Stability of the Modified Euler Method for Nonlinear Dynamic Analysis of TLP

Efficiency of numerical methods is an important problem in dynamic nonlinear analyses. It is possible to use of numerical methods such as beta-Newmark in order to investigate the structural response behavior of the dynamic systems under random sea wave loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable methods for numerical integration. The modified Euler method (MEM) is a simple numerical procedure which can be effectively used for the analysis of the dynamic response of structures in time domain. It is also very effective for response dependent systems in the field of offshore engineering. An important point is investigating the convergence and stability of the method for strongly nonlinear dynamic systems when high initial values for differential equation or large time steps are considered for numerical integrating especially when some frequencies of the system is very high. In this paper the stability of the method for solving differential equation of motion of a nonlinear offshore system (tension leg platform, TLP) under random wave excitation is presented. In this paper the stability criterion and the convergence of the numerical solution for critical time steps are presented