MATLAB与ABAQUS结合的有限元分析实践

需积分: 47 187 浏览量更新于2024-07-18 23 收藏 13.73MB PDF 举报

"利用ABAQUS和MATLAB进行有限元分析" 在工程领域，有限元分析（Finite Element Analysis，FEM）是一种广泛应用的数值计算方法，用于解决各种复杂结构和非结构问题。该技术通过将大问题分解成许多小的、简单的元素，然后对每个元素进行数学分析，最终组合成整体解决方案。ABAQUS是一款强大的商业有限元软件，能够处理静态、动态以及热力学等问题，广泛应用于机械、航空航天、土木工程等多个领域。 MATLAB则是一款强大的数值计算和数据可视化环境，其内置的MATLAB FEM工具箱使得用户可以方便地进行有限元建模、求解和后处理。MATLAB与ABAQUS结合使用，可以实现更高效的数据预处理和结果分析，例如自定义材料模型、编写定制的求解器接口以及复杂的后处理脚本。在《Introduction to Finite Element Analysis Using MATLAB and Abaqus》一书中，作者Amar Khennane详细介绍了如何利用这两种工具进行有限元分析。这本书涵盖了从基础概念到高级应用的全面内容，包括MATLAB和ABAQUS的集成使用，旨在帮助读者理解并掌握这两款软件在实际工程问题中的应用。书中可能涉及的知识点有： 1. 有限元基本理论：介绍有限元方法的基本概念，如变分原理、弱形式、单元类型和网格生成。 2. MATLAB编程基础：讲解MATLAB的基础语法和函数，用于创建有限元模型和处理数据。 3. ABAQUS基础知识：涵盖ABAQUS的主要功能，如几何建模、材料模型、边界条件设定和求解过程。 4. MATLAB与ABAQUS接口：讨论如何使用MATLAB来控制ABAQUS的运行，包括脚本接口（CAE和 Explicit Dynamics）和数据交换。 5. 自定义材料模型：介绍如何在MATLAB中开发和实施非线性或用户定义的材料模型，并将其集成到ABAQUS中。 6. 动态分析：探讨如何处理结构动力学问题，包括瞬态响应、频率响应和随机振动。 7. 后处理和结果解释：讲解如何利用MATLAB和ABAQUS的可视化工具进行结果解析和报告制作。 8. 应用案例：通过实际工程问题的实例，演示MATLAB和ABAQUS结合使用的全过程，包括问题定义、模型建立、求解和结果验证。通过学习这本书，读者不仅可以掌握有限元分析的基本技能，还能了解到如何利用MATLAB和ABAQUS的强大功能解决实际工程挑战。同时，书中强调的MATLAB编程能力对于提升分析效率和解决复杂问题具有重要意义。

List of Figures xv

FIGURE 3.1 Beamelement...................................................................... 64

FIGURE 3.2 Differential element of a beam. ................................................... 64

FIGURE 3.3 Nodal degrees of freedom ......................................................... 65

FIGURE 3.4 Statically equivalent nodal loads. ................................................. 68

FIGURE 3.5 Loading, bending moment, and shear force diagrams............................ 68

FIGURE 3.6 Support reactions for individual members. ....................................... 71

FIGURE 3.7 Beam with an internal hinge....................................................... 71

FIGURE 3.8 Beam elements with a hinge....................................................... 73

FIGURE 3.9 Example of a continuous beam. ................................................... 73

FIGURE 3.10 Example 1: Continuous beam results. ............................................ 81

FIGURE 3.11 Problem3.1. ....................................................................... 81

FIGURE 3.12 Problem 3.2 and equivalent nodal loads for elements 3 and 4. .................. 84

FIGURE 3.13 Problem3.3. ....................................................................... 87

FIGURE 3.14 Continuous beam................................................................... 90

FIGURE 3.15 Beam crosssection; dimensionsare in mm....................................... 90

FIGURE 3.16 CreatingtheBeam_Part. .......................................................... 91

FIGURE 3.17 Drawing using the connected line icon. .......................................... 91

FIGURE 3.18 Materialdefinition. ................................................................ 91

FIGURE 3.19 Creating a beam profile. ........................................................... 92

FIGURE 3.20 Enteringthe dimensions ofa profile. ............................................. 92

FIGURE 3.21 Creatinga section. ................................................................. 93

FIGURE 3.22 Editing a beam section............................................................. 93

FIGURE 3.23 Editing section assignments. ...................................................... 94

FIGURE 3.24 Beam orientation................................................................... 94

FIGURE 3.25 Assigning beam orientation. ...................................................... 94

FIGURE 3.26 Rendering beam profile. ........................................................... 95

FIGURE 3.27 Rendered beam..................................................................... 95

FIGURE 3.28 Selecting a beam element.......................................................... 96

FIGURE 3.29 Seeding a mesh by size. ........................................................... 96

FIGURE 3.30 Node and element labels. .......................................................... 97

FIGURE 3.31 Creating a node set................................................................. 97

FIGURE 3.32 Selecting multiple nodes........................................................... 98

FIGURE 3.33 Creatingelement sets. ............................................................. 98

xvi List of Figures

FIGURE 3.34 ImposingBC using createdsets................................................... 98

FIGURE 3.35 Selecting a node set for boundary conditions..................................... 99

FIGURE 3.36 Editing boundary conditions. ..................................................... 99

FIGURE 3.37 ImposingBC using createdsets..................................................100

FIGURE 3.38 Imposing a concentrated load using a node set. ................................. 100

FIGURE 3.39 Imposinga lineloadon an element set. .........................................101

FIGURE 3.40 Fieldoutput........................................................................101

FIGURE 3.41 Submitting a job in Abaqus CAE. ...............................................101

FIGURE 3.42 Plotting stresses in the bottom fiber. .............................................102

FIGURE 4.1 Beam column element with six degrees of freedom............................. 108

FIGURE 4.2 Example1: Portal frame.......................................................... 110

FIGURE 4.3 Frame with an internal hinge. .................................................... 119

FIGURE 4.4 Finiteelement discretization. .................................................... 119

FIGURE 4.5 Statically equivalent nodal loads. ................................................ 120

FIGURE 4.6 Portalframe. ......................................................................124

FIGURE 4.7 Profiles’sections;dimensionsare in mm........................................ 125

FIGURE 4.8 Creating thePortal_frame part. .................................................. 125

FIGURE 4.9 Material andprofilesdefinitions. ................................................ 126

FIGURE 4.10 Creatingsections..................................................................126

FIGURE 4.11 Editing section assignments. ..................................................... 127

FIGURE 4.12 Assigning beam orientation. ..................................................... 127

FIGURE 4.13 Rendering beam profile. ..........................................................127

FIGURE 4.14 Seeding by number................................................................ 128

FIGURE 4.15 Mesh...............................................................................128

FIGURE 4.16 Creatingthe element setRafters. ................................................129

FIGURE 4.17 ImposingBC using createdsets..................................................129

FIGURE 4.18 Imposing a line load in global coordinates. ..................................... 130

FIGURE 4.19 Imposing a line load in local coordinates. ....................................... 130

FIGURE 4.20 Analyzing a job in Abaqus CAE. ................................................131

FIGURE 4.21 Plotting stresses in the bottom fiber (interactive edition). ......................131

FIGURE 4.22 Plotting stresses in the bottom fiber (keyword edition). ........................ 134

FIGURE 5.1 Internal force components. .......................................................136

FIGURE 5.2 Stress components at a point. ....................................................136

FIGURE 5.3 Stress components on a tetrahedron.............................................. 137

List of Figures xvii

FIGURE 5.4 Equilibrium of an infinitesimal cube. ............................................139

FIGURE 5.5 Principal directionsof a stresstensor. ...........................................141

FIGURE 5.6 Tangential and normal components of the stress vector.........................142

FIGURE 5.7 Mohr’s circles. ....................................................................143

FIGURE 5.8 Schematic representation of the deformation of a solid body...................145

FIGURE 5.9 Reference and current configurations. ........................................... 146

FIGURE 5.10 Deformationsof an infinitesimalelement. ......................................147

FIGURE 5.11 Geometrical representation of the components of strain at a point. ............151

FIGURE 5.12 Monoclinic material. ............................................................. 155

FIGURE 5.13 Symmetryof rotation. ............................................................157

FIGURE 5.14 Astateofplane stress............................................................. 162

FIGURE 5.15 Stateof plane strain...............................................................163

FIGURE 5.16 Change of basis. .................................................................. 165

FIGURE 5.17 Displacement field (Problem 5.3). ...............................................167

FIGURE 5.18 Displacement field (Problem 5.5). ...............................................170

FIGURE 5.19 Strain rosette. .....................................................................171

FIGURE 5.20 Problem5.7. ...................................................................... 172

FIGURE 5.21 Displacements without the rigid walls. .......................................... 173

FIGURE 6.1 Graphical comparison of exact and approximate solution. .....................178

FIGURE 6.2 Integration bypartsin two andthreedimensions. .............................. 180

FIGURE 6.3 Infinitesimal element of the boundary. .......................................... 180

FIGURE 6.4 Graphical comparison of the exact and approximate solutions. ................186

FIGURE 7.1 Thick wall with embedded thermocouples. .....................................192

FIGURE 7.2 Finiteelement discretization. ....................................................193

FIGURE 7.3 Finite element approximation. ...................................................195

FIGURE 7.4 Geometrical illustration of the compatibility principle .........................195

FIGURE 7.5 Linear triangle.....................................................................197

FIGURE 7.6 Geometrical transformation for a triangular element............................ 200

FIGURE 7.7 Three-node triangular element with an arbitrary point O. ......................202

FIGURE 7.8 Three-node triangular reference element. .......................................204

FIGURE 7.9 Geometricaltransformation. ..................................................... 204

FIGURE 7.10 One-dimensional elements. ......................................................207

FIGURE 7.11 Two-dimensional quadrilateral elements. .......................................207

xviii List of Figures

FIGURE 7.12 Two-dimensional triangular elements............................................ 208

FIGURE 7.13 Three-dimensional tetrahedric elements. ........................................209

FIGURE 7.14 Three-dimensional brick elements. .............................................. 210

FIGURE 8.1 Positions of the sampling points for a triangle: Orders 1, 2, and 3. ............ 219

FIGURE 8.2 Gauss quadrature over an arbitrary area. ........................................219

FIGURE 8.3 Double change of variables.......................................................220

FIGURE 8.4 Coarse mesh of two 8-nodded elements. ........................................ 221

FIGURE 8.5 Eight elements finite element approximation with two 8-nodded elements.... 222

FIGURE 8.6 Estimation of rainfall using finite element approximation. .....................226

FIGURE 9.1 Discretization error involving overlapping. .....................................234

FIGURE 9.2 Discretization errorinvolving holesbetween elements. ........................235

FIGURE 9.3 Plane elements with shape distortions. ..........................................235

FIGURE 9.4 Geometricaldiscretizationerror..................................................235

FIGURE 9.5 Linear triangular element. ........................................................ 236

FIGURE 9.6 Element nodal forces. ............................................................ 239

FIGURE 9.7 Analysis of a cantilever beam in plane stress. ................................... 240

FIGURE 9.8 Finite element discretization with linear triangular elements. ..................241

FIGURE 9.9 Deflection of the cantilever beam. ............................................... 248

FIGURE 9.10 Stresses along the x-axis.......................................................... 249

FIGURE 9.11 Automatic mesh generation with the CST element. ............................252

FIGURE 9.12 Deflection of the cantilever beam obtained with the fine mesh.................253

FIGURE 9.13 Stresses along the x-axisobtained withthefine mesh. .........................253

FIGURE 9.14 CreatingtheBeam_CST Part.....................................................254

FIGURE 9.15 Drawing using the create-lines rectangle icon. ..................................254

FIGURE 9.16 Creating a partition. ..............................................................255

FIGURE 9.17 Creatinga planestress section. .................................................. 255

FIGURE 9.18 Editing section assignments. ..................................................... 255

FIGURE 9.19 Mesh controls. .................................................................... 256

FIGURE 9.20 Selecting element type. ...........................................................256

FIGURE 9.21 Seeding part by size...............................................................256

FIGURE 9.22 Mesh...............................................................................257

FIGURE 9.23 Imposing BC using geometry. ...................................................257

FIGURE 9.24 Imposing a concentrated force using geometry. .................................257

FIGURE 9.25 Analyzing a job in Abaqus CAE. ................................................258

List of Figures xix

FIGURE 9.26 Plotting displacements on deformed and undeformed shapes. .................258

FIGURE 9.27 Generating a mesh manually in Abaqus. ........................................ 261

FIGURE 9.28 Displacement contour. ............................................................ 263

FIGURE 9.29 Linear strain triangular element. .................................................263

FIGURE 9.30 Automatic mesh generation with the LST element.............................. 271

FIGURE 9.31 Deflection of the cantilever beam obtained with the LST element. ............272

FIGURE 9.32 Stresses along the x-direction obtained withtheLST element. ................ 273

FIGURE 9.33 Aluminum plate witha hole......................................................273

FIGURE 9.34 Making useof symmetry. ........................................................ 273

FIGURE 9.35 CreatingthePlate_LSTPart......................................................274

FIGURE 9.36 Creatinga planestress section. ..................................................274

FIGURE 9.37 Editing section assignments. .....................................................275

FIGURE 9.38 Mesh controls. ....................................................................275

FIGURE 9.39 Seeding edge by size and simple bias. ........................................... 276

FIGURE 9.40 Creating a node set................................................................276

FIGURE 9.41 Creating a surface. ................................................................ 277

FIGURE 9.42 Imposing BC using node sets..................................................... 277

FIGURE 9.43 Imposing a pressure load on a surface. .......................................... 278

FIGURE 9.44 Plotting the maximum in-plane principal stress (under tension)................ 279

FIGURE 9.45 Plotting the maximum in-plane principal stress (under compression)..........279

FIGURE 9.46 Linear quadrilateral element......................................................280

FIGURE 9.47 Element loading. ..................................................................283

FIGURE 9.48 Equivalent nodal loading. ........................................................ 284

FIGURE 9.49 Finite element discretization with 4-nodded quadrilateral elements. ..........285

FIGURE 9.50 Contour of the vertical displacement v

.......................................... 290

FIGURE 9.51 Contour of the stress σ

.......................................................... 291

FIGURE 9.52 Automatic mesh generation with the Q4 element. ..............................295

FIGURE 9.53 Contour of the vertical displacement v

.......................................... 295

FIGURE 9.54 Contour of the stresses along the x-axis σ

. .................................... 295

FIGURE 9.55 Creatingthe Beam_Q4 Part. .....................................................296

FIGURE 9.56 Creating a partition. ..............................................................296

FIGURE 9.57 Creatinga planestress section. ..................................................297

FIGURE 9.58 Editing section assignments. .....................................................297

FIGURE 9.59 Mesh controls. ....................................................................297

剩余485页未读，继续阅读

西伯利亚狼wy

粉丝: 2
资源: 1

MATLAB与ABAQUS结合的有限元分析实践

基于Matlab和Abaqus的有限元分析入门

MATLAB与ABAQUS在有限元分析中的应用

Python与Matlab联用在Abaqus中柴油机有限元分析后处理的研究

使用 Matlab 进行有限元分析的预处理器，可从Abaqus *.inp 文件中导入模型信息—MATLAB

1.rar_8QQ_abaqus matlab_abaqus_ matlab_zebraa8a_有限元abaqus

连接 Abaqus 和 Matlab 的软件

MATLAB有限元分析与应用.zip_matlab 有限元分析与应用_matlab有限元_有限元

MATLAB与Abaqus合作的有限元分析入门指南

MATLAB与Abaqus在有限元分析中的应用教程

MATLAB与Abaqus在有限元分析中的应用及代码实现

最新资源