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时代教育·国外高校优秀教材精选:工程中的有限元方法(原书第4版)

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时代教育·国外高校优秀教材精选:工程中的有限元方法(原书第4版)

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《时代教育·国外高校优秀教材精选:工程中的有限元方法(原书第4版)》为第4版,它通过理论与实际相结合的方式来介绍有限元方法,并结合选自于工程实际背景的例题和习题来进行叙述,有限元分析中所有实现的步骤都在包括在所提供的可独立运行的程序中,《时代教育·国外高校优秀教材精选:工程中的有限元方法(原书第4版)》保留了前几版的写作风格和叙述逻辑,可作为高年级本科生和一年级研究生的课程学习教材,对于从事实际工作的工程技术人员也可以作为重要的学习素材。
Catalogue

译者序
前言

第1章 基本概念
1.1 引言
1.2 历史背景
1.3 本书概要
1.4 应力与平衡方程
1.5 边界条件
1.6 应变-位移关系
1.7 应力-应变关系
1.8 温度效应
1.9 势能与平衡方程瑞利一里兹方法
1.10 伽辽金方法
1.11 圣维南原理
1.12 冯·米泽斯应力
1.13 叠加原理
1.14 计算机程序
1.15 小结
历史性文献
习题

第2章 矩阵代数与高斯消元法
2.1 矩阵代数
2.2 高斯消元法
2.3 方程求解的共轭梯度法
习题
程序清单

第3章 一维问题
3.1 概述
3.2 建立有限元模型
3.3 形状函数与局部坐标
3.4 势能方法
3.5 Galerkin方法
3.6 整体刚度矩阵和载荷列阵的集成
3.7 整体刚度矩阵K的性质
3.8 有限元方程边界条件的处理
3.9 二次形状函数
3.10 温度效应
3.11 实际问题的建模与边界条件的施加
习题
程序清单

第4章 桁架
4.1 引言
4.2 平面桁架问题
4.3 三维桁架问题
4.4 基于带状法和特征顶线法对整体刚度矩阵进行组装
4.5 实际问题的建模与边界条件的施加
习题
程序清单

第5章 梁和框架结构
5.1 引言
5.2 有限元列式
5.3 载荷列阵
5.4 边界条件的处理
5.5 剪切力和弯矩
5.6 具有弹性支承的梁
5.7 平面框架
5.8 三维框架
5.9 实际问题的建模与边界条件的施加
5.10 讨论
习题
程序清单

第6章 常应变三角形单元与二维问题
求解
6.1 引言
6.2 有限元模型
6.3 常应变三角形单元(csr)
6.4 建立模型和边界条件
6.5 拼片试验与收敛性
6.6 正交各向异性材料
习题
程序清单

第7章 轴对称问题
7.1 引言
7.2 轴对称列式
7.3 有限元建模轴对称三角形单元
7.4 实际问题的建模和边界条件的施加
习题
程序清单

第8章 二维等参元与数值积分
8.1 引言
8.2 四节点四边形单元
8.3 数值积分
8.4 高阶单元
8.5 轴对称问题中的四节点四边形单元
8.6 四边形单元的共轭梯度法
8.7 关于收敛性的主要结论
有关收敛性方面的参考文献
习题
程序清单

第9章 应力分析中的三维问题
9.1 引言
9.2 有限元分析列式
9.3 应力的计算
9.4 网格划分
9.5 六面体单元和高阶单元
9.6 问题的建模
9.7 有限元矩阵的波前法
习题
程序清单

第10章 标量场问题
10.1 引言
10.2 稳态热传导问题
10.3 扭转
10.4 位势流、渗流、电磁场以及管道中的流动问题
10.5 小结
习题
程序清单

第11章 动力学分析
11.1 引言
11.2 基本公式
11.3 单元质量矩阵
11.4 特征值与特征向量的求解
11.5 与有限元程序的接口及确定轴旋转临界速度的程序
11.6 GUYAN缩减
11.7 刚体模态
11.8 小结
习题
程序清单

第12章 前处理和后处理
12.1 引言
12.2 网格的生成
12.3 后处理
12.4 小结
习题
程序清单

附录 dA=detJd的证明
参考文献
部分习题答案
索引
Introduction

本书的第1版在20多年以前问世,几年之后又出版了第2版和第3版。本书曾被翻译成西班牙语、韩语、希腊语和汉语。我们收到了来自使用该书的教授、学生和从事实际工作的工程师的正面反馈意见,也了解到在过去30年中我们学校的学生使用本书的各方面情况。本书的基本出发点是提供有限元方法的清晰理论、建模方法以及具体的计算机实现程序,在这一版充分考虑了许多建议,保留了以前版本的特点,并在一些方面有所改进。
本书在以下方面作了调整:
1)介绍叠加原理。
2)对称与反对称问题的处理。
3)提供更多的例题和习题。
4)拼片试验。
5)将梁和框架结构的章节移至桁架章节之后。
6)修订了ExcelVB编程。
7)提供可在网页浏览器IE、Firefox、Chrome、Safari上运行的JavaScript程序。
8)提供与有限元编程衔接的图形处理运行程序。
书中许多章节还增加了一些新的材料,补充了实际算例和练习题,以帮助读者更好地学习和理解,而练习题更强调了对基本理论的理解和实际问题的考虑。在前面几章中增加了实际问题的建模,在第1章增加了叠加原理,清晰阐述了二维问题中对称和反对称情形的处理方法,增加了例题和练习题,并增加了对拼片试验和相关问题的讨论。所提供的程序都具有相同的编程结构,以方便读者仿照使用;同时还增加了JavaScript程序,使得读者可以采用IE、Firefox、Chrome或Safari等网页浏览器进行有限元问题的求解。所有程序都经过认真的检查,可下载程序包中包括了涉及图形程序的可执行版本。程序所采用的语言包括:VisualBasic、MicrosoftExcelVisualBasic、MATIAB、JavaScript,以及早期使用的QBASIC、FORTRAN和C,相应的求解说明也作了更新。
第1章简要介绍有限元方法的历史背景和基本概念,对平衡方程、应力.应变关系、应变.位移关系和势能原理进行评述,引入伽辽金(Galerkin)方法的概念。
第2章介绍矩阵和行列式的性质,引入高斯(Gauss)消元法,讨论对称带状矩阵方程的求解和带状矩阵“特征顶线”(skyline)的处理方法,对平方根(Cholesky分解)法和共轭梯度法也作了讨论。
第3章通过对一维问题的分析来介绍有限元方法的基本概念和表达式,涉及有限元分析的主要步骤:形状函数的表达、单元刚度矩阵的推导、整体刚度矩阵的形成、边界条件的处理、方程的求解以及应力计算;同时给出了基于势能方法和伽辽金方法的表达形式,而且考虑了温度效应的处理。
第4章给出平面及三维桁架问题的有限元表达,对于整体刚度矩阵的组装,分别给出带状矩阵和具有“特征顶线”矩阵的形式,还提供了基于这两种形式进行求解的计算机程序。
第5章讨论梁单元及埃尔米特(Hermite)形状函数的应用,涉及二维及三维框架结构。
第6章介绍用于二维平面应力和平面应变问题求解的常应变三角形单元(CST),详细给出问题的建模过程及边界条件的处理方法,对于正交各向异性材料也给出相应的处理方法。
第7章介绍轴对称物体在承受轴对称外载时的建模过程,给出相应的三角形单元表达式,还提供几个实际问题的处理方法。
第8章介绍四边形单元和高阶单元的基本概念以及采用高斯方法进行面积积分的数值方法,给出轴对称四边形单元的表达式以及基于共轭梯度法求解的过程。
第9章为三维应力分析,包括四面体单元和六面体单元,还介绍波前法的求解及其实现过程。
第10章详细介绍标量场问题的处理,在其他各章中均将伽辽金方法和能量原理作为有限元方法推导的基本原理,在本章中仅采用伽辽金方法来进行推导。采用该方法可以直接对所给出的微分方程进行处理,而无需定义一个用来求最小值的等效泛函。该章分别就稳态热传导、扭转、一般流动、渗流、电磁场、管道中流动、声学等问题给出相应的伽辽金方法表达式。
第11章为动力学问题,给出单元质量矩阵表达,对一般特征值问题的特征值(自然率频)、特征向量(模态形状)的求解进行讨论,给出求逆迭代法、雅可比(Jacobi)法、三对角化法以及显式漂移法等求解方法。
第12章介绍前处理及后处理的概念,给出二维问题网格自动划分的原理及实现方法,对于三角形和四边形单元给出由单元值求取节点应力的最小二乘方法,还介绍了后处理中的等值线技术。
对于本科生来说,书中一些较深的内容可以忽略,或根据某一新的完整内容体系,按需要来采用本书的材料,建议并鼓励在学习完第6章后就开始使用第12章中的程序,这样可以帮助读者高效率地准备各种有限元分析的数据。

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