0. 1 Key points and characteristics of finite element method

0.2 Development, Present Situation and Future of Finite Element Method 5

0.3 Overview of this book 9

Chapter 65438 +0 Basic Part

Chapter 1 theoretical basis of finite element method-weighted residual method and variational principle 13

1. 1 introduction 13

Equivalent integral form of 1.2 differential equation and weighted residual method 14

1.3 variational principle and ritz method 28

1.4 basic equations and variational principles of elasticity 36

1.5 Summary 5 1

Review question 52

Exercise 53

The second chapter is about the general principle and expression format of finite element method for elastic mechanics, page 55.

2. 1 Introduction 55

2.2 Finite Element Scheme for Plane Problems of Elasticity 56

2.3 General format of generalized coordinate finite element method 77

2.4 Properties and convergence criteria of finite element solutions 82

2.5 Finite Element Scheme for Axisymmetric Problems 85

2.6 Summary 93

Review question 94

Exercise 95

Chapter III Construction of Unit and Interpolation Function 98

3. 1 Introduction 98

3.2 One-dimensional cell 10 1

3.3 2D element 105

3.4 3D element 1 17

3.5-order spectral unit 122

3.6 Summary 127

Review questions 128

Exercise 129

The fourth chapter isoparametric element and numerical integration 130

4. 1 Introduction 130

4.2 The concept of isoparametric transformation and transformation of cell matrix 13 1

4.3 isoparametric transformation and isoparametric convergence conditions 136

4.4 General format of isoparametric elements used to analyze elastic mechanics problems 140

4.5 numerical integration method 143

4.6 Selection of numerical integration order in isoparametric element calculation 153

4.7 Summary 159

Review questions 160

Exercise 160

Chapter 5 Some practical considerations in the application of finite element method.

5. 1 Introduction 162

5.2 Establishment of finite element model 163

5.3 Nature and Treatment of Stress Calculation Results 167

5.4 substructure method 186

5.5 Utilization of structural symmetry and periodicity 192

5.6 Inspection of Unqualified Components and Sections 209

5.7 Summary 2 17

Review question 2 18

Exercise 2 19

Chapter VI Solutions of Linear Algebraic Equations 22 1

6. 1 Introduction 22 1

6.2 Gauss Elimination Method and Its Variant 222

6.3 Direct solution of banded coefficient matrix 23 1

6.4 Direct solution using external memory 237

6.5 Iterative solution 240

6.6 Summary 250

Review question 25 1

Exercise 252

Chapter 7 Finite Element Analysis Computer Program 254

7. 1 Introduction 254

7.2 finite element analysis main program 256

7.3 Pretreatment Procedure 263

7.4 Post-processing program 266

7.5 Technical Development of Finite Element Software 267

Exercise 268

The second part of the topic

Chapter 8 Further Foundation of Finite Element Method-Constrained Variational Principle 27 1

8. 1 Introduction 27 1

8.2 Constrained Variational Principle 272

8.3 generalized variational principle of elasticity 28 1

8.4 Modified Variational Principle of Elasticity 286

8.5 Finite Element Method for Incompressible (or Almost Incompressible) Elastic Mechanics Problems 289

8.6 Summary 298

Review question 299

Exercise 300

Chapter 9 Mechanical Problems of Bar Structure 302

9. 1 Introduction to Structural Units 302

9.2 Equal-section straight beam device 306

9.3 Plane Bar System 323

9.4 Space bar system 329

9.5 Summary 33 1

Review question 332

Exercise 333

Chapter 10 plate bending problem 334

10. 1 Introduction 334

10.2 nonconforming plate element based on thin plate theory 338

10.3 Coordination plate unit 348 based on thin plate theory

10.4 indlin plate element (plate element with independent interpolation of displacement and rotation) 352

10.5 thin plate element 364 based on discrete Kirchhoff theory (DKT)

10.6 stress mixed plate element 367

10.7 Summary 375

Review question 376

Exercise 377

Chapter 1 1 shell problem 378

1 1. 1 Introduction 378

1 1.2 axisymmetric shell element based on thin shell theory 38 1

1 1.3 axisymmetric shell element 389, independent interpolation of displacement and rotation

1 1.4 The planar shell unit 398 is a general shell.

1 1.5 hyperparametric shell element 406 is used for general shells.

1 1.6 shell element with relative freedom of 4 15.

1 1.7 Connection between shell unit and solid unit 4 18

1 1.8 Connection between shell element and beam element 430

1 1.9 Summary 437

Review question 438.

Exercise 439

Chapter 12 heat conduction problem 44 1

12. 1 introduction 44 1

12.2 steady-state heat conduction problem 444

12.3 transient heat conduction problem 447

12.4 thermal stress calculation 6 1

12.5 Summary 464

Review question 465

Exercise 466

Chapter 13 Dynamics problem 468

13. 1 Introduction 468

13.2 mass matrix and damping matrix 472

13.3 direct integration method 476

13.4 mode superposition method 484

Stability of the solution of 13.5 49 1

Solution of 13.6 large-scale eigenvalue problem5666/kloc-0 /5666.000000000605

13.7 methods to reduce the degree of freedom of the system 09

13.8 Summary 5 18

Review question 5 19

Exercise 520

14 chapter fluid-solid coupling problem 523

14. 1 Introduction

Basic equation and expression 524 of 14.2 inviscid small disturbance flow

14.3 (ui, p) Finite Element Analysis Format of Fluid-Structure Coupling System 527

On the dynamic characteristics of 14.4 fluid-solid coupling system56666/kloc-0 /4666.66666666666866

14.5 dynamic response analysis of fluid-solid coupling system 37

14.6 Summary 543

Review question 544.

Exercise 544

Chapter 15 Material nonlinear problem 545

1 Introduction 545

Solution of 15.2 nonlinear equations

Elasto-plastic constitutive relation of 15.3 material

15.4 elastoplastic incremental finite element analysis (FEA) 576

Some problems in the numerical method of 15.5 elastic-plastic incremental analysis56666/kloc-0 /5666686686

15.6 total amount of elastic-plastic finite element analysis50000.000000000505

Thermoelastic-plastic creep finite element analysis 600

15.8 Summary 6 13

Review question 6 14

Exercise 6 15

Chapter 16 Geometric nonlinear problem 6 17

16. 1 Introduction

16.2 measurement of strain and stress under large deformation conditions

16.3 expression format of geometrically nonlinear problem 624

16.4 finite element solution equation and solution 629

16.5 Constitutive relation under the condition of large deformation 642

16.6 structural stability and buckling problems

16.7 Example 654

16.8 Summary 659

Review question 66 1

Exercise 662

Chapter 17 Contact and collision problems 666

1 Introduction 666

17.2 contact interface conditions 667

17.3 contact problem solution 67 1

The finite element equation of 17.4 contact problem 678

17.5 method for solving finite element equation 685

17.6 several problems in connection analysis 69 1

17.7 Example 695

17.8 Summary 700

Review question 70 1

Exercise 702

Reference document 704

Master reference book 704

B. references to each chapter 704

Appendix A FEATP)7 1 1+0

A 1 finite element analysis main program source code 7 1 1

A2 preprocessor instruction 762