有限元法

The basic approach of protecting people from being hurt or killed in an accident is to improve crashworthiness of vehicles. This paper starts with discussing theories and methods for vehicle passive safety design, which included experiential methods, analytic methods, multi-body dynamics methods, crash test methods and the finite element method. Emphasis will be paid to the basic FEM theories and algorithms of impact problems. Topics discussed include the governing equation, element discretization, hourglass control, time integration, material model, shell element algorithms and contact-impact algorithms. For more reliable simulation results, this paper then conducts study on how to accurately get material model parameters by combining the FEM method with experimental method, and develops relevant material test machine and parameter calculating software. Based on that, basic typical impact simulation and test validation study are conducted. On the basis of the above work, the paper studies the thin-shell structures'crashworthiness, which was affected by the following factors: spot-weld features, shell thickness, cross-section and pre-deformation. As to vehicle parts'crashworthiness, the paper conducts simulation study of designing energy-absorbing steering system and adaptive airbag system. A practical energy-absorbing steering wheel is designed as an example. In further depth research, the paper suggests several inverse quantificational methods for vehicle crashworthiness design based on the ideal crash characteristics. The above theories and methods are applied with good results through several practical vehicles' crashworthiness design and improvement.

文中对汽车碰撞安全性的设计理论和方法进行了归类和总结，其中包括经验法、解析法、多刚体动力学法、试验法以及有限元方法等；重点介绍了碰撞有限元法的基本理论和有关算法，涉及到有限元求解控制方程、单元离散、沙漏模态控制、时间积分、材料模型和应力修正、薄壳单元算法以及接触碰撞界面算法等，探讨了有限元计算中的材料模型参数获取技术，开发了相应的材料试验装置及材料模型参数反求软件，在此基础上进行了基本的碰撞仿真算例和试验对比研究；文中通过应用有限元方法研究了薄壁构件的碰撞吸能特性，指出了设计薄壁吸能构件时需要考虑的几个主要影响因素，即焊点、壁厚、横截面和预变形等；在关于车辆部件的碰撞安全性能设计中进行了吸能转向机构和自适应安全气囊的仿真研究，提出了吸能转向机构和自适应安全气囊的仿真研究方法；文中最后探讨了整车碰撞性能的设计与改进方法，提出了以理想碰撞特性为目标，采用分段加速度或者根据碰撞时间进行设计的反推设计法、部件吸能仿真优化设计法等量化设计方法，并通过综合应用文中所讨论的相关技术进行了整车碰撞性能的设计与改进实例研究，所选定的车型是大众化的普通轿车和碰撞安全性基础较差的微型面包车，研究结果表明，本文所提出的设计与改进方法是适用而有效的，具有重要的工程实用意义和价值。

In chapter 2,all kinds of numerical methods of computational fracturemechanics are summarized,the development histories and present situation ofboundary collocation method,boundary integral method,finite difference method,boundary element method and finite element method are expounded,and theapplication of finite element method in fracture mechanics are emphaticallydiscussed.

第二章 总结了计算断裂力学中各种数值方法，论述了边界配位法、边界积分法、有限差分法、边界元法及有限元法的发展历史和现状，并着重讨论了有限元法在断裂力学中的应用。

The comparison based on FEM, SEA and the closed form solution reveals th e effectiveness of SEA in the prediction of high-frequency response. Next, the energy transmission between two coupled beams is obtained through FEM, and then the CLF used by SEA is built.

然后以耦合梁为例，通过有限元法得到两个梁之间的能量传递，并进而得到SEA所需的耦合损耗因子；将有限元计算结果和SEA结果对比验证了该方法的有效性，以期建立一种用有限元法获得SEA参数的新途径。

The discrete element method and the finite element method have their own advantages and weaknesses. Basically, the DEM was developed for predicting the failure problems accompanying with the transition from continuum to non-continuum media. However, it is not accurate to calculate the problem of continuum media. The FEM may forecast the failure area of the material reasonably, while it is hard to calculate the failure process in brittle media. Therefore it becomes a good choice to combine the two methods to construct a hybrid model.

离散元法和有限元法等数值计算方法各有其优势，同时也都存在不足之处：离散元法适于处理由连续介质向非连续介质转化的破坏问题，但对于连续体计算结果精度不高；有限元法适于预测材料破坏的区域，但难以直接用于计算脆性材料破坏过程，因此将两种方法结合可以形成一种较好的混合模型。

First, For the coronary artery stent, two kinds of loads, including the pressure named 〓 derivatively from the balloon and the counterforce named 〓 on the wall edge of the stent, have been taken into account in the analysis of the stent.〓 and 〓 were changing as the stent expanding. So, the expansion process of the stent could be considered as the process composing of many extremely short equilibrium processes, where 〓 and 〓 could be regarded as constants and the stresses, the strains and the displacements were obtained using NFEA in every processes. Then, the stresses, the strains and the displacements obtained in every processes or steps were added up to get the final structure of the coronary stent.

首先，解决了支架有限元分析的载荷非线性问题，认为医用心血管支架受到两种载荷的作用：球囊直接传递的压力〓和球囊对不锈钢支架丝壁边缘的反作用力〓，这两种载荷在支架分析中必须都考虑进去；〓为非线性载荷，随着支架扩张不断变化，处理时将支架扩张的整个过程看成由37个很短的平衡过程组成，在每个过程中取〓为常量，采用有限元法获得应力、应变、位移，最后将各过程的应力、应变、位移迭加起来就获得了不锈钢支架总的应力、应变和位移；本研究用变分法和有限元法模拟杆件拉伸证明了上述方法是合理的。

Using finite partition FEM, the material nonlinearity of 2D-beam structure was also considered. Combined with the incremental iterative method and are length method, a program for the geometric and material nonlinearity analysis of 2D-frame structure was complied.

坐标下的所有有限元列式，并采用有限分割有限元法分析结构的物理非线性，结合荷载增量法和柱面弧长法编制了相应的平面杆系结构几何、物理双非线性有限元分析程序。

This paper systematically provides an overview of recent developments in small punch test technology including empirical and computational methods for determining elasto-plastic parameters from the measured data of small punch test. The computational methods involve finite element and parameter method, inverse finite element procedure, finite element and inverse methodology, inverse identification based on artificial neural networks, finite element optimization, shape deformation and hybrid inverse procedure et al.

本文系统综述小冲杆试验的测量技术及从测量数据来确定材料弹塑性参数的各种经验方法和计算方法，例如有限元分析和参数法、反向有限元法、有限元和反方法、反向识别和人工神经网络、有限元优化和试验变形形状以及杂交反方法等。

Three moment method,the transition matrix method and finite element method in shipping shaft system alignment are used ,the application of finite element method in shipping shaft system alignment is proved to be more reasonable through an example .

并以某实船为例，利用三弯距法、迁移矩阵法和有限元法对船舶轴系进行校中计算，说明有限元法更先进合理。

Moreover, this paper makes an effort in incorporating theCosserat theory in the VCFEM for the elastic-plastic analysis of heterogeneous materialsbased on the PVP. The chapters are divided as follows: In Chapter 1, the author summarizes the study on the equivalent mechanics properties ofheterogeneous materials (including the development of the universal relationship which isirrelevant to the micro structure, the discussion of the limitations of the effective moduli, thecomputation of the effective properties of heterogeneous materials with the micromechanicsmethod and the FEM, and the equivalence of the heterogeneous micropolar materials) and thepresentation, the evolution, the corresponding numerical studies of the Cosserat model and itsapplications in engineering.

本文基于参数变分原理，构建了Cosserat体弹塑性有限元分析模型并用于求解应力集中和应变局部化问题；利用Voronoi有限元法提出了适用于非均质材料宏观弹塑性性能计算的参数二次规划算法；进一步将Cosserat模型应用到Voronoi有限元法中，提出了基于Cosserat理论的Voronoi杂交有限元法，并采用参数变分原理进行新模型的分析计算。

By dynamic stability analysis and calculation in means of FEM, the three-dimension data processing technique for arbitrary cross sections of solid masses was adopted, then the safety factor of the abutment of arch dam was provided using FEM, and corresponding programs was compiled.

采用有限元法进行动力分析计算，利用三维实体任意切面数据处理技术，提出了应用有限元法计算拱坝坝肩稳定安全系数方法，在此基础上完成了基于有限元法以坝肩动力稳定安全系数为目标的高拱坝优化设计程序。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。