隧道结构NURBS无网格弹塑性快速分析方法及其应用

Fast and Efficient Elastoplastic Analysis for Tunnel Structures via Nonuniform Rational B-Spline-Based Meshfree Method

为解决异型隧道结构建模分析困难、各类弹塑性数值计算方法精度有限、鲁棒性较低等问题,研究发展一种快速稳定的NURBS-MF(nonuniform rational B-spline-based meshfree)弹塑性分析方法,并将其应用于马蹄型隧道结构的塑性区计算中。NURBS-MF方法利用样条曲线参数化建模结构几何的优点,实现对异型结构的快速建模;通过规则参数空间的映射法则自动进行结点布设,合理地离散待分析区域,极大地降低了异型结构计算的前处理与分析难度。在此基础上推导基于NURBS映射的无网格弹塑性控制方程,提出改进的NURBS-MF弹塑性算法,以适用于异型断面结构的弹塑性快速分析。NURBS-MF弹塑性分析方法提出了一种全新的无网格结点与积分点生成方式,避免了边界积分单元被切割;没有多余的积分点且不产生额外的数值积分代价,能较为明显地降低无网格类数值方法在弹塑性分析中的计算代价、提高其鲁棒性。根据NURBS-MF弹塑性公式与Newton-Raphson迭代算法编写的弹塑性分析程序,可优化异型隧道结构的建模与计算过程。通过典型的弹塑性数值算例及某大断面异型隧道衬砌结构的数值试验表明,该方法具有简洁、稳定、精确等优点,且具有工程实用性。

In this study,a fast and stable elastoplastic analysis method using nonuniform rational B-spline-based mesh-free(NURBS-MF)method is proposed to address issues related to modeling and analyzing heterotypic tunnel structures and the limited accuracy and low robustness of various numerical simulation methods.The proposed method is then used to calculate the plastic zone of the horseshoe-shaped tunnel structure.The NURBS-MF method leverages the merits of NURBS parameterization to represent geometry,enabling fast modeling of heterotypic structures.Node mapping and structural discretization are automatically implemented through mapping rules from the canonical parametric domain,greatly streamlining the preprocessing and analysis in numerical modeling.Elastoplastic governing equations are derived in the framework of meshfree methods and NURBS mapping rules.Thus,an improved NURBS-MF elastoplastic method is proposed for fast and efficient elastoplastic analysis of tunnels with heterotypic cross-sections.The proposed method provides a new node/integral generation method that eliminates the need to cut integral elements near the boundary,resulting in no discarded invalid integral points.Compared with other meshfree methods,no extra numerical cost is incurred.An advanced algorithm is developed based on the NURBS-MF elastoplastic formulations and the Newton-Raphson iterative method,optimizing the modeling and computation of heterotypic tunnel structures.Benchmark and engineering numerical tests illustrate the conciseness,robustness,and accuracy of the proposed method,which is also applicable to other engineering scenarios.