ON SUFFICIENT AND NECESSARY CONDITIONS FOR NUMERICAL STABILITY IN NONLINEAR TRANSIENT ANALYSIS

Abstract eng:
Time integration is almost the mere practical tool to analyze nonlinear structural dynamic behaviors. However, the responses are approximations. Accordingly, numerical stability is an important issue effectual in many practical time integration analyses as well as researches involved in transient analysis. While the necessary and sufficient conditions for numerical stability of the responses obtained from time integration are clear for linear problems, major ambiguities persist for the stability of nonlinear analyses. This is the subject of discussion in this paper. The discussion starts with a new relation (developed in this paper) implying numerical stability for both linear and nonlinear systems and then using that relation not only the necessary and sufficient conditions of numerical stability of linear problems are re-obtained but also relations are suggested as necessary and sufficient conditions for numerical stability of nonlinear problems. Implementation/consideration of the suggested conditions in real analyses is also discussed.

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