改进的降阶牛顿迭代数值子结构方法

AN IMPROVED REDUCED-ORDER NUMERICAL SUBSTRUCTURE METHOD BASED ON NEWTON ITERATIVE ALGORITHM

充分利用结构在地震作用下的局部非线性特征,数值子结构方法将原本复杂的结构非线性分析转化为以初始弹性刚度迭代的主结构等效线弹性分析和屈服构件隔离子结构非线性分析。由于主结构采用常刚度迭代分析收敛速度较慢,尚有一定局限性,于是该文提出一种改进的降阶牛顿迭代数值子结构方法。在主结构系统中,将塑性自由度位移场作为基本未知量,设计牛顿算法进行非线性迭代分析,并由隔离子结构跨平台非线性分析计算得到屈服单元的内力和切线刚度。对一平面15层3跨钢结构进行地震弹塑性时程分析,模拟结果表明:该文提出的方法是准确、可靠的,接近传统牛顿算法的二次收敛,且对于局部非线性结构系统,需要集成和分解的矩阵规模远小于传统方法。

Making use of the local nonlinearities of the structures under earthquakes,the numerical substructure method(NSM)transforms the original complex structural nonlinear analysis into the equivalent linear elastic analysis of a master structure based on a fixed-point iterative algorithm and nonlinear analyses of isolated substructures for yield components.However,the NSM still has a limitation due to the low convergence speed for the master structure based on the initial elastic stiffness.In this study,an improved reduced-order NSM based on a Newton algorithm is presented.In the master structure,the displacements of nonlinear degrees of freedom are taken as unknown quantities,and the nonlinear analysis process using the Newton algorithm is conducted,in which resisting forces and tangent stiffnesses of nonlinear elements are obtained from isolated substructures.Seismic elastoplastic time-history analyses of a plane 15-storey three-bay steel structure are carried out.The numerical analysis results show that:the present method is accurate and efficient,closing to the second-order convergence of the traditional Newton algorithm,and only needs to form and decompose a much smaller matrix than that in the traditional algorithm for a local nonlinear system.