参数积分

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 order to get the exact value of the Hopf bifurcation point, we discuss the discrete version of the integro-differential equation, and use the approximation parameter as the initial value of the Newton iteration method.

为了得到Hopf参数的精确值，进一步讨论了延迟积分－微分方程的离散形式，利用Newton迭代法，得到了参数的逼近值。

The results show that the key of this algorithm is the solution of the integral operational matrix of orthogonal function.

研究结果表明：基于正交函数逼近法的分布参数系统参数辨识算法的关键在于正交函数正、反向积分运算矩阵的求解。

In chapter six, A finite element model to evaluate the mechanics properties of thin wall structure is put forwards. The 4-node quadrilateral Hughes-Liu shell element with five through-the-thickness integration points is employed. The material is assumed to satisfy the elastic-plastic yield condition with isotropic hardening. The single surface contact algorithm is taken to deal with the contact searching. The priori stabilization procedures for the numerical control of the hourglass instability and the penalty method for the evaluation of contact force are used. The classical Coulomb law of friction is employed to evaluate the friction force.

第六章采用法向方向5点积分的4节点Hughes-Liu壳单元，前置参数法砂漏控制技术，等向强化弹塑性材料模型，分步增量应力回映方法，一体化接触搜寻算法，罚参数接触力计算方法及经典摩擦定律，建立了一种计算受冲薄壁结构大变形力学特性计算的有限元模型，通过对汽车A传动轴及汽车纵向方形吸能梁的大变形力学特性分析，验证了该有限元模型的正确性。

By use of the referential variables and perturbational variables the medium parameters of wave equation were rewritten.

利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Green函数理论得到扰动参数比的积分方程。

The crack spacing of CRCP changes randomly and has a significant impact on the pavement durability and performance. The direct integration method is used to analyze the reliability for crack spacing and width. The results show that the main factors that affected the reliability are the design crack spacing and the variability of parameters. This paper presents a nomogram for reliability calculation.

CRCP的裂缝间距是随机变化的，裂缝间距的不同会对路面耐久性产生显著影响，本文使用直接积分法计算了CRCP裂缝间距的可靠度，并使用蒙特卡罗法进行了对比，分析参数的敏感性，指出影响可靠性最主要的因素是设计裂缝间距及参数的变异性，给出了CRCP可靠度计算诺谟图。

Based on a graphical stability criterion in parameter space, the range of proportional-gain is given.

基于参数空间的图解稳定性准则，在已知比例增益范围的前提下，针对稳定和不稳定开环对象，直接在积分-微分参数空间绘制和确定稳定区域，避免了复杂的数学计算。

Based on Monte Carlo method,four different weighted function moment methods for Pearson Ⅲ distribution which were developed in China are first compared by using the evaluation standard considering unbiasness and effectiveness of parameters and design values.

利用统计试验方法，以参数及设计值不偏性、有效性为评价标准，比较了现行几种权函数参数估计法，结果与以理想样本还原准则为标准所得的结论截然相反，以不偏性、有效性标准的结论是数值积分权函数法，并未对马秀峰权函数法作出改进，还从理论上比较分析以上两种评价标准，结论是理想样本还原为标准来评判估计方法的优劣存在较大缺陷，建议今后尽量不要使用该标

Permanent Magnet Synchronous Motor has the feature of strong nonlinear, coupling and parameter time-varying. The Proportional and integral part of traditional PI controller is fixed and unable to meet high precision requirements of PMSM speed control.

永磁同步电机是具有强非线性、强耦合和参数时变特性的被控对象，传统PI 控制方法作为一种线性控制其比例、积分环节的参数固定不变，不能满足永磁同步电机对高精度的要求。

In this dissertation, many works have been done on the basis of the summarization of the merits of all kinds of meshless methods after a large number of relevant references are read and studied. The basic ideas, principles of meshless methods and their development in the recent years are introduced synoptically. Applications of Element-free Galerkin method in elastic foundation plate are studied deeply and some useful conclusions are obtained as follows:(1) Comparisons between numerical solutions and analytical solutions for several different styles of weight functions, including Gaussian weight function, spline weight function and singular weight function etc, are performed. The results show that Gaussian weight function is the best one.(2) Ranges of relevant parameters for Gaussian weight function are given.(3) Influences of nodal distribution schemes and the number of Gaussian integrated dots on computational results are discussed.

在本文中，作者在认真阅读和研究所搜集到的大量参考文献、综合各种无网格法优点的基础上，首先，对无网格法的基本思想、基本原理、发展现状作了概括性的介绍；其次，对无单元Galerkin法在弹性地基板计算中的应用进行了较为深入的探讨：(1)分别对高斯型、样条型、奇异型等不同形式的权函数进行比较分析，数值计算结果与级数解析解的比较表明，高斯型权函数效果较好：(2)对高斯型权函数进行参数研究，得到地基板计算中相关参数的选取范围；(3)对不同节点分布方案和不同高斯积分对计算结果的影响等作了有益的讨论。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。