教学经典教材：有限元（第3版） [Finite Elements:Theory,Fast Solvers,and Application in Solid Mechanics] pdf epub mobi txt 电子书 下载 2025

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[德] 布拉文斯（Braess D.） 著

出版社： 世界图书出版公司

ISBN：9787510042850

版次：3

商品编码：11004217

包装：平装

外文名称：Finite Elements:Theory,Fast Solvers,and Application in Solid Mechanics

开本：24开

出版时间：2012-03-01

用纸：胶版纸

页数：365###

内容简介

This definitive introduction to finite element methods has been thoroughly updated for this third edition， which features important new material for both research and application of the finite element method.
The discussion of saddle point problems is a lughlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena.
The numerical solution ofelliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations but require an introduction to finite element methods will find this text invaluable. Specifically， the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

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目录

Preface to the Third English Edition
Preface to the First English Edition
Preface to the German Edition
Notation
Chapter Ⅰ Introduction
1. Examples and Classification of PDE's
Examples
Classification of PDE's
Well-posed problems
Problems
2. The Maximum Ptinciple
Examples
Corollaries
Problem
3. Finite Difference Methods
Discretization
Discrete maximum principle
Problem
4. A Convergence Theory for Difference Methods
Consistency
Local and global error
Limits of the con-vergence theory
Ptoblems

Chapter Ⅱ Conforming Finite Elements
1. Sobolev Spaces
Introduction to Sobolev spaces
Friedrichs' inequality
Possible singularities of H1 functions
Compact imbeddings
Problems
2. Variational Formulation of Elliptic Boundary-Value Problems of Second Order
Variational formulation
Reduction to homogeneous bound- ary conditions
Existence of solutions
Inhomogeneous boundary conditions
Problems
3. The Neumann Boundary-Value Problem. A Trace Theorem
Ellipticity in H
Boundary-value problems with natural bound-ary conditions
Neumann boundary conditions
Mixed boundary conditions
Proof of the trace theorem
Practi- cal consequences of the trace theorem
Problems
4. The Ritz-Galerkin Method and Some Finite Elements
Model problem
Problems
5. Some Standard Finite Elements
Requirements on the meshes
Significance of the differentia-bility properties
Triangular elements with complete polyno-mials
Remarks on Cl elements
Bilinear elements
Quadratic rectangular elements
Affine families
Choiceof an element
Problems
6. Approximation Properties
The Bramble-Hilbert lemma
Triangular elements with com-plete polynomials
Bilinear quadrilateral elements
In-verse estimates
Clement's interpolation
Appendix: On the optimality of the estimates
Problems
7. Error Bounds for Elliptic Problems of Second Order
Remarks on regularity
Error bounds in the energy normL2 estimates
A simple Loo estimate
The L2-projector
Problems
8. Computational Considerations
Assembling the stiffness matrix
Static condensation
Complexity of setting up the matrix
Effect on the choice of a grid
Local mesh refinement
Implementation of the Neumann boundary-value problem
Problems

Chapter Ⅲ Nonconforming and Other Methods
1. Abstract Lemmas and a Simple Boundary Approximation Generalizations of Cea's lemma
Duality methods
The Crouzeix-Raviart element
A simple approximation to curved boundaries
Modifications of the duality argument
Problems
2. Isoparametric Elements
Isoparametric triangular elements
Isoparametric quadrilateral elements
Problems
3. Further Tools from Functional Analysis
Negative norms
Adjoint operators
An abstract exis- tence theorem
An abstract convergence theorem
Proof of Theorem 3.4
Problems
4. Saddle Point Problems
Saddle points and minima
The inf-sup condition
Mixed finite element methods
Fortin interpolation
……
Chapter Ⅳ The Conjugate Gradient Method
Chapter Ⅴ Multigrid Methods
Chapter Ⅵ Finite Elements in Solid Mechanics

前言/序言

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The discussion of saddle point problems is a lughlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena.

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分析单元的力学性质

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分析单元的力学性质

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The discussion of saddle point problems is a lughlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena.

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很有学习价值，有限元的学习者必备

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根据单元的材料性质、形状、尺寸、节点数目、位置及其含义等，找出单元节点力和节点位移的关系式，这是单元分析中的关键一步。此时需要应用弹性力学中的几何方程和物理方程来建立力和位移的方程式，从而导出单元刚度矩阵，这是有限元法的基本步骤之一。

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物体离散化后，假定力是通过节点从一个单元传递到另一个单元。但是，对于实际的连续体，力是从单元的公共边传递到另一个单元中去的。因而，这种作用在单元边界上的表面力、体积力和集中力都需要等效的移到节点上去，也就是用等效的节点力来代替所有作用在单元上的力。

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这个不要买

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