Advanced finite element method in structural engineering [electronic resource] / Yu-Qiu Long ; Song Cen ; Zhi-Fei Long.
Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Confo...
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Beijing : Berlin ; New York :
Tsinghua University Press ; Springer,
©2009.
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Table of Contents:
- 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 Shell2.6 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 Elements5.4 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-T96.6 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.