Three Dimensional Simulation of Upset Forging by Using Variational Upper Bound Method

The variation principle is discussed and Rayleigh-Ritz method is proposed for construction of veloci ty field. A kinematically admissible velocity field based on polynomials was appIied to the determina tion of forging load and deformed buIge profile during upset forging of blocks. Simulation of upsetforging of rectangular blocks under various friction condjtions was performed. Comparison of the computed results with experiments and FEM shows good agreement. It is shown that this techniquecan be used for 3D simulation of metal forming process.

The study of slip line field and upper bound method based on associated flow and non-associated flow rules

At present,associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle,so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory,the theory of slip line field is put forward in this paper,and then the ultimate bearing capacity of strip footing is obtained based on the associated flow rule and the non-associated flow rule individually. These two results are identical since the ultimate bearing capacity is independent of flow rule. On the contrary,the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associated flow rule is incorrect.

OPTIMUMDESIGNOFSTREAMLINEDEXTRUSIONDIESBASEDONUPPERBOUNDMETHODANALYSIS

提出了一种通用且形状变化丰富的流线型挤压模曲面的表示方法，流线型挤压模曲面用毛坯和型材截面形状的插值来表示。毛坯和型材截面形状由带张力的曲线拟合，通过调整张力参数以拟合带有直线段的型材截面。材料在模具内的流动由上限法模拟，通过极小化挤压力优化模具曲面和动可容速度中的伪独立参数，以获得最佳模具曲面。最后讨论了摩擦条件、模具长度、面积缩减率。

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory.The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes.The iterative optimization method was adopted to obtain the safety factors.Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion,and the validity of present method could be illuminated.From the numerical results,it can also be seen that nonlinear parameter m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.

Upper bound analytical solution for surrounding rock pressure of shallow unsymmetrical loading tunnels

By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.

Force analysis of pile foundation in rock slope based on upper-bound theorem of limit

Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.

Upper bound analysis of thixotropic extrusion processes of semi-solid magnesium alloys

The methodology was used to conduct the upper bound analysis of thixotropic extrusion process of semi-solid metal. The calculated formulas of deformed power were derived. The relationship among relative stress, frictional factor and die semi-angle were obtained. The relative stress increases with increasing frictional factor, whose value increases with increasing area reduction ratio of a certain die semi-angle. The relative stress firstly decreases and then increases with increasing die semi-angle at a certain area reduction ratio. So, the optimal die semi-angle exists with the corresponding minimum relative stress. The calculated results are in agreement with the experimental ones, which are applied to directing technological practice of axis-symmetry forward extrusion of semi-solid magnesium alloys.

土质边坡的单元失效概率与失效模式研究

土质边坡系统失效概率与土体抗剪强度参数以及地下水位息息相关,在传统边坡可靠度分析中一般只考虑了土体抗剪强度参数的变异性,忽略了地下水位随机性带来的影响。该文将有限元离散技术、上限法理论、相关非高斯随机场模拟方法以及随机规划理论结合起来研究随机地下水位作用下考虑参数空间变异性的边坡系统失效概率。采用有限单元离散边坡土体,将边坡地下水位作为随机变量并考虑土体抗剪参数的空间变异性,基于塑性极限分析上限法构建边坡可靠度分析的随机规划模型;采用基于蒙特卡洛的迭代方法进行求解,得到边坡稳定性系数和速度场;根据边坡中单元的失效信息首次采用AP聚类分析方法来估算边坡的系统失效概率,发展了边坡系统可靠度分析理论。对一个经典的边坡算例进行了系统分析并与极限平衡分析方法、有限元方法结果进行对比,结果表明:随机地下水位作用下考虑参数空间变异性时,边坡存在多种失效模式,AP聚类分析方法可以根据失效单元的位置信息识别出边坡所有失效模式以及对应的失效概率;基于Matlab编制了高效的上限法并行程序,大大提高了计算效率。

数据驱动与机理耦合的冷轧电机功率智能预测方法

电机功率计算在保证生产安全、制定轧制规程以及发挥设备能力等方面起到了重要作用。为提高计算精度,本文提出一种机理模型与数据驱动方法相结合的电机功率预测模型。首先,机理模型部分采用上界法得到解析解,然后将部分功率解析解(塑性变形功率、张力功率和剪切功率)与相关变量输入长短时记忆(long short-term memory,LSTM)网络中训练,以提取变量数据之间的深度特征和时序相关性。结果表明:本文提出的时序耦合预测模型相对误差不超过±3.9%,且在相邻卷带钢轧制规程变化较大时,预测效果明显优于上界法和人工神经网络(artificial neural networks,ANN);从残差分布直方图中可以看到,上界法由于遗漏了摩擦系数和损失功率与其他参数间的强耦合关系,导致残差集中在±50 kW附近且不符合正态分布,而ANN和本模型均基本遵循正态分布,但本模型拟合精度更高;对比更广泛的模型评估指标,本模型具有更好的综合预测性能。此外,通过模型输出结果分析了电机功率与轧制长度、轧制速度之间的关系,表明本模型除具有高预测精度外,还与已知的参数间物理规律有较强一致性。

地震作用下双层土质边坡稳定性上限分析

为探究地震作用对双层土质边坡稳定性的影响,基于极限分析上限理论,建立了地震作用下双层土质边坡旋转破坏机构。采用拟静力法简化地震荷载作用,推导了双层土质边坡安全系数表达式。分析土体黏聚力比、边坡坡角以及地震作用对双层土质边坡稳定性及其滑动面参数的影响。研究结果表明:在水平地震作用下,随着黏聚力比的增大,边坡安全系数呈非线性增大且潜在滑动面变浅;当水平地震作用增强时,边坡失稳破坏范围显著加大;随着竖向地震系数及黏聚力比的增大,边坡安全系数略微降低;水平地震作用增强时,竖向地震作用对边坡稳定性的影响逐渐增大,此时需要考虑竖向地震的影响。

双金属板材异步轧制复合轧后层厚建模与分析

根据双层金属复合板材同径异速异步轧制复合问题,利用流函数法和上界法建立了异步轧制轧后层厚的数学计算模型。进行异步轧制有限元模拟,将有限元模拟结果与理论结果进行对比,所建立的理论模型误差范围为2.55%~4.17%。该模型不仅可以快速计算轧后复合板的层厚比,在单一工况下,还能快速掌握不同工艺参数(压下量、初始板厚、异速比、层厚比)对轧后层厚比的影响规律,对设置和优化生产工艺提供了重要参考。

球形分层大地格林函数的理论推导和数值计算

目前球形分层大地格林函数在理论推导和数值计算方面还存在着较大的困难。首先,通过球形分层电磁理论推导无穷勒让德级数形式的格林函数,并提出勒让德级数权重函数的递推算法。在此基础上,提出求解球形分层格林函数的复镜像方法,将格林函数的无穷级数求和转化为复镜像位函数的叠加,并推导算法的误差上限计算公式,通过算例验证方法的准确性。针对地球尺度级别球形分层格林函数的数值奇异问题和极缓慢收敛特性,提出基于多精度算法的解决方案,进一步证明复镜像法在计算速度和精度上的优势。所提方法能够解决球形分层格林函数的理论和计算难题,为求解地球尺度级别球形分层格林函数提供有效解决方案。

薄煤层N00工法巷道顶板控制机理及分区补偿支护技术

薄煤层N00工法的提出,革新了传统的煤矿开采模式、关键技术与装备系统,并取得了成功应用。而新开采模式下的巷道围岩控制技术尚不完善,为实现薄煤层N00工法巷道顶板结构的安全稳定,考虑其工艺流程和顶板变形特点,将巷道划分为超前硐室、垮落成巷两个阶段。并基于Hoek-Brown非线性岩体强度破坏准则,确定了巷道顶板不同阶段的锚杆/索预紧力的计算公式,提出了巷道顶板锚杆/索预紧力及长度设计方法。此外,结合数值模拟研究了不同阶段巷道顶板锚杆/索支护作用机理及不同锚杆/索支护组合对围岩应力分布的影响,揭示了锚杆/索支护关键参数对顶板稳定性的影响机制。最后,综合理论与数值模拟分析结果,提出了分区补偿支护技术,确定了锚杆/索预紧力、长度及选材的设计原则,该技术在现场取得了良好的应用效果。

地震荷载作用下非饱和土边坡三维极限承载力研究

研究旨在对地震荷载作用下非饱和土边坡稳定性进行分析。为了考虑地震荷载时间效应、边坡放大效应及土体阻尼特性的影响,采用修正拟动力法对边坡动力响应进行描述。采用考虑基质吸力影响下非饱和土广义黏聚力和饱和土摩擦角定义非饱和土剪切强度参数。基于三维离散破坏模型,采用极限分析上限法构建了地震荷载作用下非饱和土边坡三维极限承载力分析模型,通过已发表文献结果验证了所提出模型的有效性。最后,提供了非饱和土边坡三维极限承载力设计图表。研究结果表明:①与二维破坏模型相比较,所提出三维破坏模型能实现对边坡稳定性更为准确的评估;②忽略非饱和土剪切强度参数影响往往导致边坡稳定性评估结果偏于保守。

可折叠防沉板不排水单向承载力上限解

海底可折叠防沉板是有效解决独立式防沉板因面积过大而带来安装施工困难且费用高问题的一种新型海洋浅基础。服役期间,其不排水承载力、破坏机制严重依赖两翼间距和地基土不排水强度分布规律。为揭示可折叠防沉板的承载特性并建立其承载力计算方法,结合数值模拟和理论分析的手段,揭示了不排水条件下可折叠防沉板在竖向V、水平H、弯矩M荷载作用下的地基破坏机制及其随两翼间距、土体不排水强度分布的演变规律。进而基于揭示的破坏机制,分别建立了对应的运动许可速度场,联立虚功率方程和内部能量耗损函数建立了可折叠防沉板单向承载力上限解,并编制了求解程序。通过与数值计算结果对比,不排水承载力上限解高于数值解9.0%以内,计算精度较高。成果解决了传统独立式防沉板承载力计算理论不适用于可折叠防沉板的问题。

预留土支护基坑旋转破坏模式下的极限抗力上限解

对于支撑式或锚拉式支挡结构,进行预留土辅助支护时需验算绕支点的抗倾覆稳定性,然而目前还未找到合理的计算方法。基于极限分析上限定理,提出预留土支护基坑的3种可能破坏模式,运用斜条分法对被动区土体进行离散,并构建相容速度场,分别推导3种破坏模式下基坑抗倾覆力矩的计算表达式,采用遗传算法编程,分析支挡结构与土体间摩擦系数、土体黏聚力及预留土几何参数等对破裂角及抗倾覆力矩的影响规律。结果表明:当墙背光滑且土体黏聚力为零时,利用朗肯被动土压力理论计算得到的抗倾覆力矩为一上限解;存在黏聚力时,朗肯被动土压力理论计算值偏于保守,存在摩擦系数时,库伦土压力理论计算的抗倾覆力矩偏大;与预留土宽度和坡度相比,预留土高度对抗倾覆力矩的影响更加显著。

非均质断层破碎带盾构开挖面极限支护力上限解

盾构施工穿越断层破碎带具有普遍性,而现有的黏聚力沿深度线性变化模型不能充分反应断层破碎带的倾斜性和非均质性,针对这一问题,引入非均质方向角和非均质系数角分别描述断层破碎带的倾斜性、非均质性和非均质系数大小,提出空间非均质分布函数模型。将模型应用于极限分析上限法,推导了盾构穿越断层破碎带隧道开挖面极限支护压力的计算公式,通过算例和工程实例验证了空间非均质分布函数模型的合理性,分析了在不同非均质方向下内摩擦角、黏聚力、埋深比、非均质系数对开挖面稳定性的影响。结果表明:非均质系数角α=90°时,非均质方向角μ的变化对隧道开挖面支护压力无影响;非均质方向角μ≠0°且非均质系数ρ>0时,开挖面支护压力随非均质方向角、内摩擦角、黏聚力、埋深比、非均质系数的增加而减小;非均质方向角μ=0°且H/D≥1时,开挖面支护压力不受埋深比变化影响。非均质方向角对破坏模式形状的影响大于对破坏范围的影响,内摩擦角对破坏模式的形状和范围均有较大影响,非均质方向角和内摩擦角的增大使得开挖面前方塌落体由拱顶往下滑的趋势转变为由前方滑落,针对不同非均质方向角和内摩擦角的断层破碎带的加固侧重点应有所不同。研究结果为确定断层破碎带中盾构开挖面极限支护压力提供了一种可行的计算方法。

基于上限法的闭式冷正挤压棒料脱膜状态分析

考虑一种非磷系润滑膜的脱膜长度,通过上限法分析模型对棒料的闭式冷正挤压工艺进行了分析。通过实验获得了脱膜长度随锥模半角和断面收缩率的变化规律。实验结果表明,随断面收缩率的增长,脱膜长度快速增长。随着锥模半角的增长,脱膜长度也在增长,但是锥模半角增大到一定程度后,脱膜长度的增长幅度减小。求得总功率为最小时的最佳锥模半角,范围是15°~28°,最佳锥模半角随脱膜长度的增加而增加。在成形载荷方面,与DEFORM商用有限元分析软件的仿真结果进行了比较,上限法算得的成形载荷略大于有限元仿真结果,而且两者的载荷曲线较为相近,证明了该上限法分析模型的合理性,也表明上限法更有利于成形设备的选型。