Advanced finite element method in structural engineering （新型有限元论 : 结构工程中的高等有限元方法
发布日期:2009-06-23 浏览次
【内容简介】本书是在中文专著《新型有限元沦》(2004年版)的基础上补充了2004年于2008年期间的新成果所撰写的英文专著，是龙驭球院士、岑松博士和龙志飞教授及具研究组多年来在新型有限元方面研究成果的系统论述。全书分为20章。除首尾两章外，其余18章分为3篇：第1篇是变分原理进展，介绍分区和含参变分原理2项成果；它们为构造新型有限元起到理论指导作用。第2篇是有限元法进展初论，重点介绍广义协调元；这是在协调元与非协调元之间另辟的新路，使协调问题和收敛问题得到合理解决，单元构造方案可以灵活优选，学科内容得到充实更新；广义协调元是新型有限元方面的主要成果，在《新型有限元论:结构工程中的高等有限元方法》中起核心作用。第3篇是有限元法进展续论，补充介绍4项成果，包括分区混合元法、解析试函数法、第一和第二类四边形面积坐标法和样条函数有限元法，在《新型有限元论:结构工程中的高等有限元方法》中起锦上添花作用。木书还结合7项成果的论述，介绍了总共108个相关的新单元。
《新型有限元论:结构工程中的高等有限元方法》可作为高等学校力学、土木、机械等专业研究生和高年级本科生的教材和参考书，也可供相关领域教师和科技人员参考。
【目次】Chapter 1 Introduction??The Evolutive Finite Element Method.
1.1 Brief Review of the Features of Finite Element Method
1.2 Finite Element Method and Variational Principles
1.3 Research Areas of FEM
1.4 Advances in FEM and Outline of This Book
References
PART I Advances in Variational Principles
Chapter 2 The Sub-Region Variational Principles
2.1 Introduction
2.2 The Sub-Region Variational Principle for Elasticity
2.3 The Sub-Region Variational Principle for Elastic Thin Plate
2.4 The Sub-Region Variational Principle for Elastic Thick Plate
2.5 The Sub-Region Variational Principle for Elastic Shallow Shell
2.6 The Sub-Region Mixed Energy Partial Derivative Theorem
References
Chapter 3 Variational Principles with Several Adjustable Parameters
3.1 Introduction
3.2 Several Patterns of Functional Transformation
3.3 Generalized Variational Principle Involving Several Adjustable
Parameters
3.4 Variable-Substitution-Multiplier Method
References
PART II Advances in Finite Element Method-
Generalized Conforming Elements
Chapter 4 Generalized Conforming Element Theory
4.1 Introduction
4.2 Conforming and Nonconforming Elements??Some Consideration
about "Conforming"
4.3 The First Pattern of Generalized Conforming Element??Replacing
Nodal Conforming by Line Conforming Conditions
4.4 The Variational Basis of Generalized Conforming Element??Duality
4.5 The Synthesis of Energy Method and Weighted Residual Method??Flexibility
4.6 The Convergence of Generalized Conforming Element
References
Chapter 5 Generalized Conforming Thin Plate Element I?? Introduction
5.1 Introduction
5.2 The Generalized Conforming Conditions and Their Equivalent
Forms for Thin Plate Elements
5.3 General Formulations of the Generalized Conforming Thin Plate
Elements
5.4 Several Construction Schemes of the Generalized Conforming
Thin Plate Elements
5.5 A Collection of the Recent Generalized Conforming Thin Plate
Elements
References
Chapter 6 Generalized Conforming Thin Plate Element II??Line-Point and SemiLoof Conforming Schemes
6.1 Line Conforming Scheme??Elements TGC-9 and TGC-9-1
6.2 Line-Point Conforming Scheme??Rectangular Elements
6.3 Line-Point Conforming Scheme??Triangular Elements
6.4 Super-Basis Line-Point Conforming Scheme??Elements GCIII-R12 and GCIII-T9
6.5 Super-Basis Point Conforming Scheme??Elements MB1-T9 and MB2-T9
6.6 SemiLoof Conforming Scheme
References
Chapter 7 Generalized Conforming Thin Plate Element III??Perimeter-Point and Least-Square Conforming Schemes,
7.1 Perimeter-Point Conforming Scheme??Elements LR12-1
and LR12-2
7.2 The Application of Perimeter Conforming Conditions??Verification
for the Convergence of the Element ACM
7.3 Super-Basis Perimeter-Point Conforming Scheme??Verification and
Improvement of the Element BCIZ
7.4 Least-square Scheme??Elements LSGC-R12 and LSGC-T9
References
Chapter 8 Generalized Conforming Thick Plate Element
8.1 Summary of the Thick Plate Theory
8.2 Comparison of the Theories for Thick Plates and Thin Plates
8.3 Thick/Thin Beam Element
8.4 Review of Displacement-based Thick/Thin Plate Elements
8.5 Generalized Conforming Thick/Thin Plate Elements (1)??Starting with Assuming (ψ,γ)
8.6 Generalized Conforming Thick/Thin Plate Elements (2)??Starting with Assuming (w,γ)
8.7 Generalized Conforming Thin/Thick Plate Elements??From Thin to Thick Plate Elements
References
Chapter 9 Generalized Conforming Element for the Analysis of the Laminated Composite Plates
9.1 Introduction
9.2 Fundamental Theory
9.3 New Element CTMQ20 for the Analysis of Laminated
Composite Plates
9.4 The Hybrid-Enhanced Post-Processing Procedure for Element
Stresses
9.5 Vibration Analysis of Laminated Composite Plates
9.6 Numerical Examples
References
Chapter 10 Generalized Conforming Element for the Analysis of
Piezoelectric Laminated Composite Plates
10.1 Introduction
10.2 The First-Order Shear Deformation Theory of Piezoelectric
Laminated Composite Plate
10.3 New Piezoelectric Laminated Composite Plate Element CTMQE
10.4 The "Partial Hybrid"-Enhanced Post-Processing Procedure for Element Stresses
10.5 Numerical Examples
References
Chapter 11 Generalized Conforming Membrane and Shell Elements
11.1 Introduction
11.2 Generalized Conforming Isoparametric Membrane Element
11.3 Membrane Elements with Drilling Freedoms??Definition of the
Drilling Freedom and the Corresponding Rectangular and
Quadrilateral Elements
11.4 Membrane Elements with Drilling Freedoms??Triangular Elements
11.5 Flat-Shell Elements??Triangular Thick/Thin Shell Element..
GMST 18
11.6 Shallow Shell Element??Variational Principle and Membrane
Locking Problem
11.7 Shallow Shell Element??Triangular Element SST21 with
Mid-Side Nodes
11.8 Shell Element for Geometrically Nonlinear Analysis??Triangular Flat-Shell Element GMST 18
11.9 Shell Element for Geometrically Nonlinear Analysis??Rectangular Shallow Shell Element SSR28
References
PART HI Other Advances in Finite Element Method
Chapter 12 Sub-Region Mixed Element I??Fundamental Theory
and Crack Problem
12.1 Review of the Sub-Region Mixed Element Method
12.2 Basic Equations of the Sub-Region Mixed Element Method
12.3 2D Crack Problem
12.4 Cracked Thick Plate Problem
12.5 Surface Crack Problem in a 3D Body
References
Chapter 13 Sub-Region Mixed Element II??V-Notch Problem
13.1 Introduction
13.2 Plane V-Notch Problem
13.3 Plane V-Notch Problem in a Bi-Material
13.4 Anti-Plane V-Notch Problem in a Bi-Material
13.5 V-Notch Problem in Reissner Plate
13.6 3D V-Notch Problem
References
Chapter 14 Analytical Trial Function Method I??Membrane and
Plate Bending Elements,
14.1 Recognition of the Analytical Trial Function Method
14.2 4-Node Membrane Elements Based on the Analytical Trial
Function Method
14.3 Avoiding Trapezoidal Locking Phenomenon by ATF Elements,
14.4 The Basic Analytical Solutions of the Thick Plate Theory and
ATF Elements Free of Shear Locking
14.5 Development of Quadrilateral Thin-Thick Plate Element Based
on the Analytical Trial Function Method
14.6 Analytical Trial Function Method for Developing a Triangular
Thick Plate Element Based on a Thin Plate Element
References
Chapter 15 Analytical Trial Function Method II?? Singular Elements
with Crack and Notch
15.1 Introduction
15.2 The Basic Analytical Solutions of the Plane Crack Problem
15.3 Element ATF-MS with Crack Formulated by the Analytical
Trial Function Method
15.4 Error Analysis of Element ATF-MS with Crack.
15.5 Analysis of Zero Energy Mode in Element and in Structural
System
15.6 The Basic Analytical Solutions of the Plane Notch Problem
15.7 Element ATF-VN with Notch Formulated by the Analytical
Trial Function Method
15.8 Error Analysis of Element ATF-VN with Notch
References
Chapter 16 QuadrilateralArea Coordinate Systems, Part I??Theory and Formulae
16.1 Introduction
16.2 The Isoparametric Coordinate Method and the Area Coordinate
Method
16.3 Two Shape Characteristic Parameters of a Quadrilateral
16.4 The Definition of Quadrilateral Area Coordinates (QACM-I)
16.5 Two Identical Relations Among Area Coordinates (QACM-I)
16.6 Transformation Relations Between theArea Coordinate System
(QACM-I) and the Cartesian or Isoparametric Coordinate System
16.7 Differential Formulae (QACM-I)
16.8 Integral ……
【关闭】
新书报道