基于Novozhilov理论带隔板连续弯箱位移参数的动态Bayes估计

推导了基于Novozhilov理论的简支弯箱有限曲条控制方程,并结合柔度法解决了带隔板连续弯箱的求解问题。首次建立了带隔板连续弯箱位移参数的动态Bayes误差函数,推导了相应的动态Bayes均值和方差表达式,提出步长的一维自动寻优方案后,结合共轭梯度法研究了带隔板连续弯箱位移参数的动态Bayes估计方法,同时给出了带隔板连续弯箱位移参数具体估计步骤。通过典型算例分析,总结了带隔板连续弯箱位移参数先验信息准确性判定方法及位移参数动态Bayes随机估计的其它重要结论。     

多室弯箱力学参数的非线性动态Markov优化识别研究

对于多室弯箱结构,基于误差理论建立了多室弯箱力学参数的非线性动态Markov误差函数和方差计算公式,并根据正交函数系理论推导了固体壳单元计算列式;利用直接优化理论研究了多室弯箱力学参数的动态识别方法,其中最优步长采用一维自动寻优方案确定。同时给出了多室弯箱力学参数的非线性动态Markov优化识别的具体步骤,并研制了相应的计算程序。研究结果表明:基于正交函数系理论构造的固体壳单元是正确的;动态误差函数能同时考虑多位移考察点和多量测次数的系统响应信息;直接理论用于多室弯箱力学参数的非线性Markov优化识别时表现出良好的数值稳定性和收敛性,具有较高的计算效率。     

带柔性隔板弯曲连续箱梁有限条法分析

本文利用凝聚矩阵求隔板与箱联结点赘余力,进而分析带柔性隔板的曲线连续箱梁及其隔板的内力,并对刚、柔性隔板与无隔板多跨曲箱梁以及直条法与曲条法进行分析比较,表明本文计算结果是令人满意的,从中得到有关结论。     

带柔性隔板弯曲连续箱梁有限条法分析

本文利用凝聚矩阵求隔板与箱联结点赘余力，进而分析带柔性隔板的曲线连续箱梁及其隔板的内力，并对刚、柔性隔板与无隔板多跨曲箱梁以及直条法与曲条法进行分析比较，表明本文计算结果是令人满意的，从中得到有关结论。     

求解接触问题的一种新的实验误差法

提出了一种带松弛因子的UZAW算法求解实验误差法中给定状态下的位移和接触力满足的等式方程，并证明了该算法是R超线性收敛的。整个区域被划分为多个子区域，不同子区域位移场的求解是独立的。还提出了一种带参数的以不完全因子分解为基础的预条件子共轭梯度法求解不同子区域位移场，该算法在块体规模较大时更加有效。     

Karman型F交异性矩形薄板非线性弯曲的统一求解方法

本方对Karman型四边支承正交异性薄板在5种不同边界条件下的几何非线性弯曲进行了统一分析.所设的位移函数均为梁振动函数.它们精确地满足边界条件,利用Galerkin方法和位移函数的正交属性,转换控制方程为非线性代数方程.用"稳定化双共轭梯度法"求解稀疏矩阵线性方程组以及"可调节参数的修正迭代法"求解非线性代数方程组,最后给出了相应的数值结果.     

单支开口薄壁梁屈曲分析的Riccati有限条传递矩阵法

针对单支开口薄壁梁屈曲问题,通过采用半解析有限条法推导薄壁梁的条元控制方程、传递矩阵基础形成单元传递方程、Riccati变换改善数值计算稳定性,提出了开口单支薄壁梁屈曲分析的Riccati有限条传递矩阵法。为了验证该方法的正确性与高效性,通过提出的Riccati有限条传递矩阵法和有限元法分析了一般支撑条件下两种不同截面形式的薄壁梁屈曲临界载荷与屈曲模态,计算发现两种方法的结果具有很好的一致性,且与传递矩阵法相比,Riccati有限条传递矩阵法数值稳定性好。因此,Riccati有限条传递矩阵法可计算广义边界条件的薄壁结构屈曲问题。     

功能梯度材料结构分析的半解析数值方法研究

一种典型的半解析数值方法——线法被引入功能梯度材料的结构分析。首先推导了功能梯度材料位移形式的平衡方程和边界条件,然后阐述了线法功能梯度材料结构分析的基本步骤和数值原理。该方法的基本思想是通过有限差分将问题的控制方程半离散为定义在沿梯度方向离散节线上的常微分方程组,然后应用B样条函数Gauss配点法求解该常微分方程组得到问题的解答。为演示线法在功能梯度材料结构分析中的应用,给出了线性梯度和指数梯度功能梯度材料板分别受恒定位移、均匀拉伸载荷和弯曲载荷作用的数值算例。与相应问题解析解和其他数值方法的比较表明,线法的计算结果具有很高的精度,而且不需要任何特殊的考虑就能够有效模拟材料内部物性参数的连续变化,也无需事先选取满足特定条件的待定场函数,是一种非常适合功能梯度材料结构形式和材料特点的半解析数值方法。     

薄壁杆侧向稳定分析有限杆元模型

根据位移变分原理,建立有限杆元模型,对薄壁杆进行侧向稳定分析。在考虑截面扭转、翘曲同时,特别考虑了反映剪力滞后现象的杆壁中面上剪应交的影响。推导出薄壁杆侧向屈曲能量方程可适用求解常用边界条件,任意棱形截面形状的薄壁杆的屈曲特征值问题。     

线性规律功能梯度材料断裂行为实验研究

焦散线方法与高速摄影技术结合,对线性规律功能梯度材料的I型静、动态断裂特性进行实验研究,并利用有限元软件进行数值模拟. 首先推导了线性规律功能梯度材料静、动态裂尖的焦散线初始曲线方程和参数方程,提出通过迭代方法根据功能梯度材料的复杂焦散线方程求解应力强度因子. 为对比材料梯度对断裂行为的影响,利用重力沉降法制备了3种梯度变化规律的试件. 然后对功能梯度材料试件进行三点弯曲实验,通过CCD和高速摄影装置采集试件焦散线图像,提取各种静、动态断裂参数. 最后通过与有限元模拟结果进行对比,证明在功能梯度材料断裂实验中焦散线方法的有效性,并详细分析了不同梯度变化规律对材料静、动态断裂性能的影响.      

Dynamic Bayesian estimation of displacement parameters of continuous curve box based on Novozhilov theory

The finite strip controlling equation of pinned curve box was deduced on basis of Novozhilov theory and with flexibility method, and the problem of continuous curve box was resolved. Dynamic Bayesian error function of displacement parameters of continuous curve box was found. The corresponding formulas of dynamic Bayesian expectation and variance were derived. After the method of solving the automatic search of step length was put forward, the optimization estimation computing formulas were also obtained by adapting conjugate gradient method. Then the steps of dynamic Bayesian estimation were given in detail. Through analysis of a classic example, the criterion of judging the precision of the known information is gained as well as some other important conclusions about dynamic Bayesian stochastic estimation of displacement parameters of continuous curve box.     

Powell dynamic identification of displacement parameters of indeterminate thin-walled curve box based on FCSE theory

The FCSE controlling equation of pinned thinwalled curve box was derived and the indeterminate problem of continuous thin-walled curve box with diaphragm was solved based on flexibility theory. With Bayesian statistical theory,dynamic Bayesian error function of displacement parameters of indeterminate curve box was founded. The corresponding formulas of dynamic Bayesian expectation and variance were deduced. Combined with one-dimensional Fibonacci automatic search scheme of optimal step size,the Powell optimization theory was utilized to research the stochastic identification of displacement parameters of indeterminate thin-walled curve box. Then the identification steps were presented in detail and the corresponding calculation procedure was compiled. Through some classic examples,it is obtained that stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step size is solved by adopting Fibonacci search method. And the Powell identification of displacement parameters of indeterminate thin-walled curve box has satisfied numerical stability and convergence,which demonstrates that the presented method and the compiled procedure are correct and reliable.During parameters’ iterative processes,the Powell theory is irrelevant with the calculation of finite curve strip element(FCSE) partial differentiation,which proves high computation effciency of the studied method.     

The analysis of thin walled composite laminated helicopter rotor with hierarchical warping functions and finite element method

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free bending as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method is introduced to form a numerical algorithm. Both static and natural vibration problems of sample box beams are analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor. The project supported by the National Natural Science Foundation of China (19932030)     

Powell’s optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell’s optimization theory is used to perform the stochastic identification of material constants  of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell’s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element (FCSE) method. Some classical examples show that Powell’s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell’s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses are simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.     

剪力滞效应对箱形梁挠度影响的研究

从剪力滞翘曲应力的轴向平衡条件出发,选取双室箱梁的合理翘曲位移函数,引入相应于剪力滞翘曲变形的惯性矩和惯性积等几何特性,用能量变分法建立薄壁箱梁剪力滞效应分析的控制微分方程。通过求解控制微分方程,导出集中荷载和均布荷载作用下简支箱梁和悬臂箱梁的挠度公式及有限梁段单元刚度矩阵,模型试验和ANSYS壳单元计算结果证实了其正确性。结合简支、悬臂和连续箱梁数值算例,具体分析剪力滞效应对箱梁挠度的提高程度。结果表明,无论在集中荷载还是均布荷载作用下,剪力滞效应对简支箱梁的挠度均有显著提高。在集中荷载作用下,剪力滞效应对连续箱梁挠度的提高可达14%;对于跨宽比约为4.0～6.0的简支箱梁,可将按初等梁计算的跨中挠度乘以提高系数1.05～1.11;计算悬臂箱梁的挠度时,一般可以忽略剪力滞效应的影响。     

逆迭代法的一种变通应用

本文利用逆迭代法与共轭梯度法配合使用时的“广义力”一致出现之规律,将大型结构动力分析的有限元(条)网格以族排列,然后将单元族分批集于“广义力”向量之中,从而避开了传统的结构刚度阵与质量阵的集成过程,大大节约了计算机内存。整个过程极为简明、有效。     

大坝混凝土三维细观力学数值模型研究

在细观结构层次上将大坝混凝土作为骨料、固化水泥砂浆及其粘结界面组成的复合材料,建立了大坝混凝土三维细观力学数值模型。该模型既能够反映混凝土及其细观各相材料在荷载作用下的损伤演化过程,又考虑了动载作用的应变率强化效应。给出了该数值模型求解方法,并编制出能够在普通PC机上运行的串行程序。加载过程既可按荷载控制又可按位移控制。同时,为了减少求解自由度应用了分尺度方法以使最小骨料和固化水泥砂浆混合后其力学性能与一种复合介质等效。通过混凝土湿筛和三级配试件的静、动(冲击)弯拉数值计算验证了本文计算方法和程序正确有效。另外,在串行程序的基础上,优化了刚度矩阵的存储方式,采用双门槛不完全Cholesky分解(ICT)预条件的共轭梯度法(CG),完成了能够在Sun Fire 6800服务器实现并行计算的并行程序改造,从而大大提高了计算效率。     

高层筒体结构整体稳定及二阶位移分析的改进条元法

根据柱壳理论,构造了一种柱壳曲条,本文结合柱壳曲条和平壳条元求解高层筒体结构的整体稳定及二阶位移。采用三次H erm ite插值函数模拟条元横截面的翘曲位移变化,能较好地反映筒体受力“剪切滞后”效应;采用一族能较好地逼近弯剪型变形曲线的正交多项式作基函数来描述位移沿竖向变化。用最小势能原理建立稳定及二阶位移分析方程。该方法适用于任意平面形状的高层建筑筒体结构及剪力墙结构的稳定及二阶位移分析。与其它方法相比,该方法具有精度高、通用性强、计算量小等优点。