Stability Analysis of Ubiquitous Direct Time Integration Methods

M. Naguib, A. A. Ghaleb, F. M. Amin

Abstract: A brief implementation guide was introduced for direct time integration algorithms including the central difference, Houbolt, Newmark, Wilson-?, HHT-?, WBZ-?, Generalized-? and Bathe Methods. Later, the stability and accuracy concepts were introduced with summarizing the procedures for spectral analysis for any direct time integration algorithm. Bathe method has shown superiority in different aspects based on spectral analysis. A similarity in spectral performance was found between Houbolt and a special case ofWBZ-?. The central difference method also showed similar spectral performance to that shown in a special case of HHT-?.

Keywords: Direct Time Integration, Stability Analysis, Central Difference, Houbolt, Newmark, Wilson-?, HHT-?, WBZ-?, Generalized-?, Implicit Bathe method