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

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

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

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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

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

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

评分☆☆☆☆☆

有限元法（FEA，Finite Element Analysis）的基本概念是用较简单的问题代替复有限元分析（FEA，Finite Element Analysis）利用数学近似的方法对真实物理系统（几何和载荷工况）进行模拟。还利用简单而又相互作用的元素，即单元，就可以用有限数量的未知量去逼近无限未知量的真实系统。杂问题后再求解。它将求解域看成是由许多称为有限元的小的互连子域组成，对每一单元假定一个合适的(较简单的）近似解，然后推导求解这个域总的满足条件(如结构的平衡条件），从而得到问题的解。这个解不是准确解，而是近似解，因为实际问题被较简单的问题所代替。由于大多数实际问题难以得到准确解，而有限元不仅计算精度高，而且能适应各种复杂形状，因而成为行之有效的工程分析手段。选择位移模式

评分☆☆☆☆☆

还没看，不错吧！

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

质量不错，价格优惠！

评分☆☆☆☆☆

不错，慢慢学习

评分☆☆☆☆☆

在有限单元法中，选择节点位移作为基本未知量时称为位移法；选择节点力作为基本未知量时称为力法；取一部分节点力和一部分节点位移作为基本未知量时称为混合法。位移法易于实现计算自动化，所以，在有限单元法中位移法应用范围最广。

评分☆☆☆☆☆

语言优美清晰，较适合作为有限元理论的入门书籍

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金典好书

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