THE INCREMENT STIFFNESS MATRIX AND TOTAL QUANTUM STIFFNESS IN NONLINEAR ANALYSES

In this paper, the expressions of both increment stiffness matrix and total quantum stiffness matrix in nonlinear analyses are derived in detail, and their relationship is discussed in mathematical meaningThe results given in our paper will be of great importance to the analyses of nonlinear numerical and nonlinear stability in finite element methods.

Derivative of a Determinant with Respect to an Eigenvalue in the Modified Cholesky Decomposition of a Symmetric Matrix, with Applications to Nonlinear Analysis

In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct solution method in computational linear algebra. We apply our proposed formula to a technique used in nonlinear finite-element methods and discuss methods for determining singular points, such as bifurcation points and limit points. In our proposed method, the increment in arc length (or other relevant quantities) may be determined automatically, allowing a reduction in the number of basic parameters. The method is particularly effective for banded matrices, which allow a significant reduction in memory requirements as compared to dense matrices. We discuss the theoretical foundations of our proposed method, present algorithms and programs that implement it, and conduct numerical experiments to investigate its effectiveness.

Lie algebraic analysis for the beam transport in the spherical electrostatic analyser

This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.

Gender differences in nonlinear motor performance following concussion

Purpose:To quantify differences in nonlinear aspects of performance on a seated visual-motor tracking task between clinically asymptomatic males and females with and without a self-reported mild traumatic brain injury history.Methods:Seventy-three individuals with a self-reported concussion history(age:21.40±2.25 years,mean±SD)and 75 without completed the visual-motor tracking task(age:21.50±2.00 years).Participants pressed an index finger against a force sensor,tracing a line across a computer screen(visual-motor tracking).The produced signal's root-mean-square error(RMSE),sample entropy(SampEn,a measure of regularity),and average power(AvP)between 0 and 12 Hz were calculated.Results:Males with a history of 0 or 1 concussion had greater RMSE(worse performance)than females with 0(p<0.0001)and 1 concussion(p=0.052).Additionally,females with 2+concussions exhibited lower SampEn than females with no history(p=0.001)or a history of 1 concussion(p=0.026).Finally,females with 2+concussions had lower 8-12 Hz AvP than males with 2+concussions(p=0.031).Few differences were observed in the male participants.Conclusion:Females with a self-reported history of multiple concussions exhibited lower SampEn in the visual-motor tracking-task force output structure as compared to those with no reported history of concussion and their male counterparts.Lower SampEn and lower power between 8 and12 Hz indicated persistent impairment in visual processing and feed-forward or predictive motor control systems.

Nonlinear numerical assessment of the seismic response of hillside RC buildings

Major damage has been reported in hilly areas after major earthquakes,primarily because of two special conditions:the variation in the seismic ground motion due to the inclined ground surface and the irregularities caused by a stepped base level in the structure.The aim of this study is to evaluate possible differences in the responses of Chilean hillside buildings through numerical linear-elastic and nonlinear analyses.In the first step,a set of response-spectrum analyses were performed on four simplified 2D structures with mean base inclination angles of 0°,15°,30°,and 45°.The structures were designed to comply with Chilean seismic codes and standards,and the primary response parameters were compared.To assess the seismic performance of the buildings,nonlinear static(pushover)and dynamic(time-history)analyses were performed with SeismoStruct software.Pushover analyses were used to compare the nonlinear response at the maximum roof displacement and the damage patterns.Time-history analyses were performed to assess the nonlinear dynamic response of the structures subjected to seismic ground motions modified by topographic effects.To consider the topographic modification,acceleration records were obtained from numerical models of soil,which were calculated using the rock acceleration record of the Mw 8.01985 Chilean earthquake.Minor differences in the structure responses(roof displacements and maximum element forces and moments)were caused by the topographic effects in the seismic input motion,with the highly predominant ones being the differences caused by the step-back configuration at the base of the structures.High concentrations of shear forces in short walls were observed,corresponding to the walls located in the upper zone of the foundation system.The response of the structures with higher angles was observed to be more prone to fragile failures due to the accumulation of shear forces.Even though hillside buildings gain stiffness in the lower stories,resulting in lower design roof displacement,maximum roof displacements for nonlinear time-history analyses remained very close for all the models that were primarily affected by the drifts of the lower stories.Additionally,vertical parasitic accelerations were considered for half the time-history analyses performed here.The vertical component seems to considerably modify the axial load levels in the shear walls on all stories.

THE ACTIVATION METHOD FOR DISCRETIZED CONSERVATIVE NONLINEAR STABILITY PROBLEMS WITH MULTIPLE PARAMETER AND STATE VARIABLES

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory

一座空旷砖混厂房结构的隔震加固

介绍一栋砖混单层厂房的隔震加固方案,对加固后结构与原结构的地震反应作了对比分析,分析结果表明隔震加固大大提高了原结构的抗震性能。对加固所用的隔震支座性能作了具体分析,提供了支座的设计与试验对比结果,并对砌体结构隔震加固中采用的"夹梁托墙"技术的可行性作了试验研究,结果表明:支座的设计分析结果与试验结果吻合较好,夹梁具有良好的工作性能。

材料非线性性质的解析表达

将材料拉伸实验曲线由比例极限到屈服极限（或名义屈服限）的非线性段，用一个含有四个参数的解析式子来表达。在此基础上，根据材料特性及最小二乘法原理，对９种金属材料的拉伸实验数据进行曲线拟合，得到各自相应的参数值。最后通过误差分析，验证了上述解析式的可用性，并阐述了它的实际意义。

重组竹工字梁抗弯特性研究及模拟分析

开展了6根腹板与翼缘板之间采用异氰酸酯胶黏剂胶接和螺栓连接的重组竹工字梁抗弯试验研究,考察重组竹工字梁抗弯承载力特性和破坏模式。试验表明:重组竹工字梁的破坏模式为腹板受拉区撕裂破坏;随着荷载的增加,截面各部位应变发展迅速,尤其是腹板边缘处应变发展最快,首先进入塑性变形并发生撕裂破坏;继续加载,该裂纹发生纵向延伸,逐渐形成通缝,并且螺栓连接处出现撕裂。此时,试件两端上、下翼缘变形明显小于腹板边缘处,翼缘和腹板之间变形极其不协调,上翼板下端与腹板上边缘发生脱胶现象,说明腹板和翼缘连接处的剪应力传递效果不佳,影响了构件的刚度和承载力。重组竹工字梁破坏时挠度较大,工字梁的受力变形明显,6根试验工字梁的延性系数为6.0~9.0,说明重组竹工字梁的延性较好,并且工字梁的设计控制因素是变形而不是承载力。进行重组竹工字梁抗弯特性的非线性有限元模拟,分析得到的工字梁荷载-位移曲线与试验结果吻合较好,工字梁的变形及应力分布特征均与试验相一致。

考虑铁窗影响时变压器绕组短路轴向非线性振动的研究

本文研究在非轴对称电动力作用下,变压器绕组短路的轴向非线性振动。首先,利用线饼轴向位移x(θ,t)对θ的傅氏级数展开并分离变量,给出系统的拉格朗日函数,导出系统的多维动力学方程;其次,对于位移和电动力在取双正弦分布时,给出了具体公式,并考虑了油的附加质量、阻尼以及乾摩擦等的影响;第三,就多个线圈具有不同弹性特性时,给出了预压位移的牛顿迭代格式;编制了相应的通用计算程序,通过凝聚和变步长,克服了求解方程中的刚性和计算量的矛盾。对一个17MVA电力变压器的计算表明,铁窗内、外的位移响应及轴向力都有较大的不同,较一维分析更接近试验结果。说明了多维分析具有一定的学术与实践价值。

基于多新息理论的EKF改进算法

针对标准的扩展卡尔曼滤波算法(EKF)在强非线性系统中估计精度较低的问题,提出了一种改进的扩展卡尔曼滤波算法(MI-EKF),使得滤波精度得到很大的提高。MI-EKF是在标准EKF基础上,结合多新息理论,不仅考虑了系统当前的测量值,而且也充分考虑了之前时刻的有用信息,从而使得MI-EKF的滤波精度和稳定性得到改善。最后,讨论了新息数量对改进算法精度的影响,仿真结果表明包含两个新息的MI-EKF算法滤波效果最佳。

深海钢悬链立管时域疲劳寿命预估研究

研究了钢悬链立管(SCR)时域非线性动力分析用于疲劳寿命预估。随着海洋工业不断往深海进发,过去10年内钢悬链立管成为众多油田开发的优选方案。然而,对于钢悬链立管设计而言疲劳是个关键难题。钢悬链立管的非线性动力特性显著,与频域方法相比,时域分析能够模拟非线性水动力载荷以及结构的非线性特性。数值模拟了海洋环境载荷作用下SCR的非线性结构动力响应,利用S-N曲线对立管进行整体疲劳寿命预估。对影响SCR疲劳寿命的各参数进行敏感度分析,输入的敏感度分析参数包括拖曳力系数、浮力因子、海床土体硬度等,研究表明疲劳寿命的预估结果与这些参数相关,所给出的结论便于设计人员更好理解钢悬链立管动力特性,选择合适的参数用于立管疲劳设计。

非对称大跨度钢管混凝土拱桥非线性稳定性分析

探讨了钢管混凝土拱桥几何非线性和材料非线性稳定性分析方法,并运用通用有限元程序对某铁路大桥进行分析.结合该桥的特点,在稳定性分析中引入了钢管混凝土构件的轴压本构关系,以考虑材料非线性对稳定的影响.结果表明:几何非线性对该桥稳定性影响较小,而材料非线性对稳定性影响较大,这些结论对钢管混凝土稳定性分析具有指导意义.

焊接孔长度对钢框架梁-柱刚性节点性能的影响

对焊接孔长度扩大的钢框架梁-柱刚性节点进行了空间非线性有限元分析.分析结果表明,焊接孔长度的扩大显著地降低了梁-柱连接面处的对接焊缝和焊接孔切角端开裂以及翼缘脆性破坏的可能性,但过长的焊接孔也会导致梁侧向稳定的丧失.

GPS导航中非线性Kalman滤波的方法分析

介绍了非线性Kalman滤波常使用的扩展Kalman滤波、平淡Kalman滤波和基于Bancroft算法的两步滤波法,分析了三种方法的优点和不足,为GPS导航方法的选择提供了参考。

局部构造对钢框架梁-柱刚性节点性能的影响

对焊接孔尺寸变化的钢框架梁 柱刚性节点进行了空间非线性有限元分析。结果表明 ,焊接孔长度的扩大显著地降低了梁 柱连接面处对接焊缝和焊接孔切角端开裂以及翼缘脆性破坏的可能性 ,但过长的焊接孔也会导致梁翼缘侧向稳定的丧失。焊接孔高度的降低只有利于目前常用的焊接孔长度较短的“标准型”节点。

基于影响因子分析的滑坡位移预测模型研究

将滑坡的影响因素引入到滑坡的位移预测模型中,从滑坡的位移动态变化特征和响应组成组分研究入手,将滑坡的位移分解为趋势项、周期项、脉动项和随机项,针对每一项进行研究,分别选取合适的影响因子变量和函数关系来模拟,并将各项耦合在一起得到位移的初步预测模型。通过对监测数据进行非线性多元统计回归分析,得到位移的最终预测模型。以长江三峡库区的新滩滑坡为实例,通过验证研究,发现将滑坡的影响因子引入滑坡的预测预报模型中的思路是有效可行的,而且可以明显地改善预测预报的时间尺度。

软弱岩体Berger模型及井巷流变地压

在室内对硅藻岩进行了主要物理力学指标测定和蠕变试验的基础上，分析了软弱岩体的流变特性。根据Ｂｅｒｇｅｒ模型，建立了软弱岩体的流变状态方程和蠕变方程来分析支护前围岩移动规律和支护后流变地压的增长规律。

PC系杆拱桥施工阶段暂态结构安全控制

以某在建的PC系杆拱桥为研究对象,采用Ansys程序的几何非线性有限元接触分析方法,模拟系梁与支架的关系,建立了模拟该桥张拉吊杆施工过程的空间分析模型,采用三种加临时横撑的方案来控制施工时暂态结构的安全性,计算了张拉吊杆过程中三方案不同状态下结构的弯矩、位移及稳定系数,试图通过分析找到最佳的加临时横撑的方案,进而为整桥施工模型的建立和同类桥梁的施工控制提供参考.

极正交各向异性圆板非线性弯曲的定性分析及单调迭代解

本文对极正交各向异性圆板在任意轴对称载荷和边界条件下的非线性弯曲问题进行了较为系统的研究.首先,将边值问题归结为等价的积分方程,并且借助于广义函数得到了线性问题的一般解答.其次,对导出的非线性积分方程解的性质作了较为细致的讨论,例如边缘皱褶,非负性和奇性等.然后,构造了解的双边单调迭代格式,并给出了迭代格式的收敛性判据和误差估计,同时还讨论了解的全局存在唯一性.最后,给出了一个数值例子来说明本文方法和结论的应用.本文某些结果是由作者新得到的。