LS-DYNA用户入门示例手册

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"Introductory Examples Manual for LS-DYNA® Users" 是一份针对LS-DYNA初学者的官方教程，提供了不同领域的基础指南。 LS-DYNA是一款强大的非线性动力学有限元分析软件，广泛应用于工程模拟，如碰撞、爆炸、流固耦合等问题。该软件以其高效的动态响应计算能力而闻名，可以处理复杂的几何形状、材料行为和接触问题。LS-DYNA的理论手册，如引用的07/24/19版(r:11261)，通常会深入探讨软件的数学模型、算法以及各种物理现象的模拟方法。本手册的目的是通过一系列示例，帮助用户理解和掌握LS-DYNA的基本用法。这些例子可能涵盖了结构力学、流体力学、热传导、材料行为（如塑性、弹性和粘性）、接触力学、以及耦合现象等多个方面。每个例子通常会包括问题描述、模型设置、输入文件详解、结果解释和后处理等步骤，旨在让学习者逐步了解如何建立和运行LS-DYNA模型。在学习过程中，用户将了解到如何定义网格、材料属性、边界条件和荷载，以及如何选择适当的求解器设置。此外，还会涉及LS-DYNA特有的功能，如自动接触检测、材料硬化模型、瞬态动力学分析等。对于每个示例，用户应尝试理解背后的物理原理，并学会如何通过调整参数来优化模拟结果。 LS-DYNA的用户界面，如LS-PrePost，是一个用于前处理和后处理的强大工具。通过它，用户可以创建、编辑和可视化几何模型，分配材料属性，设定边界条件，以及查看和分析模拟结果。掌握LS-PrePost的使用是充分利用LS-DYNA的关键。在实际应用中，LS-DYNA被广泛应用于汽车碰撞安全分析、航空航天结构分析、地质灾害模拟等领域。用户手册中的示例通常会从简单的问题开始，逐渐引入更复杂的情况，以便逐步提升用户的技能水平。最后，值得注意的是，LS-DYNA及相关产品（如LS-OPT和LS-PrePost）是Livermore Software Technology Corporation (LSTC)的注册商标，所有权归LSTC所有。软件受到多项美国专利的保护，这表明其在技术和知识产权上的独特地位。 "Introductory Examples Manual for LS-DYNA® Users"是入门LS-DYNA的宝贵资源，它通过实践案例帮助用户熟悉软件操作，理解非线性动力学模拟的基本概念和技术，从而在解决实际工程问题时能更加得心应手。

Table of Contents LS-DYNA Theory Manual

0-12 (Table of Contents) LS-DYNA Draft

27 Time Integration .................................................................................................................................. 27-1

27.1 Background......................................................................................................................... 27-1

27.2 The Central Difference Method ........................................................................................... 27-3

27.3 Stability of Central Difference Method ................................................................................ 27-3

27.4 Subcycling (Mixed Time Integration) .................................................................................. 27-5

28 Rigid Body Dynamics .......................................................................................................................... 28-1

28.1 Rigid Body Joints ................................................................................................................ 28-6

28.1.1 Penalty types ...................................................................................................... 28-6

28.1.2 Lagrange multiplier types ................................................................................... 28-8

28.2 Deformable to Rigid Material Switching ........................................................................... 28-11

28.3 Rigid Body Welds ............................................................................................................. 28-12

29 Contact-Impact Algorithm .................................................................................................................. 29-1

29.1 Introduction ......................................................................................................................... 29-1

29.2 Kinematic Constraint Method ............................................................................................. 29-1

29.3 Penalty Method ................................................................................................................... 29-2

29.4 Distributed Parameter Method ........................................................................................... 29-3

29.5 Preliminaries ........................................................................................................................ 29-4

29.6 Slave Search ....................................................................................................................... 29-5

29.7 Sliding With Closure and Separation .................................................................................. 29-9

29.7.1 Standard Penalty Formulation ............................................................................ 29-9

29.7.2 Soft Constraint Penalty Formulation ................................................................. 29-10

29.7.3 Segment-based Penalty Formulation ............................................................... 29-11

29.8 Recent Improvements in Surface-to-Surface Contact ..................................................... 29-11

29.8.1 Improvements to the Contact Searching.......................................................... 29-12

29.8.2 Accounting For the Shell Thickness ................................................................. 29-14

29.8.3 Initial Contact Interpenetrations ....................................................................... 29-15

29.8.4 Contact Energy Calculation .............................................................................. 29-16

29.8.5 Contact Damping .............................................................................................. 29-17

Friction ......................................................................................................................... 29-1 9

29.9 Tied Interfaces .................................................................................................................. 29-21

29.10 Strongly Objective Tied Contacts ................................................................................... 29-24

29.10.1 Kinematics ...................................................................................................... 29-26

29.10.2 Translational constraint................................................................................... 29-27

29.10.3 Bending and torsion constraint ...................................................................... 29-28

29.11 Sliding-Only Interfaces .................................................................................................... 29-28

29.12 Bucket Sorting ................................................................................................................ 29-2 9

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29.12.1 Bucket Sorting in TYPE 4 Single Surface Contact ......................................... 29-31

29.12.2 Bucket Sorting in Surface to Surface and TYPE 13 Single Surface Contact . 29-33

29.13 Single Surface Contact Algorithms in LS-DYNA ............................................................ 29-34

29.14 Surface to Surface Constraint Algorithm ........................................................................ 29-36

29.15 Planar Rigid Boundaries ................................................................................................. 29-40

29.16 Geometric Rigid Boundaries ........................................................................................... 29-41

29.17 VDA/IGES Contact .......................................................................................................... 29-42

29.18 Simulated Draw Beads ................................................................................................... 29-45

29.19 Edge to Edge Contact .................................................................................................... 29-48

29.20 Beam to Beam Contact .................................................................................................. 29-50

29.21 Mortar Contact ................................................................................................................ 29-52

29.21.1 Kinematics ...................................................................................................... 29-52

29.21.2 Constitutive relation ........................................................................................ 29-53

29.21.3 Contact nodal forces ...................................................................................... 29-54

29.21.4 Treatment of beams, sharp solid and shell edges ......................................... 29-54

29.21.5 Characteristic length and contact release ...................................................... 29-58

29.21.6 Outputs for debugging implicit models .......................................................... 29-59

29.21.7 Initial penetrations ........................................................................................... 29-6 0

29.21.8 2D Mortar contact ........................................................................................... 29-62

29.21.9 Tied and tiebreak option ................................................................................. 29-65

30 Geometric Contact Entities ................................................................................................................. 30-1

31 Nodal Constraints ............................................................................................................................... 31-1

31.1 Nodal Constraint Sets ......................................................................................................... 31-1

31.2 Linear Constraint Equations ............................................................................................... 31-1

32 Vectorization and Parallelization ......................................................................................................... 32-1

32.1 Vectorization ....................................................................................................................... 32-1

32.2 Parallelization ...................................................................................................................... 32-4

33 Airbags ................................................................................................................................................ 33-1

33.1 Control Volume Modeling ................................................................................................... 33-1

33.2 Equation of State Model ..................................................................................................... 33-3

33.3 Airbag Inﬂation Model ......................................................................................................... 33-5

33.4 Wang's Hybrid Inﬂation Model ........................................................................................... 33-7

33.5 Constant Volume Tank Test ............................................................................................. 33-10

34 Dynamic Relaxation and System Damping ........................................................................................ 34-1

34.1 Dynamic Relaxation For Initialization .................................................................................. 34-1

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34.2 Mass Weighted Damping.................................................................................................... 34-4

34.3 Dynamic Relaxation—How Fast Does it Converge? .......................................................... 34-4

35 Heat Transfer ...................................................................................................................................... 35-1

35.1 Conduction of Heat in an Orthotropic Solid ....................................................................... 35-1

35.2 Thermal Boundary Conditions ............................................................................................ 35-2

35.3 Thermal Energy Balances ................................................................................................... 35-4

35.4 Heat Generation .................................................................................................................. 35-4

35.5 Initial Conditions ................................................................................................................. 35-4

35.6 Material Properties .............................................................................................................. 35-4

35.7 Nonlinear Analysis............................................................................................................... 35-5

35.8 Units .................................................................................................................................... 35-5

36 Adaptivity ............................................................................................................................................ 36-1

37 Implicit ................................................................................................................................................. 37-1

37.1 Introduction ......................................................................................................................... 37-1

37.2 Equations ............................................................................................................................ 37-2

37.2.1 Discretization ...................................................................................................... 37-2

37.2.2 Constraints .......................................................................................................... 37-3

37.2.3 Reaction forces due to constraints ..................................................................... 37-5

37.3 Implicit Statics..................................................................................................................... 37-6

37.3.1 Linearization ........................................................................................................ 37-6

37.3.2 Linear theory ....................................................................................................... 37-8

37.3.3 Quasi-Newton iterations ................................................................................... 37-10

37.3.4 Tangent stiffness reformations ......................................................................... 37-14

37.3.5 Line search ........................................................................................................ 37-1 5

37.3.6 Convergence check .......................................................................................... 37-16

37.3.7 Automatic time stepping ................................................................................... 37-18

37.4 Implicit Dynamic s .............................................................................................................. 37-1 9

37.4.1 Newmark time integration ................................................................................. 37-19

37.4.2 Practical considerations ................................................................................... 37-20

37.4.3 Linear theory ..................................................................................................... 37-20

38 Arc-length ........................................................................................................................................... 38-1

38.1 Overview ............................................................................................................................. 38-1

38.2 Nonlinear equations ............................................................................................................ 38-4

38.3 Newton iterations ................................................................................................................ 38-5

38.4 Arc-length constraint – predictor step ................................................................................ 38-7

LS-DYNA Theory Manual Table of Contents

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38.5 Arc-length constraint – corrector steps .............................................................................. 38-8

39 Sparse Direct Linear Equation Solvers ............................................................................................... 39-1

39.1 Sparsity Preserving Orderings ............................................................................................ 39-1

39.2 Multifrontal Algorithm .......................................................................................................... 39-2

39.3 The Five Solver Options ...................................................................................................... 39-3

39.4 Treating Matrix Singularities ............................................................................................... 39-4

40 Sparse Eigensolver ............................................................................................................................. 40-1

40.1 The Eigenvalue Problem for Rotating Systems .................................................................. 40-2

41 Boundary Element Method ................................................................................................................. 41-1

41.1 Governing Equations .......................................................................................................... 41-1

41.2 Surface Representation ...................................................................................................... 41-2

41.3 The Neighbor Array ............................................................................................................. 41-3

41.4 Wakes ................................................................................................................................. 41-6

41.5 Execution Time Control ...................................................................................................... 41-6

41.6 Free-Stream Flow ............................................................................................................... 41-7

42 SPH ..................................................................................................................................................... 42-1

42.1 SPH Formulation ................................................................................................................. 42-1

42.1.1 Deﬁnitions ........................................................................................................... 42-1

42.1.2 Discrete Form of Conservation Equations .......................................................... 42-3

42.1.3 Applications to Conservation Equations ............................................................ 42-4

42.1.4 Formulation Available in LS-DYNA ..................................................................... 42-4

42.2 Sorting ................................................................................................................................. 42-5

42.3 Artiﬁcial Viscosity ................................................................................................................ 42-5

42.4 Time Integration .................................................................................................................. 42-6

42.5 Initial Setup ......................................................................................................................... 42-6

43 Element-Free Galerkin ........................................................................................................................ 43-1

43.1 Moving least-squares ......................................................................................................... 43-1

43.2 Integration constraint and strain smoothing ....................................................................... 43-3

43.3 Lagrangian strain smoothing for path-dependent problems.............................................. 43-5

43.4 Galerkin approximation for explicit dynamic computation ................................................. 43-5

43.5 Imposition of essential boundary condition ........................................................................ 43-6

43.6 Mesh-free Shell ................................................................................................................... 43-8

43.6.1 Mesh-free Shell Surface Representation ............................................................ 43-8

43.6.2 Updated Lagrangian Formulation and Co-rotational Procedure ...................... 43-1 0

44 Linear shells ........................................................................................................................................ 44-1

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44.1 Shells for Linear Analysis .................................................................................................... 44-1

44.2 Wilson’s Shell (element #20) ............................................................................................... 44-1

44.2.1 Plate Element ...................................................................................................... 44-1

44.2.2 Membrane Element ............................................................................................. 44-4

44.3 Assumed Strain/Membrane with Drilling Degree-of-freedom (element #18) ..................... 44-7

44.3.1 Membrane Element ............................................................................................. 44-7

44.3.2 Plate Element ...................................................................................................... 44-7

44.4 Differences between Element Types 18 and 20. ................................................................ 44-8

45 Random Geometrical Imperfections ................................................................................................... 45-1

45.1 Introduction to Random Geometrical Imperfections Using Karhunen-Loève Expansions 45-1

45.2 Methodology ....................................................................................................................... 45-1

45.2.1 Generation of random ﬁelds using Karhunen-Loève expansion ........................ 45-1

45.2.2 Solution of Fredholm integral of the second kind for analytical covariance

functions ........................................................................................................................ 45-2

45.2.3 Generating eigenfunctions from experimentally measured ﬁelds ...................... 45-4

46 Frequency Domain .............................................................................................................................. 46-1

46.1 Frequency Response Functions ......................................................................................... 46-1

46.1.1 FRF Computations .............................................................................................. 46-1

46.1.2 About the damping ............................................................................................. 46-3

46.2 ACOUSTIC FEM .................................................................................................................. 46-4

46.2.1 Theory basis ........................................................................................................ 46-4

47 Rotor Dynamics .................................................................................................................................. 47-1

47.1 Introduction ......................................................................................................................... 47-1

47.2 Two Coordinate systems .................................................................................................... 47-1

47.3 Forces in the Rotating Coordinate System......................................................................... 47-2

47.4 Transformation between Coordinate Systems ................................................................... 47-3

47.5 Equation of Motion in Rotating Coordinate System ........................................................... 47-4

47.6 Equation of Motion in Fixed Coordinate System ................................................................ 47-6

47.7 Arbitrary Rotation Axis ........................................................................................................ 47-6

48 References .......................................................................................................................................... 48-1

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