Enhanced studies on a composite time integration scheme in linear and non-linear dynamics

In Bathe and Baig (Comput Struct 83:2513-2524, 2005), Bathe (Comput Struct 85:437-445, 2007), Bathe and Noh (Comput Struct 98-99:1-6, 2012) Bathe et al. have proposed a composite implicit time integration scheme for non-linear dynamic problems. This paper is aimed at the further investigation of the scheme's behaviour for use in case of linear and non-linear problems. Therefore, the examination of the amplification matrix of the scheme will be extended in order to get in addition the properties for linear calculations. Besides, it will be demonstrated that the integration scheme also has an impact on some of these properties when used for non-linear calculations. In conclusion, a recommendation for the only selectable parameter of the scheme will be given for application in case of geometrically non-linear calculations.