Virtual-pulse time integral methodology, a new approach for computational dynamics: Part 1 - Theory for linear structural dynamics

Desong Sha, Xiaoqin Chen, Kumar K. Tamma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For computational dynamics problems, direct time integration and mode superposition are the most widely employed approaches. Of the two, direct time stepping methods have been quite popular in many commercial codes because of their various inherent advantages. However, for numerous engineering applications, mode superposition techniques continue to be the choice of many analysts, especially for linear systems and for long time responses. To date, much progress has been made in the development and understanding of direct time integration methods for computational dynamics problems encountered in engineering. Besides investigations encompassing accuracy and stability properties of these time integration schemes, the related developments include single step, multi-step, mixed and/or variable time integration features and the like. Unlike past practices customarily employed for computational dynamics, the present paper introduces a new VIrtual-Pulse (VIP) time integral methodology which offers several attractive and effective features. The proposed method possesses a unique solution methodology of its own, thus avoiding the need to employ any existing time stepping methods. The present paper primarily serves to lay down the fundamental developments towards establishing the theoretical basis via new perspectives for subsequent applications to general computational structural dynamics. However, for expository purposes, attention is confined only to linear structural dynamic systems in this paper; and Rayleigh damping is considered here, although non-Rayleigh damping can be readily permitted but is not described here. As a consequence, the characteristics of the methodology include: 1) an explicit unconditionally stable representation, 2) second-order accuracy, 3) much less algorithmic damping than direct time integration methods advocated in existing commercial codes; if an undamped system is considered, the algorithmic damping is zero, 4) the relative period error is zero, and 5) self-starting features. Theoretical details of the developments, the stability and accuracy characteristics are described. Illustrative numerical examples are presented to validate the proposed methodology for computational dynamic problems.

Original languageEnglish (US)
Title of host publicationNew Methods in Transient Analysis
PublisherPubl by ASME
Pages131-139
Number of pages9
ISBN (Print)0791810887
StatePublished - Dec 1 1992
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA
Duration: Nov 8 1992Nov 13 1992

Publication series

NameAmerican Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
Volume246
ISSN (Print)0277-027X

Other

OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAnaheim, CA, USA
Period11/8/9211/13/92

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Sha, D., Chen, X., & Tamma, K. K. (1992). Virtual-pulse time integral methodology, a new approach for computational dynamics: Part 1 - Theory for linear structural dynamics. In New Methods in Transient Analysis (pp. 131-139). (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP; Vol. 246). Publ by ASME.