大型结构局部非线性问题的数值子结构方法的验证与改进

Verification and improvement of numerical substructure method for local nonlinear problems of large structures

对超高层建筑、超大跨度桥梁和高速铁路等重大工程进行有限元动力分析时,由于结构的模型非常大,自由度数有数千万,计算成本往往非常高,计算效率比较低.虽然数值子结构方法能较好地解决这类问题,但是仍然存在不足:通过子结构静力分析得到的非线性修正力项不适用于动力子结构问题;且使用不迭代算法的数值子结构方法要求计算步长很小,导致计算时间较长.针对这些问题,本文将非线性修正力计算从子结构静力分析拓展到动力分析问题中,可更精确地考虑子结构的动力效应;另外提出隔离子结构的响应预测修正方法,可增加计算步长,极大地提高计算效率.通过数值算例将改进的数值子结构方法与完整结构的标准解进行对比,验证了此改进方法的精度和计算误差.

For the finite element dynamic analysis of major projects such as super high-rise buildings,super-long-span bridges and high-speed railways,the model of the structure appears large,and the number of degrees of freedom reaches tens of millions,thus leading to high computational costs and low computational efficiencies.The numerical substructure method can better solve such problems.However,deficiencies remain.The nonlinear correction force term obtained by the substructure static analysis is not applicable to the dynamic substructure problem,and the numerical substructure method using the non-iterative algorithm requires a small calculation step size,resulting in a long calculation time.For the purpose of trackling these problems,this paper expands the nonlinear correction force calculation from the substructure static analysis to the dynamic analysis problem.Due to this expansion,substructure dynamic effects can be more accurately considered.In addition,the response prediction correction method of the isolation substructure is proposed,and can increase the calculation step size as well as greatly improve the efficiency of calculation.The improved numerical substructure method is compared with the standard solution of the complete structure by numerical examples.The accuracy and computational error of the improved method are verified by the system.