2017
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa35131
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Abstract: The advantages of using the generalised-alpha scheme for first-order systems for computing the numerical solutions of second-order equations encountered in structural dynamics are presented. The governing equations are rewritten so that the second-order equations can be solved directly without having to convert them into state-space. The stability, accuracy, dissipation and dispersion characteristics of the scheme are discussed. It is proved through spectral analysis that the proposed scheme has improved dissipation properties when compared with the standard generalised-alpha scheme for second-order equations. It is also proved that the proposed scheme does not suffer from overshoot. Towards demonstrating the application to practical problems, proposed scheme is applied to the benchmark example of three degrees of freedom stiff-flexible spring-mass system, two-dimensional Howe truss model, and elastic pendulum problem discretised with non-linear truss finite elements.
Item Description: The advantages of applying the generalised-alpha scheme for first-order systems to the second-order equations encountered in structural dynamics are presented. The additional computational cost is restricted to the storage of an additional set of history variables. The stability, accuracy, dissipation and dispersion characteristics of the scheme are assessed. The proposed scheme has improved dissipation properties when compared to the standard generalised-alpha scheme for second-order equations and it does not suffer from overshoot. These properties are demonstrated in a number of linear and nonlinear benchmark problems. This article represents a strong contribution to the area of solid dynamics.
Keywords: Structural dynamics; Time integration; Generalised-alpha scheme; Numerical dissipation; Overshoot
College: College of Engineering
Start Page: 226
End Page: 238