强震作用大型结构非线性响应高效数值方法

This study would present both the accurate computational models and efficient time-integration numerical methods for obtaining reliable solutions to the large-scale structures subjected to strong earthquakes. Firstly, employing the generalized transfer matrix method, an accurate computational model is designed for the 2D and 3D seismic free field incidents to engineering structures, and an efficient numerical method is arrived at for all types of irregular fields. The new method is both analytical and effective. Secondly, for the infinite domain, based on the combined bi-directional transferring wave operators, the higher-order accurate artificial boundary conditions for both two-dimensional and three-dimensional elastic wave problems are obtained. The new truncated boundary conditions are in discrete form, being applicable to the domain-dependent numerical methods, such as finite element and finite volume methods. In addition, the compatiability equations for the corner points at artificial boundaries are also established. As for the finite doamin truncated from the unbounded domain, the domain-dependent numerical method is used. When dealting with the dynamic contact problems, a new incremental computational model is proposed for the state vector consisting of both the contact force and contact displacement, followed by a new dynamic contact force algorithm. Furthermore, for accurate modelling the dynamic contact status, the contact relation should include the contact displacements togethor with the contact velocities. The iterative-programming algorithm for solving dynamic contact problem is arrived at. Finally, the backward-forward Euler differentiation formula is designed, resulting in a self-starting, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method is applicable to linear as well as general nonlinear analyses; it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; and it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors. This study aims at solving the common but key problems of computational mechanics, resulting from the large-scale structures subjected to strong earthquakes. The obtained results not only can give really insight into the fundamental methods of computational mechanics, but also can be powerful tools with some notable features for practical nonlinear dynamic analyses.

针对强震作用大型结构动力非线性响应，研究准确的力学模型与高效的数值方法。首先，基于广义传递矩阵法探索适用于地震动自由场输入的二维、三维精细化模型和计算方法；其次，一方面针对半无限远场地基，通过组合双向波动算子，构造二、三维高阶精度、弹性波、离散型人工边界条件，以及人工边界角点的协调方程；另一方面针对近场有限区域，研究动态接触力-接触位移状态向量增量的计算模型以及动接触力算法，建立位移-速度动态接触摩擦条件，并发展基于迭代-数学规划相结合的高效算法；最后，对大规模动力非线性数值模拟问题，构造Euler前向-后向组合的高效时域数值积分方法，具有自起步、无算法参数、单求解器、二阶精度，且适用于线性与非线性问题，特别是刚性与接触问题。本项研究解决大型结构抗震问题中的共性的、核心的计算力学问题，不但能拓宽计算固体力学基本理论方法，而且能为强地震作用大型工程结构非线性响应提供准确、高效的计算手段。

本项目针对强震作用大型结构动力非线性响应，研究了准确的力学模型与高效的数值方法。首先，基于广义传递矩阵法探索适用于地震动自由场输入的二维、三维精细化模型和计算方法；其次，研究了动态接触力-接触位移状态向量增量的计算模型以及动接触力算法，建立位移-速度动态接触摩擦条件，并发展基于迭代-数学规划相结合的高效算法；对大规模动力 非线性数值模拟问题，构造Euler前向-后向组合的高效时域数值积分方法，具有自起步、无算法参数、单求解器、二阶精度，且适用于线性与非线性问题；第三，应用振动台试验探索了砂土液化阻尼器，直接测得阻尼力与速度关系曲线，并应用于大坝泄洪振动减振控制中，不但提高了大坝极限抗震能力，而且获得了与计算模型相适宜的阻尼器模型；最后，探索了高土石坝建设中振动利用问题，研制无人驾驶碾压筑坝技术，智能控制碾压密实参数，具有不漏碾、不过碾、不交叉碾压、不超速、自主决策碾压过程的特点。另外，还研发了连续碾压施工压实质量的振动能量在线检测方法。本项研究解决大型结构抗震问题中的共性的、核心的计算力学问题，不但拓宽了计算固体力学基本理论方法，而且为强地震作用大型工程结构非线性响应提供了准确、高效的计算手段。