基于向量式有限元的深水顶张力立管动力响应分析

摘要

The vector form intrinsic finite element (VFIFE)method also called the finite particle method (FPM)is an innovative method in the structural behavior analysis based on the vector mechanics and numerical calculations.With this method,a structure was discretized into a series of mass particles connected by massless elements only bearing internal forces.The motion of mass paticles obeyed Newton's second law.Their motion equations were solved using the explicit time domain integration and the central difference method.VFIFE was adoped for the first time to analyze the dynamic behavior of a top tensioned riser (TTR)and the plane beam element was adoped to simulate interaction forces between mass particles.The particle motion equation of the riser was derived and the corresponding solving program was compiled with Matlab.The dynamic behavior of the riser under sea current and wave excitations was calculated and the results were compared with those with the finite element method (FEM).The results showed that the VFIFE method is correct and effective to analyze the dynamic behavior analysis of a riser and it has more advantages than traditional methods.%向量式有限元法亦称有限质点法是以向量式力学与数值计算为基础的一种结构行为分析的创新性方法。该方法将结构离散为一系列质点的集合，质点间采用单元连接，单元没有质量，只承受内力，质点的运动则直接采用牛顿第二定律来表达，采用中央差分的显式积分法求解质点群各时刻运动方程。首次将该方法应用于顶张力立管的动力行为分析中，采用平面弯曲杆件元模拟质点间的相互作用力，推导了立管质点运动公式，编制相应 Matlab 求解程序，计算了立管在海流、波浪作用下的动力响应特性并与基于传统有限元法的结果进行了对比分析，表明该方法在立管行为分析中的正确和有效性，并指出了该方法在处理其它立管形式行为分析中的优势。