论结构非线性动力分析中的数值稳定性（Ⅰ）

本文在严格、完整的基础上,利用矩阵范数理论研究了结构非线性动力分析中数值积分格式的稳定性问题,给出了判别单自由度非线性动力方程积分格式稳定性的一般数学准则。为了实际应用方便,文中还给出了一个简化判稳准则。     

基础隔震结构的非线性动力分析

新的建筑抗震设计规范将隔震结构列入其中，探讨分析了结构基础隔震应用中应注意的问题，提出了非线性动力时程分析计算模型并编制了程序。借助该程序，分析了基础隔震结构在地震作用下的层间位移、加速度和剪力等地震反应并与未隔震相同结构建筑的地震反应进行了对比。     

结构拟动力试验力控制实现技术

本文研究了大刚度结构拟动力实验的有关技术问题，基于结构动力分析和电液伺服作动器工作原理，阐述了作动器在力控制方式下实现大刚主结构拟动力实验的可行性，提出了减小实验误差的若干处理技术。通过作者所完成的四个自由度１：３钢筋混凝土结构模型拟动力实验，说明所述方法的有效性。     

滑动隔震结构的非线性动力可靠性分析

利用等效非线性系统法得到了滑移隔震结构在高斯白噪声作用下位移与速度响应联合概率密度函数的解析式,并在此基础上进行了滑移体系的动力可靠性分析.     

杆系结构的动力几何非线性分析

本文详细分析了杆系结构由于轴力作用而产生的梁柱效应。从理论上证明了对杆系结构进行动力分析时,只要单元划分得足够小,就完全可以不计梁柱效应,且由此而产生的误差与有限元法本身的误差同是量级的。本文并给出了轴力作用下的一致质量阵。     

结构动力方程的显式级数积分格式

将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合,根据指数矩阵的Taylor级数展开式,提出了动力方程的显式级数解,并设计了相应的时程积分算法.该算法的精度可根据Taylor级数展开式的项数进行灵活控制.算例的结果表明:在满足稳定性条件的前提下,随着时间步长的增加,其精度优于传统的时程积分法.通过稳定性的分析,指出其稳定性条件是显然满足的.     

结构动力分析的动态有限单元法

本文就前人和作者运用动态有限单元法处理实际结构振动分析的情况,阐述动态有限单元法的基本概念和原理及其存结构振动分析中的应用问题。作者认为,这种动力分析方法具有较好的发展前景。     

动力边界积分方程法及其应用

文中简要介绍了作者在国家地震局工程力学研究所学习和工作期间，该所动力边界积分方程法及其应用课题研究组这几年来的研究成果。     

大刚度结构力控制拟动力实验方法

由于受到拟动力实验加载系统和量测系统精度限制，对大刚度结构采用位移控制的拟动力实验方法已失效，本文提出了适用于大风度结构的力控制拟动力试验方法，阐述了方法的原理与步骤，并用实验实例验证了该方法是可行的和可靠的。     

结合动量方程及显式γ函数法的拟动力试验方法

研究了一种适合实时或快速拟动力试验的数值积分方法--动量方程方法,阐述了动量方程方法的原理,结合显式γ函数法求解隐式方程,得到了拟动力试验实用的显式位移表达式.选用合适的参数,对一根悬臂钢柱进行了拟动力试验.试验结果与中心差分法得到的试验结果吻合较好,从而验证了积分方法的可行性和有效性,可以作为速度相关型结构或构件拟动力试验的数值积分方法.     

Lanczos method for dynamic analysis of damped structural systems

In this paper we extend the Lanczos algorithm for the dynamic analysis of structures⁷ to systems with general matrix coefficients. The equations of dynamic equilibrium are first transformed to a system of first order differential equations. Then the unsymmetric Lanczos method is used to generate two sets of vectors. These vectors are used in a method of weighted residuals to reduce the equations of motion to a small unsymmetric tridiagonal system. The algorithm is further simplified for systems of equations with symmetric matrices. By appropriate choice of the starting vectors we obtain an implementation of the Lanczos method that is remarkably close to that in Reference 7, but generalized to the case with indefinite matrix coefficients. This simplification eliminates one of the sets of vectors generated by the unsymmetric Lanczos method and results in a symmetric tridiagonal, but indefinite, system. We identify the difficulties that may arise when this implementation is applied to problems with symmetric indefinite matrices such as vibration of structures with velocity feedback control forces which lead to symmetric damping matrices. This approach is used to evaluate the vibration response of a damped beam problem and a space mast structure with symmetric damping matrix arising from velocity feedback control forces. In both problems, accurate solutions were obtained with as few as 20 Lanczos vectors.     

Nonlinear analysis for dynamic lateral pile response

An analysis of pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behavior, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. Furthermore, the effect of neighbouring piles is taken into account for piles in a group. The validity of the approach was examined and a reasonable agreement with field tests and more rigorous solutions was found. Equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are presented.     

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.     

A modal superposition pseudo-force method for dynamic analysis of structural systems with non-proportional damping

A modal superposition pseudo-force method for the dynamic analysis of structural systems with non-proportional damping is presented. The method combines the advantages of the classical modal superposition method and the pseudo-force method. When the system damping is non-proportional, the dynamic equilibrium equations in generalized coordinates are coupled through the damping terms. In the present method, these coupled equations are solved by an iterative process in which the coupling terms are treated as pseudo-forces. A proof of the convergence of the iterative process is given. Numerical examples show the good convergence characteristics of the process and the good accuracy of the obtained results.     

结构动力学方程的显式积分格式

本文从空间解耦有限元常微分方程组出发，探讨了结构动力学方程的高精度显式积分格式。通过被积函数的拉格朗日多项式内插和分部积分导出了波动数值模拟的一组显式时步积分公式。这组公式是时间和空间解耦的，即波场内任一离散节点在任一时刻的波动数据可以用这组公式依据该节点及其邻近节点在该时刻之前的n＋1个时刻的波动数据显式地算出（n为非负整数），阐明了这组公式的如下特点：第一，其截断误差的量级不超过0（Δt^n＋3），Δt为时间步距。第二，它不仅可用于线性波动的数值模拟，而且可用于本构方程具有强非线性情形。第三，这组公式也可推广应用于一系列数学物理暂态问题的数值求解。针对一个简单的时不变系统初步分析了此组积分格式的稳定性。但是，对其稳定性尚需作进一步研究。     

求解结构动力响应的小波分解法

本文用时程分析、振型迭加和小波变换3种方法,对一个10层建筑结构的地震动力响应进行了计算和比较,三者的结果完全一致,从而说明了线性时不变系统结构动力响应的唯一性定律是正确的。由于时程分析法可以用于非线性系统,而振型分解法只能用于线性系统,小波变换不但可以用于非线性,更可以用来进行多尺度分析的能谱计算,它能使抗震分析从传统的滞回耗能模型,提高到以结构损伤和延性评价的体系上来。     

Nonlinear dynamic analysis of complex structures

A general step-by-step solution technique is presented for the evaluation of the dynamic response of structural systems with physical and geometrical nonlinearities. The algorithm is stable for all time increments and in the analysis of linear systems introduces a predictable amount of error for a specified time step. Guidelines are given for the selection of the time step size for different types of dynamic loadings. The method can be applied to the static and dynamic analysis of both discrete structural systems and continuous solids idealized as an assemblage of finite elements. Results of several nonlinear analyses are presented and compared with results obtained by other methods and from experiments.     

Precise integration method without inverse matrix calculation for structural dynamic equations

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.     

结构动力分析阻尼模型研究

提出了结构动力时程分析修正的Ｒａｙｌｅｉｇｈ阻尼模型和一个基于单元特性的阻尼参数方法,可用于合理确定复杂阻尼结构的阻尼参数,工程应用实例表明,阻尼参数的计算对时程响应计算结果的影响是十分明显的,必须在分析结构体系振动特性的基础上慎重确定阻尼参数,以避免为为放大或滤掉主要振型,造成虚假的结论。