有限元法

By taking the advantages of SPH and standard finite element methods,a coupled method is proposed,in which the computational model is made up of finite elements in initial time and the large distortional elements are converted automatically into smoothed particles.

扼要讨论了光滑粒子法的离散思想，充分利用光滑粒子法和有限元方法各自的优点，提出了一种初始时刻用有限元建模，计算过程中大变形单元自动转换为光滑粒子的耦合算法。

is applied to construct the three-dimension model for finite element analysis. Short circuit and open circuit of the field winding and the teeth and slots structure of the rotor are discussed. An appropriate three-dimensional mesh is made. The corner point problem of conductor is eliminated. Furthermore, a new memory structure for sparse complex matrix and a PCCG method based on it are introduced to save memory and computation time.

在汽轮发电机失磁异步运行转子三维涡流场数值计算模型中，应用了〓法建立了三维有限元计算模型，考虑了转子绕组的开、短路状态及转子齿槽结构，形成了合适的三维剖分网格，解决了三维电磁场有限元计算中角点奇异的问题，创立了一种新的稀疏矩阵的存储格式以及基于该格式的预处理复数共轭梯度法从而减少内存开销和加快了求解速度。

Based on interval analysis and displacement finite element method, the static displacement response analysis of structure comes down to solve the interval finite element control equation.

现有的理论和方法采用区间分析和位移法有限元理论对其进行分析，最终归为位移法区间有限元控制方程的求解。

The convergence of the traditional nonlinear equations is related to the selected initial value, but the convergence of the fixed point method is not related to it.

传统的非线性有限元方程组的数值求解法（牛顿-拉普森迭代法与共轭梯度法）只能求解单值性有限元方程，且其收敛行为与初始值的选择有关，而不动点方法在求解非线性方程组时的收敛行为不受初始值选择的影响，在大范围内是一致收敛的。

Analyzed on the tunnels that used EPB method in different soils, the more logical three-dimensional finite element model is based, which can reality represented the soil transfiguration. 3 Due to the engineering example, a 3D FEM simulation model was founded. The model was used to study the rules of soil deformation and surface settlement during shield tunneling. 4 The characteristics of loess include the module, conglutination force and inner friction angle of the loess, affected the soil deformation. 5 The influence factors to the surface settlements such as the depth of soil, the outer diameter of the shield tunnel, the released stress at the cutting face, the fill ratio of the shield tail void, pouring-slurry press, thrusts and lengths of shield and digging steps were studied using the FEM method. References is brought forward in the loess areas of Xi'an was proposed.

通过对不同土质条件下盾构法进行地铁隧道施工的有限元分析，全面反映盾构推进对土体变形的影响情况； 3根据有关勘测资料，建立合理的盾构法施工三维非线性有限元模型，对盾构法施工引起的地层变位和地表位移情况进行计算，分析了盾构施工引起的地层变形规律和地面沉降规律； 4研究了黄土特性(地基模量、粘聚力和内摩擦角)对盾构法施工中土体变形的影响； 5利用三维有限元对盾构施工过程中影响地面沉降的因素(覆土厚度、隧道外径、开挖面压力变化量、注浆压力、盾尾空隙填充率、开挖步长、盾构机的长度和推进力等)进行研究，为今后西安地区地铁的建设提供参考。

The contents of this course include: the mathematical basis of FEM, the generic solution principles and expressions of elastic mechanics issue, the construction of element and its interpolation function, iso-parametric element and numerical integral, solution of linear equations, some practical issues of FEM modeling, brief introduction to typical commercial FEM packages, FEM for truss, plate blending and shell, and FEM for heat exchange and dynamics.

课程内容主要包括：有限单元法的数学基础、弹性力学问题有限单元法的一般原理和表达格式、单元和插值函数的构造、等参单元和数值积分、线性方程组解法、有限元建模的若干实际问题、典型商用有限元分析软件简介、杆件结构力学问题的有限单元法、平板弯曲问题的有限单元法、一般壳体问题的有限单元法、热传导问题的有限单元法、动力学问题的有限单元法等。

First, this article introduced 2 grade of rotary kiln principle of work and the equipment, to rolled the circle mechanics behavior to carry on the analysis, proposed - rolled the circle - under roller's rotary kiln overall modelling based on the tube body - kiln liner - big tooth ring, to rolled the circle - under roller's contact stress to carry on the finite element analysis the method, and obtained rolled the circle contact stress the size and the distribution rule, finally indicated that rolled the circle contact stress mainly to have two main peak values and the sudden change in one week, appeared is rolling the circle and the under roller contact area; Then, rolls the circle the stress to regard as is the principal stress unknown plane stress test, the use quite mature modern test technology, proposed rolls the circle stress test the principle and the plan, and to rolled the circle the stress to carry on the scene test, the stress which the scene test analysis result and the finite element analysis calculated has compared, had proven the whole method modelling's finite element analysis method's rationality and rolled the circle - under roller contact stress the result accuracy; Finally, uses ANSYS APDL the re-development technology, in view of 2 grades of rotary kilns, rolled the circle - under roller contact stress the overall finite element analytic method to carry on the re-development.

首先，本文介绍了2档回转窑工作原理和装置，对滚圈的力学行为进行了分析，提出了基于筒体-窑衬-大齿圈-滚圈-托轮的回转窑整体建模，对滚圈-托轮的接触应力进行有限元分析的方法，并得到了滚圈接触应力的大小和分布规律，结果表明滚圈接触应力在一周内主要存在两个主要的峰值和突变，都出现在滚圈与托轮接触区域；然后，把滚圈的受力看成是主应力未知的平面应力的测试，利用比较成熟的现代测试技术，提出了滚圈应力测试的原理和方案，并对滚圈的应力进行了现场测试，现场测试分析结果与有限元分析计算出的应力相比较，证明了整体法建模的有限元分析方法的合理性和滚圈-托轮接触应力的结果的正确性；最后，利用ANSYS的APDL的二次开发技术，针对2档回转窑，就滚圈-托轮接触应力的整体有限元分析法进行了二次开发。

However, in designing the beamless slabs with equivalent frame method, the stress is an average values along the depth of section, which varies with the normal service state. Compared with the results by finite element method, the results gained by equivalent frame method cannot satisfy the requirement under the normal service state. Therefore, the tendons of beamless slabs should be designed and arranged based on the results of FEM taking account into vertical load and prestressed load.

本文通过分析，认为采用等代框架法进行无梁板设计时，其内力是基于截面平均的结果，在正常使用状态与实际受力状态有很大的不同，通过对比等代框架法和有限元计算的正常使用极限状态应力可知，按等代框架法设计的预应力布置并不能保证其正常使用极限状态的要求，据此提出了应根据无梁板在竖向荷载和预应力共同作用下弹性有限元分析结果进行预应力筋布置的建议。

For some rock slopes, which have not distinct failure surface, but have complicated structure or load on the top and so on, a stability analysis of this type slopes by finite element method is presented, the failure surface is defined by certain rule or strain zone from the computed model, and then the safety factor of the rock slope is abtained by finite element method and limit equilibrium methodAt last, using ANSYS , a famous commercial finite element analysis software, a example of high-steep slope which is bearing the load of the LongGe Mansion is presented, the stability of this slope is studied, as a paradign the the stability evalution of complicated high-steep slope under the action of load of building , the chapter gives some meritable reference in stability assessment of rock slopes using numerical simulation by three-dimension elastic-plastic finite element.

并用有限单元法建立边坡的具体模型，应用折减边坡岩体参数、逐级施加荷载等与边坡工作环境相似的方法进行模拟计算，根据计算结果，采用一定的判别准则或图形可视化方法，确定出边坡的滑裂面，再采用刚体极限平衡法或有限单元法计算其安全系数；最后，通过某一工程实例，用大型有限元程序对边坡在建筑物荷载作用下的稳定性进行分析研究，并以此作为计算分析复杂高边坡在高层建筑物作用下的稳定性评价的一个范例，在采用有限元弹塑性数值模拟岩质边坡稳定性方面提供一些有价值的参考。

3D-CTM (Coupled Thermo-Mechanical Forming Simulation) software for precision forging process of aero-engine blade was developed. The key technologies of 3D coupled rigid-viscoplastic thermo-mechanical FEM simulation of blade forging process were studied systematically. By using the remeshing method of contracting from the boundary to the inner, new mesh system from old distorted mesh system can be obtained. A method of modifying the position of nodes touching on the die according to its original normal was proposed to avoid "dead lock" problem due to uncontinuity of normal of scatted die meshes. The pseudo-static iterative algorithm was used to simplify the coupled thermo-mechanical computation. In particular, formulations to determine relaxation factor β was established for rigid viscoplastic FEM adopting penalty function method, and an improved cubic factor rapid algorithm derived from these formulations was proposed by combining with the advantage of advance and retreat search method.

采用基于边界构形的内缩法，实现了三维畸变网格的重新划分；提出了初矢修正法对触模节点的位置进行修正，解决了由于离散的模具网格的法矢不连续造成的&死锁&问题；采用准静态迭代法简化了速度场和温度场耦合计算过程；特别是针对减速因子β的选取，建立了适用于三维复杂成形过程刚粘塑性罚函数法有限元三次因子法的计算公式，并结合进退搜索法提出了改进的三次因子快速算法，提高了模拟计算效率和稳定性，在此基础之上，开发了面向叶片精锻过程的三维刚粘塑性热力耦合有限元模拟分析系统(3D-CTM)，系统的可靠性得到了圆柱体镦粗的验证。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。