Long / Cen Advanced Finite Element Method in Structural Engineering

1. Auflage 2009
ISBN: 978-3-642-00316-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 706 Seiten

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 Conforming Element method, to name one -  and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.

Mr. Yu-Qiu Long is Professor in the Department of Civil Engineering at Tsinghua University, and a member of the Chinese Academy of Engineering. His research is mainly in structural mechanics, shell structures, finite element method and variational principles. He has published 21 books and 235 papers, which have been cited more than 2000 times. To date, he has obtained 22 awards, at the national and provincial levels, for his achievements.

Dr. Song Cen is Associate Professor in the School of Aerospace at Tsinghua University,  a Chinese Association of Computational Mechanics committee member, and a member of the International Association for Computational Mechanics. His research is mainly in computational solid mechanics and structural engineering. He has won several awards for his research work, including the Nationwide Excellent Doctoral Dissertation Award and The Young Researcher Fellowship Award, awarded by the First M.I.T. Conference on Computational Fluid and Solid Mechanics.

Autoren/Hrsg.

Long, Yu-Qiu

Cen, Song

Long, Zhi-Fei

Inhaltsverzeichnis

1;Contents;10
2;Chapter 1 Introduction— The Evolutive Finite Element Method;16
2.1;1.1 Brief Review of the Features of Finite Element Method;16
2.2;1.2 1.2 Finite Element Method and Variational Principles;18
2.3;1.3 1.3 Research Areas of FEM;20
2.4;1.4 1.4 Advances in FEM and Outline of This Book;21
2.5;References;24
3;Chapter 2 The Sub-Region Variational Principles;28
3.1;2.1 Introduction;28
3.2;2.2 2.2 The Sub-Region Variational Principle for Elasticity;29
3.3;2.3 2.3 The Sub-Region Variational Principle for Elastic Thin Plate;41
3.4;2.4 2.4 The Sub-Region Variational Principle for Elastic Thick Plate;53
3.5;2.5 2.5 The Sub-Region Variational Principle for Elastic Shallow Shell;64
3.6;2.6 2.6 The Sub-Region Mixed Energy Partial Derivative Theorem;71
3.7;References;77
4;Chapter 3 Variational Principles with Several Adjustable Parameters;79
4.1;3.1 3.1 Introduction;79
4.2;3.2 3.2 Several Patterns of Functional Transformation;80
4.3;3.3 3.3 Generalized Variational Principle Involving Several Adjustable Parameters;88
4.4;u;89
4.5;u;89
4.6;u;91
4.7;u;91
4.8;u,;93
4.9;u,;93
4.10;u,;93
4.11;3.4 3.4 Variable-Substitution-Multiplier Method;96
4.12;References;98
5;Chapter 4 Generalized Conforming Element Theory;100
5.1;4.1 4.1 Introduction;100
5.2;4.2 4.2 Conforming and Nonconforming Elements— Some Consideration about “ Conforming”;101
5.3;4.3 4.3 The First Pattern of Generalized Conforming Element — Replacing Nodal Conforming by Line Conforming Conditions;102
5.4;4.4 4.4 The Variational Basis of Generalized Conforming Element— Duality;105
5.5;4.5 4.5 The Synthesis of Energy Method and Weighted Residual Method— Flexibility;108
5.6;4.6 4.6 The Convergence of Generalized Conforming Element;110
5.7;References;110
6;Chapter 5 Generalized Conforming Thin Plate Element Element — Introduction;112
6.1;5.1 5.1 Introduction;112
6.2;5.2 5.2 The Generalized Conforming Conditions and Their Equivalent Forms for Thin Plate Elements;113
6.3;5.3 5.3 General Formulations of the Generalized Conforming Thin Plate Elements;116
6.4;5.4 5.4 Several Construction Schemes of the Generalized Conforming Thin Plate Elements;118
6.5;5.5 5.5 A Collection of the Recent Generalized Conforming Thin Plate Elements Elements Elements Elements;122
6.6;References;129
7;Chapter 6 Generalized Conforming Thin Plate Element Element — Line- Point and SemiLoof Conforming Schemes;131
7.1;6.1 6.1 Line Conforming Scheme— Elements TGC-9 and TGC- 9- 1;131
7.2;6.2 6.2 Line-Point Conforming Scheme— Rectangular Elements;141
7.3;6.3 6.3 Line-Point Conforming Scheme—Triangular Elements;157
7.4;6.4 6.4 Super-Basis Line-Point Conforming Scheme— Elements GC GC - R12 and GC GC - T9;166
7.5;6.5 6.5 Super-Basis Point Conforming Scheme— Elements MB1- T9 and MB2- T9;175
7.6;6.6 6.6 SemiLoof Conforming Scheme;178
7.7;References;185
8;Chapter 7 Generalized Conforming Thin Plate Element Element — Perimeter- Point and Least- Square Conforming Schemes;187
8.1;7.1 7.1 Perimeter-Point Conforming Scheme— Elements LR12- 1 and LR12- 2;187
8.2;7.2 7.2 The Application of Perimeter Conforming Conditions — Verification for the Convergence of the Element ACM;192
8.3;7.3 7.3 Super-Basis Perimeter-Point Conforming Scheme — Verification and Improvement of the Element BCIZ;198
8.4;7.4 7.4 Least-Square Scheme— Elements LSGC-R12 and LSGC- T9;209
8.5;References;213
9;Chapter 8 Generalized Conforming Thick Plate Element;214
9.1;8.1 8.1 Summary of the Thick Plate Theory;214
9.2;8.2 8.2 Comparison of the Theories for Thick Plates and Thin Plates;226
9.3;8.3 Thick/Thin Beam Element;243
9.4;8.4 Review of Displacement-based Thick/Thin Plate Elements;246
9.5;8.5 Generalized Conforming Thick/Thin Plate Elements (1);248
9.6;— Starting with Assuming (;248
9.7;,;248
9.8;);248
9.9;8.6 Generalized Conforming Thick/ Thin Plate Elements (2);260
9.10;— Starting with Assuming (w,;260
9.11;) );260
9.12;8.7 Generalized Conforming Thin/Thick Plate Elements — From Thin to Thick Plate Elements;271
9.13;References;277
10;Chapter 9 Generalized Conforming Element for the Analysis of the Laminated Composite Plates;279
10.1;9.1 Introduction;279
10.2;9.2 Fundamental Theory;281
10.3;9.3 New Element CTMQ20 for the Analysis of Laminated Composite Plates;286
10.4;9.4 The Hybrid-Enhanced Post-Processing Procedure for Element Stresses;297
10.5;9.5 Vibration Analysis of Laminated Composite Plates;301
10.6;9.6 Numerical Examples;303
10.7;References;312
11;Chapter 10 Generalized Conforming Element for the Analysis of Piezoelectric Laminated Composite Plates;315
11.1;10.1 Introduction;315
11.2;10.2 The First-Order Shear Deformation Theory of Piezoelectric Laminated Composite Plate;317
11.3;10.3 New Piezoelectric Laminated Composite Plate Element CTMQE;320
11.4;10.4 The “Partial Hybrid”-Enhanced Post-Processing Procedure for Element Stresses;325
11.5;10.5 Numerical Examples;329
11.6;References;334
12;Chapter 11 Generalized Conforming Membrane and Shell Elements;336
12.1;11.1 Introduction;336
12.2;11.2 Generalized Conforming Isoparametric Membrane Element;337
12.3;11.3 Membrane Elements with Drilling Freedoms— Definition of the Drilling Freedom and the Corres-ponding Rectangular and Quadrilateral Elements;345
12.4;11.4 Membrane Elements with Drilling Freedoms — Triangular Elements;357
12.5;11.5 Flat-Shell Elements— Triangular Thick/ Thin Shell Element GMST18;368
12.6;11.6 Shallow Shell Element— Variational Principle and Membrane Locking Problem;381
12.7;11.7 Shallow Shell Element—Triangular Element SST21 with Mid- Side Nodes;386
12.8;11.8 Shell Element for Geometrically Nonlinear Analysis — Triangular Flat- Shell Element GMST18;393
12.9;11.9 Shell Element for Geometrically Nonlinear Analysis — Rectangular Shallow Shell Element SSR28;397
12.10;References;409
13;Chapter 12 Sub-Region Mixed Element Element — Fundamental Theory and Crack Problem;414
13.1;12.1 Review of the Sub-Region Mixed Element Method;414
13.2;12.2 Basic Equations of the Sub-Region Mixed Element Method;417
13.3;12.3 2D Crack Problem;420
13.4;12.4 Cracked Thick Plate Problem;427
13.5;12.5 Surface Crack Problem in a 3D Body;435
13.6;References;444
14;Chapter 13 Sub- Region Mixed Element Element — V- Notch Problem;447
14.1;13.1 Introduction;447
14.2;13.2 Plane V-Notch Problem;447
14.3;13.3 Plane V-Notch Problem in a Bi-Material;459
14.4;13.4 Anti-Plane V-Notch Problem in a Bi-Material;466
14.5;13.5 V-Notch Problem in Reissner Plate;472
14.6;13.6 3D V-Notch Problem;490
14.7;References;502
15;Chapter 14 Analytical Trial Function Method Method — Membrane and Plate Bending Elements;504
15.1;14.1 Recognition of the Analytical Trial Function Method;504
15.2;14.2 4-Node Membrane Elements Based on the Analytical Trial Function Method;507
15.3;14.3 Avoiding Trapezoidal Locking Phenomenon by ATF Elements;509
15.4;14.4 The Basic Analytical Solutions of;513
15.5;the Thick Plate;513
15.6;Theory and ATF Elements;513
15.7;Free;513
15.8;of Shear Locking;513
15.9;14.5 Development of Quadrilateral Thin-Thick Plate Element Based on the Analytical Trial Function Method;515
15.10;14.6 Analytical Trial Function Method for Developing a Triangular Thick Plate Element Based on a Thin Plate Element;519
15.11;References;525
16;Chapter 15 Analytical Trial Function Method Method — Singular Elements with Crack and Notch;527
16.1;15.1 Introduction;527
16.2;15.2 The Basic Analytical Solutions of the Plane Crack Problem;528
16.3;15.3 Element ATF-MS with Crack Formulated by the Analytical Trial Function Method;532
16.4;15.4 Error Analysis of Element ATF-MS with Crack;534
16.5;15.5 Analysis of Zero Energy Mode in Element and in Structural System;538
16.6;15.6 The Basic Analytical Solutions of the Plane Notch Problem;544
16.7;15.7 Element ATF-VN with Notch Formulated by the Analytical Trial Function Method;547
16.8;15.8 Error Analysis of Element ATF-VN with Notch;551
16.9;References;554
17;Chapter 16 Quadrilateral Area Coordinate Systems, Part Part — Theory and Formulae;555
17.1;16.1 Introduction;555
17.2;16.2 The Isoparametric Coordinate Method and the Area Coordinate Method;556
17.3;16.3 Two Shape Characteristic Parameters of a Quadrilateral;558
17.4;16.4 The Definition of Quadrilateral Area Coordinates ( QACM- QACM- );562
17.5;16.5 Two Identical Relations Among Area Coordinates ( QACM- QACM- );565
17.6;16.6 Transformation Relations Between the Area Coordinate System ( QACM- QACM- ) and the Cartesian or Isoparametric Coordinate System;567
17.7;16.7 Differential Formulae (QACM- QACM- );569
17.8;16.8 Integral Formulae (QACM- QACM- );571
17.9;16.9 The Proof of the Basic Formulae (A) and (B) ( QACM- QACM- );574
17.10;16.10 The Proof of the Basic Formulae (C) (QACM- QACM- );578
17.11;16.11 The Quadrilateral Area Coordinate System with Only Two Components ( QACM- QACM- );579
17.12;References;589
18;Chapter 17 Quadrilateral Area Coordinate Systems, Part Part — New Tools for Constructing Quadrilateral Elements;591
18.1;17.1 Introduction;591
18.2;17.2 Sensitivity Analysis of Isoparametric Elements to Mesh Distortion;592
18.3;17.3 Brief Review of the Finite Element Models Formulated by Quadrilateral Area Coordinate Methods;595
18.4;17.4 4-Node Quadrilateral Membrane Elements Formulated by the Area Coordinate Method;598
18.5;17.5 Geometrically Nonlinear Analysis Using Element AGQ6- AGQ6-;610
18.6;17.6 Quadrilateral Membrane Elements with Drilling Degrees of Freedom Formulated by the Area Coordinate Method;615
18.7;17.7 8-Node Quadrilateral Membrane Elements Formulated by the Area Coordinate Method Method Method;622
18.8;17.8 Quadrilateral Thin Plate Element Formulated by the Area Coordinate Method;629
18.9;17.9 Quadrilateral Thick Plate Element Formulated by the Area Coordinate Method;637
18.10;17.10 Quadrilateral Laminated Composite Plate Element Formulated by the Area Coordinate Method;644
18.11;References;646
19;Chapter 18 Spline Element Element — Analysis of High- Rise Building Structures;650
19.1;18.1 Introduction;650
19.2;18.2 Spline Beam Elements;651
19.3;18.3 Spline Plane Membrane Elements;655
19.4;18.4 Analysis of Shear Wall Structures by Spline Elements;657
19.5;18.5 Analysis of Frame-Tube Structures by Spline Elements;664
19.6;References;670
20;Chapter 19 Spline Element Element — Analysis of Plate/ Shell Structures;672
20.1;19.1 Spline Elements for Thin Plate Bending;672
20.2;19.2 Spline Elements for Thick/Thin Beam and Plate;674
20.3;19.3 Spline Elements for Shallow Shell;679
20.4;19.4 Spline Elements for Thick/Thin Shell;681
20.5;19.5 Spline;690
20.6;Elements;690
20.7;for Geometrically Nonlinear;690
20.8;Analysis[;690
20.9;References;698
21;Chapter 20 Concluding Remarks;700
21.1;20.1 Seven New Achievements in the Finite Element Method;700
21.2;20.2 Five New Element Series with 108 New Element Models;702
21.3;20.3 New Solution Strategies for Five Challenging Problems;708
21.4;References;709
22;Appendix;712
22.1;A The equivalent equation of the functional stationary condition ( 2- 45);712
22.2;B The node conditions derived from the stationary condition ( 2- 77);713
22.3;C l;714
22.4;and;714
22.5;in Eq. (13-137);714
22.6;D;715
22.7;s;715
22.8;and t;715
22.9;in Eq. (13-144);715