Comparative analysis of implicit and explicit numerical methods in dynamic problems solving

Abstract

Theoretical basics formulation of the implicit Newmark-method and the explicit central difference method for numerical integration of dynamic motion equations is presented in this paper. According to theoretical assumptions, algorithms for the integration of dynamic motion equation are developed. Algorithms are implemented into the software package PAK. Verification of the developed algorithms has been done for elementary examples which have analytical solutions. At the end of the comparative result analysis obtained by applying both methods of numerical integration, dynamic behavior analysis of buildings on the surface soil due to impact of the wagon wheels in motion on underground railway tracks.