教学经典教材：有限元（第3版） [Finite Elements:Theory,Fast Solvers,and Application in Solid Mechanics] 下载 mobi epub pdf 电子书 2024

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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.

内页插图

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

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

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没看呢呵呵

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当采用位移法时，物体或结构物离散化之后，就可把单元总的一些物理量如位移，应变和应力等由节点位移来表示。这时可以对单元中位移的分布采用一些能逼近原函数的近似函数予以描述。通常，有限元法我们就将位移表示为坐标变量的简单函数。这种函数称为位移模式或位移函数。

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京东好烦啊、不让我领自营图书券！！

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分析单元的力学性质

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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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金典好书

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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.

评分☆☆☆☆☆

当采用位移法时，物体或结构物离散化之后，就可把单元总的一些物理量如位移，应变和应力等由节点位移来表示。这时可以对单元中位移的分布采用一些能逼近原函数的近似函数予以描述。通常，有限元法我们就将位移表示为坐标变量的简单函数。这种函数称为位移模式或位移函数。

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英语书籍，定价49:00元，有点偏高。专业性很强的书籍，适合计算数学有限元方向的读者学习。可以当作研究生教材

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