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Advanced Finite Element Method in Structural Engineering

:	Yu-Qiu Long, Song Cen, Zhi-Fei Long
:	Advanced Finite Element Method in Structural Engineering
:	Springer-Verlag
:	9783642003165
:	1
:	CHF 172.60
:

:	Maschinenbau, Fertigungstechnik
:	English

:	706
:	DRM
:	PC/MAC/eReader/Tablet
:	PDF

Ad anced 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.

	Contents	10
	Chapter 1 Introduction— The Evolutive Finite Element Method	16
	1.1 Brief Review of the Features of Finite Element Method	16
	1.2 1.2 Finite Element Method and Variational Principles	18
	1.3 1.3 Research Areas of FEM	20
	1.4 1.4 Advances in FEM and Outline of This Book	21
	References	24
	Chapter 2 The Sub-Region Variational Principles	28
	2.1 Introduction	28
	2.2 2.2 The Sub-Region Variational Principle for Elasticity	29
	2.3 2.3 The Sub-Region Variational Principle for Elastic Thin Plate	41
	2.4 2.4 The Sub-Region Variational Principle for Elastic Thick Plate	53
	2.5 2.5 The Sub-Region Variational Principle for Elastic Shallow Shell	64
	2.6 2.6 The Sub-Region Mixed Energy Partial Derivative Theorem	71
	References	77
	Chapter 3 Variational Principles with Several Adjustable Parameters	79
	3.1 3.1 Introduction	79
	3.2 3.2 Several Patterns of Functional Transformation	80
	3.3 3.3 Generalized Variational Principle Involving Several Adjustable Parameters	88
	u	89
	u	89
	u	91
	u	91
	u,	93
	u,	93
	u,	93
	3.4 3.4 Variable-Substitution-Multiplier Method	96
	References	98
	Chapter 4 Generalized Conforming Element Theory	100
	4.1 4.1 Introduction	100
	4.2 4.2 Conforming and Nonconforming Elements— Some Consideration about “ Conforming”	101
	4.3 4.3 The First Pattern of Generalized Conforming Element — Replacing Nodal Conforming by Line Conforming Conditions	102
	4.4 4.4 The Variational Basis of Generalized Conforming Element— Duality	105
	4.5 4.5 The Synthesis of Energy Method and Weighted Residual Method— Flexibility	108
	4.6 4.6 The Convergence of Generalized Conforming Element	110
	References	110
	Chapter 5 Generalized Conforming Thin Plate Element Element — Introduction	112
	5.1 5.1 Introduction	112
	5.2 5.2 The Generalized Conforming Conditions and Their Equivalent Forms for Thin Plate Elements	113
	5.3 5.3 General Formulations of the Generalized Conforming Thin Plate Elements	116
	5.4 5.4 Several Construction Schemes of the Generalized Conforming Thin Plate Elements	118
	5.5 5.5 A Collection of the Recent Generalized Conforming Thin Plate Elements Elements Elements Elements	122
	References	129
	Chapter 6 Generalized Conforming Thin Plate Element Element — Line- Point and SemiLoof Conforming Schemes	131
	6.1 6.1 Line Conforming Scheme— Elements TGC-9 and TGC- 9- 1	131
	6.2 6.2 Line-Point Conforming Scheme— Rectangular Elements	141
	6.3 6.3 Line-Point Conforming Scheme—Triangular Elements	157
	6.4 6.4 Super-Basis Line-Point Conforming Scheme— Elements GC GC - R12 and GC GC - T9	166
	6.5 6.5 Super-Basis Point Conforming Scheme— Elements MB1- T9 and MB2- T9	175
	6.6 6.6 SemiLoof Conforming Scheme	178
	References	185
	Chapter 7 Generalized Conforming Thin Plate Element Element — Perimeter- Point and Least- Square Conforming Schemes	187
	7.1 7.1 Perimeter-Point Conforming Scheme— Elements LR12- 1 and LR12- 2	187
	7.2 7.2 The Application of Perimeter Conforming Conditions — Verification for the Convergence of the Element ACM	192
	7.3 7.3 Super-Basis Perimeter-Point Conforming Scheme — Verification and Improvement of the Element BCIZ	198
	7.4 7.4 Least-Square Scheme— Elements LSGC-R12 and LSGC- T9	209
	References	213
	Chapter 8 Generalized Conforming Thick Plate Element	214
	8.1 8.1 Summary of the Thick Plate Theory	214
	8.2 8.2 Comparison of the Theories for Thick Plates and Thin Plates	226
	8.3 Thick/Thin Beam Element	243
	8.4 Review of Displacement-based Thick/Thin Plate Elements	246
	8.5 Generalized Conforming Thick/Thin Plate Elements (1)	248
	— Starting with Assuming (	248
	,	248
	)	248
	8.6 Generalized Conforming Thick/ Thin Plate Elements (2)	260
	— Starting with Assuming (w,	260
	) )	260
	8.7 Generalized Conforming Thin/Thick Plate Elements — From Thin to Thick Plate Elements	271
	References	277
	Chap