关于一类非主型方程古沙及柯西问题的一个注记

通过证明一系列的递推关系式,将文献中对常数p<1的限制推广到p>1且p≠奇数的情况。     

一类非主型方程古沙及柯西问题的解

应用文献提出的双曲型方程的Riemann函数法,并利用超几何函数的特殊性质对一类非主型方程的古沙问题和柯西问题提供求解的方法,给出了解的表达式。     

Riccati方程的降阶与广义系统的最优预见控制

研究了一类广义离散时间线性系统的预见控制问题.首先通过对系统方程,误差向量和可预见的目标值信号取差分,构造出一个扩大误差系统,把广义系统的预见控制问题转化为一个形式上的普通广义系统的控制问题.然后利用广义系统最优控制理论的结果,得到广义系统的带有预见前馈补偿的控制器.同时通过详细推导,把一个阶数很高的矩阵Riccati方程降为一个阶数很低的Riccati方程,从而使闭环系统可以实现.     

一类非齐次线性微分方程的求解方法

介绍求解二阶和三阶常系数非齐次线性微分方程的积分因子降阶方法,实例说明其应用,旨在开拓学生的解题思路,提高学生的解题能力.     

一类差分方程的解法及其在经济领域中的应用

差分方程模型是一种重要的确定性离散模型,其中较常用的有N阶常系数线性非齐次差分方程模型,用待定系数法解此类方程,研究此类方程在市场经济分析中的应用,给出蛛网模型的三阶差分模型.     

Hilbert空间上一类半线性随机发展方程的稳定性

讨论Hilbert空间上半线性随机发展方程dY(t)=[AY(t)+f(Y(t))dt+G(Y(t))]dw(t)的稳定性。为此引进了适度解的正则性和常返性等概念,利用Liapunov直接法得到了此类随机发展方程的随机渐近稳定性、随机指教稳定性、p-稳定性和几乎必然指数稳定性的充分性判据。这些结果不但推广了有限维情形的工作,同时也发展了A.Ichikawa的工作。     

多组元Fe-W-B合金本构方程及热加工图的研究

为解决铸造高硼合金难热加工以及硼化物呈网状分布的问题,本文以多组元Fe-W-B合金为例,采用Gleeble-3500热模拟实验机研究了其在变形温度800℃～1150℃、应变速率0.01s^-1～10s^-1条件下的高温流变行为。结果表明,多组元Fe-W-B合金的高温流变应力状态主要受温度和应变速率影响,具体表现为流变应力随着应变速率降低和变形温度升高而减小,真应力-应变曲线表现出动态回复型和动态再结晶型特征。本文还构建了Arrhenius型热变形本构方程并对其准确性进行了验证;根据热加工图确定了多组元Fe-W-B合金最佳热加工窗口并进行锻造验证。锻后,多组元Fe-W-B合金中的网状硼化物被有效破碎并且力学性能大幅提升。     

二维非饱和土壤水流方程基于POD方法的有限元格式

将特征正交分解(Proper Orrhogonal Decomposition,POD)应用于二维非饱和土壤水流方程通常的有限元格式,将其简化为一个计算量少但具有足够高精度的POD有限元格式,并给出POD有限元解的误差估计.数值例子表明:POD有限元解能有效地表达土壤水流的运动特征,保证了POD有限元解和通常有限元解误差足够小,而且POD有限元格式有较少的自由度,比通常的有限元格式大大节省了计算量和内存容量,从而验证POD方法的有效性.     

二阶线性非散度型抛物方程解的局部正则性估计

发展了Acerbi等的方法,得到了一类具有小BMO系数的二阶线性非散度型抛物方程解的二阶偏导数在Orlicz空间中的局部正则性估计.这种正则性估计可以应用于W2P,1解的存在性问题.     

基于非协调F?ppl-von Kármán方程组的冷轧带材后屈曲分析

为了揭示冷轧带材前屈曲面内残余应力与后屈曲挠度、后屈曲残余应力的关系,引入非协调F?ppl-von Kármán方程组,建立了两边自由无限长带条后屈曲的非线性偏微分方程组边值问题模型。根据冷轧带材后屈曲挠度具有轧制方向单波长周期性变化的特点,将非线性偏微分方程组边值问题分离变量而形成非线性常微分方程组边值问题。将边值问题中涉及的各物理量无量纲化,并分析这些物理量的数量级,进而确定出带有待定系数的无量纲挠度函数的形式。然后将总势能写成只与无量纲挠度函数有关的形式,并利用Ritz法确定各待定系数。最后采用其他文献中的计算结果与本文提出方法的计算结果进行对比,发现较为吻合,并解释了产生误差的原因。同时针对某冷轧厂产品计算出后屈曲释放后的残余应力,并计算了使带钢保持平直的最小张应力,为板形仪的合理应用提供了参考。     

Use of a finite element method to calculate roll profiles for broad-strip mills

A model is proposed to calculate the polishing profiling of rolls in broad-strip mills using a finite element method, and it is applied to develop new roll profiles. The finite element method is used to determine the polishing profiling of a roll with a complex shape, which substantially decreases the nonuniformity of reduction and drawing over the strip width. This profiling can be executed on numerical control roll grinders.     

Simulation of electromagnetically induced hyperthermia: a finite element gridding method

A finite element gridding method for simulating electromagnetically (EM) induced hyperthermia is presented. The method uses patient CT data as its primary input, with critical structures manually outlined (on a graphics workstation) for explicit demarcation. The paper outlines the various stages involved in mesh creation, including procedures for conforming the finite element representation of critical structures to their smooth boundaries, modelling of heating equipment, and modelling of the outer boundaries. The procedure for generating the finite element model is illustrated for an example treatment. Additionally, the results of computing the SAR in six patients are compared to measured values. The comparison reveals agreement between the model prediction and actual treatment within the limits of measurement error.     

Semi-automatic computer construction of three-dimensional shapes for the finite element method

Seven patients with idiopathic Parkinson's disease, aged 62 to 76 years, average duration of the disease approximately eleven years, suffering from severe hallucinosis and paranoid delusions of different degree, in whom conventional therapeutic strategies (administration of benzodiazepines and mild neuroleptics) had no antipsychotic effect, received clozapine, a non-classical highly potent neuroleptic, while blood count was strictly monitored. Paranoid ideas disappeared in all seven patients after a maximum of four days administration of 25-125 mg/day. No deterioration of parkinsonian symptoms, quantified according to UPDRS was seen. Given the protection of clozapine, we could increase the L-dopa dose in two cases, thereby improving the patients' motor function. Blood count showed no abnormalities in any of the patients during an average observation period of seventeen months. Our results support the assumption that clozapine has a potent antipsychotic effect in the treatment of psychotic decompensation in advanced Parkinson's disease in carefully selected patients. We saw no negative influence of the neuroleptic on extrapyramidal symptoms.     

Numerical simulation of macrosegregation: a comparison between finite volume method and finite element method predictions and a confrontation with experiments

Micro-macrosegregation calculations have been performed for a rectangular cavity containing either a Pb-48 wt pct Sn alloy or a Sn-5 wt pct Pb alloy. The numerical results calculated with a finite volume method (FVM) and a finite element method (FEM) are compared with experimental results previously obtained by Hebditch and Hunt. The two methods are based on the same average conservation equations governing heat and mass transfer and the same assumptions: lever rule, equal and constant density of the solid and liquid phases (except in the buoyancy term), permeability of the mushy zone given by the Carman-Kozeny relation, and no transport of the solid phase. Although the same parameters are used in both calculations, small differences are observed as a result of the different formulations. In particular, the instabilities appearing in the mushy zone (channels) of the Sn-5 wt pct Pb alloy are more pronounced with the FVM formulation as compared with FEM, whereas the opposite trend is observed for the Pb-48 wt pct Sn alloy. Nevertheless, the final segregation maps at the end of solidification compare fairly well with the experimental findings.     

三维Boussinesq方程有限元格式的POD降维模型

针对帝国理工大学三维海洋模型(Boussinesq方程)的无结构有限元格式,用特征正交分解方法(POD)得到了降维模型.并且给出了POD降维模型的误差估计.最后,通过数值算例验证了POD方法的可行性和有效性.     

增强假设变形梯度有限元方法稳定性计算

讨论了非协调增强假设变形梯度有限元的基本理论、所采用的本构关系和有限元列式.为了克服原先由Simo建议的方法中所固有的缺陷,即在模拟压缩变形时容易出现奇异能量模式而导致计算失稳甚至崩溃,对原方法中有关内变量和应力更新算法进行了改进.计算结果表明,改进的方法在模拟压缩和拉伸模型时,具有较好的计算稳定性.     

基于有限元方法的疲劳裂纹闭合行为

裂纹闭合行为将很大程度改变疲劳裂纹扩展行为。针对316L不锈钢,结合常幅加载和单个拉伸过载试验和动态数值模拟方法,对疲劳裂纹扩展行为中的裂纹闭合现象开展了一系列研究工作。详细对比了不同扩展阶段的裂纹闭合行为随裂纹长度、应力比和过载影响因素的变化,以及对裂纹扩展速率的影响。同时,研究了单个拉伸过载和裂纹闭合行为之间的内在联系和机理。结合裂纹闭合理论和有限元计算结果,等效应力强度因子被用来描述316L不锈钢的裂纹扩展过程,并提出316L不锈钢的裂纹扩展速率的预测模型。     

一种新的静态轧制过程有限元模拟方法

提出了一种将欧拉法与拉格朗日法结合起来的静态轧制过程有限元模拟新方法.其主要内容包括:在轧制件纵向上用欧拉坐标, 厚度和宽度方向上用拉格朗日坐标,时间变量是独立的,计算轧制件厚度和宽度方向上的实际位移时采用的流线形积分改用沿纵向的欧拉坐标一元积分.     

Thermomechanical analysis of direct chill casting using finite element method

The transient nature of the start-up phase is the most critical phase in the direct chill (DC) casting during which the quality of the ingot is questioned. The hot crack and cold crack are the two major problems in the DC casting which originate during and after the solidification. In this work, the thermal, metallurgical, and the mechanical fields of DC casting are modeled. The attention is focused on the mushy state of alloy where the chances are high for the hot tearing. The heat conduction and metallurgical phase-change phenomenon are modeled together in a strongly coupled manner. An isothermal staggered approach is followed to couple the thermal and mechanical parts within a time step. Finite element method is used to discretize the thermal and mechanical field equations. A temperature-based fixed grid method is followed to incorporate the latent heat. The mushy state of alloy is characterized through the Norton-Hoff viscoplastic law and the solid phase is modeled through the Garafalo law. An axisymmetric round billet is simulated. The casting material is considered as AA1201 aluminum alloy. It is found that all the components of stress and viscoplastic strain are maximum at the billet center. Further, the start-up phase stresses and strains are always higher than the steady state phase. Therefore, the chances of hot crack formation are higher during the start-up phase and specifically at the billet center. It is proved that through the ramping procedure, the vulnerability of start-up phase can be lowered.