Verfügbarkeit: Building better products with finite element analysis

Building better products with finite element analysis:

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Bibliographische Detailangaben
Hauptverfasser:	Adams, Vince 1963- (VerfasserIn), Askenazi, Abraham (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Santa Fe, NM Onword Press 1999
Ausgabe:	1st. edition
Schlagworte:	Finite element method Finite-Elemente-Methode Produktentwicklung CAD
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	xxxii, 587 Seiten Illustrationen, Diagramme
ISBN:	156690160X

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Datensatz im Suchindex

_version_	1805087946484744192
adam_text	List of Figures and Tables xxii Introduction xxix Who Will Benefit From This Book xxix New FEA Users xxx Experienced FEA Users xxx All Engineers xxx Managers and Supervisors xxx How This Book Is Organized xxxi The Importance of "Classical Engineering" xxxii Introduction to FEA and the Analytical Method 1 Chapter 1: Introduction to FEA in the Product Design Process 3 A Brief History of Computer aided Engineering 4 Enter the Design Analyst 7 Rapid Product Development Process 8 Who Should Use FEA? 15 Pointing FEA in the Right Direction 16 Analytical Problem Solving Process 17 Process 17 What is the goal of the analysis? 17 Predictive engineering versus failure verification 18 Trend analysis versus absolute data 18 Selecting required output data 19 What input is required for the solution and what level of uncertainty does it introduce? 19 What is the most efficient means to solve the problem? 20 Introduction to the Assumptive Approach 20 Common Misconceptions About FEA 21 Meshing is Everything 21 FEA Replaces Testing 22 Finite Element Analysis is Easy 23 Finite Element Analysis Is Hard 24 Learning the Interface Equals Learning FEA 25 Summary 25 v/ Building Better Products with Finite Element Analysis Chapter 2: Fundamentals 27 First Principles 27 Body Under External Loading 27 Area Moments of Inertia 31 Definitions 32 Stress and Strain 34 What Is Stress? 35 Principal Stresses 36 Strain 38 Principal Strain 39 Fundamental Stress States 40 Stress in Flexure 40 Stress in Shear 43 Stress in Torsion 44 Stress in Pressure 46 Stress in Contact 48 Stress in Thermal Expansion 50 Stress Concentration Factors 51 Material Properties 52 Types of Materials 52 Common Material Properties 53 Ductile versus Brittle Material Behavior 55 Safety Factor 56 Failure Modes 57 Results Interpretation 57 Typical Failure Modes 57 Classic Failure Theories 58 Ductile Failure Theory 59 Brittle Failure Theory 60 Other Failure Theories 62 Buckling 62 Fatigue 66 Creep 70 Dynamic Analysis 72 Modal Analysis 72 Frequency Response Analysis 80 Transient Response Analysis 84 Summary 87 Chapter 3: FEA Capabilities and Limitations 89 Actual Performance versus FEA Results 90 How FEA Calculates Data 93 Contents vii ASimple Model 94 H elements versus P elements 97 Correctness versus Accuracy 99 The Correct Answer 99 The Accurate Answer 99 Key Assumptions in FEA for Design 100 Four Primary Assumptions 100 Geometry 100 Properties 101 Mesh 102 Boundary Conditions 102 Linear Static Assumption 103 Linear 103 Material Properties 104 Geometry Concerns 104 Boundary Conditions 105 Using the Linear Assumption 105 Static Assumption 105 Transient Response 106 Frequency Response 107 Random Response 107 Using the Static Assumption 107 Other Commonly Used Assumptions 108 Geometry 108 Material Properties 109 Boundary Conditions 110 Fasteners Ill General Ill Summary 112 Finite Element Modeling Basics 113 Chapter 4: Common Model and Element Types 115 Common Modeling Types 116 Plane Stress Modeling 117 Identifying Plane Stress Models 117 Geometry in a Plane Stress Model 118 Plane Strain Modeling 120 Axisymmetric Modeling 121 Orientation of an Axisymmetric Model 123 vf/f Building Better Products w/ffi Finite Element Analysis Identifying an Axisymmetric Model 124 Loading 125 Constraints 126 Symmetry 127 Reflective Symmetry 128 Near symmetry 128 Loading 129 Constraints 129 Cyclic Symmetry 130 Boundary Conditions 131 Using Reflective Symmetry to Approximate Cyclic Symmetry 131 Anti symmetry 133 Additional Benefits of Symmetry 134 Beam Models 135 Two Basic Types of Beam Elements 136 Rod Elements 136 Beam Elements 136 Beam Coordinate System 137 Stress Recovery in Beams 138 Beams in Torsion 139 Convergence 140 Section Orientation 140 Plate and Shell Modeling 141 Shell Element Basics 141 Orientation 142 Stress Recovery 144 Identifying Shell Model Candidates 145 Accuracy 149 Special Shell Elements 150 Additional Benefits 151 Solid Element Modeling 152 Identifying Solid Model Candidates 152 Solid Element Basics 153 Tet versus Brick Meshes 154 Solid Modeling Tips 154 Special Elements 155 Spring Elements 155 Damper Elements 156 Mass Elements 157 Mass Moment of Inertia 158 Rigid Elements 159 Uses of Rigid Elements 160 Contact Modeling 160 Contents ix Gap Elements 161 Gap Elements as Cables 163 Slide Line Elements 163 Slide Lines in 3D Contact 164 General Contact Elements 166 Friction in Contact Elements 166 Crack Tip Elements 167 Part versus Assembly Modeling 167 Component Contribution Analysis 168 Turning the One Disadvantage into an Advantage 169 Considering Interactions in Terms of Boundary Conditions 169 Isolating the Performance of Each Part 170 Keep It Simple 171 Transitional Meshing 171 Use Test Models to Debug Idealizations 173 Summary 173 Chapter 5: CAD Modeling for FEA 175 Design versus Analytical Model 176 Building CAD Models for Eventual FEA Use 179 Solid Chunky Parts 180 Building Clean Geometry 181 Short Edges 182 Sliver Surfaces 184 Voids in Solids 186 High Order Surfaces and Edges 187 Corrupt Geometric Definition 188 Parent child Relationships 189 Guidelines for Part Simplification 191 Guidelines for Geometry Planning 192 Additional Considerations 192 Working with Existing Geometry 193 Geometry Guidelines for Working with Existing Geometry 193 Symmetry 193 Boundary Condition Adjustments 194 Feature Suppression versus Submodeling 196 Feature Suppression 198 Submodeling 201 Mid plane Extraction 203 Adjusting Features 204 Knowing When to Bail 205 Working with Limited Geometry Tools 206 x • Building Better Products with Finite Element Analysis Developing Geometry Specifically for Analysis 208 Start Simple 208 The Burden of Commitment 209 Guidelines for Analytical Geometry 210 Elements and Model Types 210 Plan for Boundary Conditions 212 Plan for Assembly Features 213 Plan for Automatic Optimization 213 Topology Constraints 214 Relationship Constraints 216 Test the Limits of Geometry Variables 217 Summary 218 Chapter 6: Assigning Properties 219 Introductory Concepts 220 Property Names 220 Comments and Descriptions 221 Colors 221 Material Properties 222 Types of Materials 222 Stiffness Properties 223 Other Properties 223 Units 224 Nonlinear Material Properties 224 General Element Properties 225 Beams 225 Advanced Beam Properties 227 Shells 228 Advanced Shell Properties 228 Solids 229 Special Element Properties 229 Mass Elements 229 Springs 231 Dampers 231 Contact Elements 231 Gap Elements 232 Slide Line Elements 233 Friction 233 Summary 233 Chapter 7: Finite Element Model Building 235 Setting UpfheModel 236 Grouping and Layering 236 Contents xi Resource Requirements 236 Element Selection 237 Manual versus Automatic Meshing 238 Modeling Speed 238 Solution Speed 239 Accuracy 239 Convergence 239 Perception 240 Manual and Automatic Mixed Meshes 240 P elements and H elements 240 Meshing Beam Models 241 Guidelines for Beam Element Size 241 Other Beam Modeling Issues 242 Meshing Shell Models 242 Other Methods of Creating Shell Models 245 Element Shape Quality 246 Mapped Meshing 247 Biasing a Mesh 247 Transitioning Mesh Densities 248 Controlling a P element Mesh 249 Manual Meshing of Solid Models 249 Methods for Meshing Solids 250 Extruding and Revolving Surface Meshes 250 Automeshing Solids 251 Element Quality Issues 252 Meshing a Solid Model 253 Debugging a Failed Automesh 254 Transition Elements 255 Rigid Elements 255 Constraint Equations 257 Summary 257 Chapter 8: Boundary Conditions 259 What Are Boundary Conditions? 261 A Simple Example 261 Types of Boundary Conditions 263 Spatial versus Elemental Degrees of Freedom 264 Boundary Conditions and Accuracy 264 Overconstrained Models 265 Redundant Constraints 265 Excessive Constraints 266 Coupled Strain Effects 267 xii Building Better Products with Finite Element Analysis Understiffened Models 270 Underconstrained Models 270 Insufficient Part Stiffness 270 Local versus Global Accuracy 271 Singularities 271 Bracketing Boundary Conditions 274 Review of General Boundary Condition Concepts 276 Preparing Geometry for Boundary Conditions 276 Applying Boundary Conditions to Geometry 276 Using Load and Constraint Sets 277 Coordinate Systems 278 Constraints 280 Constraints on Different Element Types 281 Conditional Equilibrium 282 Symmetry 282 Enforced Displacement 285 Loads 288 Units 288 Load Distribution 289 Load Orientation 291 Nonlinear Forces 291 Types of Loads 292 Forces and Moments 292 Pressure Loads 293 Acceleration Loads 294 Temperature Loads 294 Checking Applied Loads 295 Comparison of Boundary Condition Schemes 295 Summary 300 Chapter 9: Solving the Model 303 Multiple Load and Constraint Cases 304 Final Model Checb 305 Free Node Check 306 Model Continuity Check 306 Sanity Checks 308 Material Properties 308 Boundary Conditions 308 Mass 308 System Resources 309 Element Check 310 When the Solution Fails 310 Contents x/ii Insufficient System Resources 310 Insufficiently Constrained Models 311 Solve Model for First Mode 311 Abrupt Change in Stiffness 312 Summary 312 Chapter 10: Convergence 313 Importance of Convergence 313 Understanding Convergence 314 Uncertainty versus Error 317 Error Estimates 317 Relating Error Estimates to Convergence 319 More Examples 320 P elements versus H elements 322 Element Quality versus Convergence 323 Summary 324 Chapter 11: Displaying and Interpreting Results 325 Method for Viewing Results 326 Displacement Results 326 Animation 326 Magnitude of Deformed Shape 328 Stress Results 329 Fringe Quality 330 Convergence 331 Stress Magnitude 331 Centroidal versus Corner Stress 332 Entire Model versus Individual Components or Groups 333 Types of Output Data 334 Displacements 334 Rotations 334 Velocities and Accelerations 334 Strain Quantities 335 Max, Mid, Min Principal Strain 335 Normal and Shear Strain 335 Shell Membrane and Transverse Shear Strain 335 Strain Energy 336 Stress Quantities 336 Max, Mid, Min Principal Stress 336 Normal and Shear Stresses 336 Von Mises Stress 337 Reaction and Resultant Forces and Moments 338 xjy Building Better Products with Finite Element Analysis Line Element Results 338 Strain and Stress 338 Resultant Force and Moments 339 Rigid Element Forces 339 Shell Element Results 340 Location 340 Measures ^40 Types of Results Displays 340 Animation 341 Fringe 341 Averaged versus Unaveraged versus Continuous Tone 342 Isolines and Isosurfaces 343 Query 344 Vector Plots 345 Orientation of Principal Stress 345 Graphs 346 Results Interpretation: Quality Inspection and Verification Techniques 347 Convergence Issues 347 Correlation to Expectations (Common Sense) 347 Qualification and Review of Assumptions 348 Correlation to Closed Form Equations 348 Use of Test Models 349 Correlation to Testing 349 Relation to Problem Goals 350 Bulk Calculations on Results 350 Combined Load Sets 350 Fatigue Estimates 351 Mohr's Criterion 352 Summary 353 Chapter 12: Optimization: Tying It All Together 355 Engineering versus Analysis 355 Avoiding "Emotional Commitment" 356 Optimization 357 Ask Questions 357 Phase I Optimization: Brainstorming 359 Extrusion 366 Injection Molding 367 Sheet Metal Weldment 368 Phase II Optimization: Fine Tuning 371 Summary 374 Contents xv Advanced Modeling Techniques and Applications 377 Chapter 13: Modeling Assemblies and Weldments 379 Design Model versus Analysis Model 380 Assembly Type Controls Usability of CAD Model 380 Continuous Load Bearing Structures 381 Jointed Assemblies with Free Degrees of Freedom 383 Mixed Assembly Modeling 385 Realistic Interpretation of Local Joint Results 386 Component Contribution Analysis 387 Treat Continuous Subassemblies as Single Component 387 Use Free Body Diagrams or Kinematics to Develop Boundary Conditions . 387 Optimize Each Component on Its Own Merits 388 Combine into Assemblies One Component at a Time 388 Use Test Models of Joints 389 Identify Fasteners Requiring Detailed Results 389 Consider Submodeling for More Detailed Local Results 389 Examine Results Local to Each Joint 389 Review Performance of Each Part at Each Step 390 Review Complete Assembly for Conformance to Global Expectations 390 Submodel Portions of System Using Assembly Reactions 390 Modeling Continuous Load Bearing Assemblies 391 Solid Assemblies 391 Weldments 391 Bolted Castings or Machined Parts 393 Sheet Metal Assemblies 394 Weldments 394 Continuous Welds 394 Skip or Partial Welds 395 Plug or Spot Welds 395 Riveted or Bolted Assemblies 396 More on Continuous Assemblies 396 Plastic Assemblies 396 Printed Circuit Boards 397 Construction Assemblies 398 Modeling Jointed Interfaces 399 Identify Critical Information Up Front 399 Rotational Joints 400 Bolts, Rivets, and Pins 401 Detailed Fastener Interfaces 402 Rotational Bearings 404 xyj Building Belter Products with Finite Element Analysis Translational Joints 407 Sliding Contact 407 Linear Bearings 408 Guide Pins and Rods 409 Slots 409 Summary 409 Chapter 14: Thermal ExpansionAnalysis 411 Thermal Expansion Basics 412 Material Properties 412 Boundary Conditions 414 Local Temperature Loads 414 Constraints 415 Other Uses for Thermal Expansion 415 Modeling Weld Stress 415 Injection Molded Part Shrinkage 417 Press fit Analysis 419 Spring Preload 421 Example of Incorrectly Used Thermal Expansion 421 Summary 423 Chapter 15: Nonlinear Analysis 425 Basic Concepts in Nonlinear Analysis 426 Why Use Nonlinear Analysis? 426 Exact Performance Data Required 427 Contact Is Inevitable 427 Large Displacement in Flexible Parts 428 Detailed Stress Input to Fatigue Analyses 428 Manufacturing and Forming Simulation 428 Identifying Nonlinear Behavior 428 Fundamental Conditions of Linearity 429 Stress strain 429 Strain Displacement 429 Load Continuity 429 Common Symptoms of Nonlinear Behavior 430 Stress Levels Approach the Yield Point 430 Coupled Displacements Are Restrained 431 Large Displacements Are Expected 431 Unreasonably High Deflections Are Observed 431 Two Surfaces or Curves Penetrate 432 Direct versus Iterative Solutions 432 Overview of Nonlinear Solution Algorithm 433 Load Cases, Load Steps, and Convergence 433 Load Steps 433 Contents xvli Load Cases 435 Methods for Updating Model Stiffnesses 436 Three Common Types of Nonlinear Behavior 438 Material Nonlinearity 439 Material Definitions 439 Revisiting Young's Modulus 439 Yield Criteria 440 Hardening Rules 440 Commonly Used Material Models 441 Geometric Nonlinearity 445 Using Geometric Nonlinear FEA 446 Boundary Nonlinearity 447 Contact 447 Follower Forces 448 Other Types of Nonlinearity 448 Hyperelastic 448 Nonlinear Transient 449 Creep 450 Nonlinear Buckling Analysis 450 Bulk Metal Forming 451 Nonlinear Results Data 451 Nonlinear Solution Methodology 452 Use Test Models to Debug Materials or Contact 452 Building and Running Model as Linear System 453 Set Up Nonlinear Solution Parameters 454 Run Nonlinear Analysis with Large Displacements 455 Run Contact Conditions 455 Enable Nonlinear Material Model 456 When Convergence Is Not Obtained 456 Finite Element Modeling for Nonlinear Analysis 457 Modeling Nonlinear Behavior with Linear Tools 460 Moderately Nonlinear Large Displacements 460 Moderately Nonlinear Material Problems 461 Use Linear Methods to Simulate Contact 461 Springs 462 Constraints 462 Reaction Forces 463 Multipoint Constraints 463 Summary 463 Chapter 16: Buckling Analysis 465 Possible Scenarios 466 Accuracy Issues 467 xyi',1 Building Better Products with Finite Element Analysis Simple Buckling Analyses and Correlation to Theory 468 Summary 475 Chapter 17: Modal Analysis 477 A Simple Modal Analysis 478 Basicsof Modal Analysis 479 Reasons to Perform Modal Analyses 480 Boundary Conditions 482 Preparing for a Dynamic Analysis 483 Dealing with Resonant Frequencies 484 Meshing a Part for Modal Analyses 484 Other Uses for Modal Analyses 486 Summary 487 Chapter 18: Dynamic Analysis 489 Frequency Response 490 Definitions 490 Input 491 Constraints 492 Phase Offset 492 Amplitude Offset 493 Frequency Response Results 494 Revisiting Amplitude Offsets 494 Transient Response 495 Input 495 Constraints 495 Solution Parameters 495 Results Output 496 Random Response 496 Solution Methods 497 Constraints 498 Modal versus Direct Solvers 498 Damping 500 Summary 501 [ftelitr 0 Integrating Simulation into Product Design Strategy 503 Chapter 19: Overview of Popular Industry Offerings 505 Packaging 506 Contents xix Three Key Components of Any FEA Solution 506 Preprocessor 507 Solver 507 Postprocessor 508 Open Systems 508 Integrated Systems 509 CAD embedded Systems 510 Proprietary Systems 510 Options 511 Contact Information for Vendors 530 Chapter 20: Key Elements of a Successful FEA Implementation 531 Key Success Factor: Evaluation 532 Economic Needs 532 Cost of Delay 532 Product Development Costs 533 Missed Sales 533 Lost Market Share 533 Summarizing Cost of Delay 535 Product Musts versus Product Wants 535 Product Musts 535 Product Wants 536 Summarizing the Economic Benefits of FEA 536 Technological Needs 537 Personnel Resources 538 Give Users the Best Chance to Succeed 539 Should Designers Be Doing FEA? 539 Project Schedule Resources 541 Hardware Resources 542 RAM Requirements 542 Hard Disk Requirements 542 Swap Space 542 Scratch Space 543 Storage Space 544 Graphics Cards 545 System Data Bus 545 Hardware Evaluation Summary 545 Evaluating FEA Suppliers 546 Evaluating FEA Systems 546 CAD Compatibility 547 Finite Element Modeling: The Preprocessor 548 Solution Accuracy 548 xx Building Better Products with Finite Element Analysis Support and Training 548 Key Success Factor: Implementation 549 Implementation Plan 549 Training 550 Internal Training and Coaching Programs 550 External Training and Coaching 551 Choosing a Coach 551 After All That 553 Initial Project 554 Management Buy in 554 Key Success Factor: Verification 554 Economic Verification 554 Technical Verification 555 A Practical Verification Process 555 Summary 556 Chapter 21: Trends and Predictions for the Future of FEA 559 Faster Computing Speed and Algorithms 559 Self adapting, Self converging Technologies 560 Multiphysics, Multisolution Technologies 560 CAD embedded Systems 561 Other Advancing Technologies 561 Internet Based Support, Training, and Solvers 561 Windows NT/UNIX Convergence 562 Automation Technologies for Results Verification 562 More Accessible Use of Manufacturing Technologies 563 Sophisticated Bulk Calculations on Results 563 Improved Optimization Algorithms 563 Summary 564 Bibliography 566 Index 568 Fig. 1.1. Tensile testing was performed by Galileo 4 Fig. 1.2. Railroad engineering utilized truss calculations and drove the development of fatigue analysis methods 4 Fig. 1.3. Actua rapid prototyping equipment from 3D Systems 9 Fig. 1.4. Solid model built in SolidWorks. . 10 Fig. 1.5. Relative acceptance and age of the three enabling technologies 11 Fig. 1.6. Traditional product development process 12 Fig. 1.7. Relative cost of product change at the different stages of the design process 13 Fig. 1.8. Cost versus knowledge dilemma. 13 Fig. 1.9. Product development using predictive engineering 14 Fig. 1.10. Improved tracking of cost versus product knowledge with simulation 14 Fig. 2.1. General free body diagram (a). Resultant forces and moments (b). Second law equivalent (c) 28 Fig. 2.2. Uniaxial spring and damper system (a). Planar body motion (b) 30 Fig. 2.3. Submerged wall (a). Beam in pure bending (b). Bar in pure torsion (c) 32 Fig. 2.4. Rectangular and polar moments of inertia (a). Parallel axis theorem (b) 32 Fig. 2.5. General stress elements in equilibrium 35 Fig. 2.6. General plane stress element (a). Orientation of principal stress (b). Orientation of maximum shear stress (c). 36 Fig. 2.7. Mohr's circle diagram for plane stress (a) and triaxial stress (b) 38 Fig. 2.8. Deformation of a uniform bar under uniaxial loading 38 Fig. 2.9. FEA of a beam in flexure 40 Fig. 2.10. Straight beam in flexure 41 Fig. 2.11. Curved beam in flexure 42 Fig. 2.12. FEA of a cantilever beam in shear. 43 Fig. 2.13. Straight rectangular section beam in shear 43 Fig. 2.14. FEA of a round bar in torsion. . 44 Kg. 2.15. Solid round bar in torsion 44 Fig. 2.16. FEA of a thick cylinder under pressure 46 Fig. 2.17. Cylinder under pressure (a). Press fit cylinders (b) 46 Fig. 2.18. FEA of two spheres in contact 48 Fig. 2.19. Forced contact of two spheres (a) and two cylinders (b) 48 Fig. 2.20. FEA of a shaft subject to a temperature change with the ends fully constrained. . .50 Fig. 2.21. FEA of a drilled plate under tension. 51 Fig. 2.22. Typical engineering stress strain diagram of a ductile material specimen subject to uniaxial tensile loading 54 Fig. 2.23. Comparison of three ductile failure theories 60 Fig. 2.24. Comparison of three brittle failure theories 61 Fig. 2.25. Effective length factors for common end conditions of centrally loaded columns. 63 Fig. 2.26. Critical stress in columns as a function of slenderness ratio 64 Fig. 2.27. Buckling FEA of a complex shell structure 65 Fig. 2.28. Eccentrically loaded column (a). Maximum unit load for different values of load eccentricity and column slenderness ratio (b) 65 Fig. 2.29. Typical S N diagram for steel 66 Fig. 2.30. Sinusoidal fluctuating stress, amplitude versus time 68 Fig. 2.31. Stages of creep failure 71 Fig. 2.32. Free vibration of a cantilever beam, first mode 73 Fig. 2.33. Free vibration of systems which are overdamped, critically damped (a), or underdamped in cases where 0O = Ao and 60=0(b) 75 Fig. 2.34. Discretized beam model with 3D spring and damper systems 77 Fig. 2.35. Modal FEA of a cantilever beam, first four modes 78 Fig. 2.36. Two degree of freedom system 78 Fig. 2.37. Damped single degree of freedom system subject to harmonic excitation 81 xxif Building Bette Fig. 2.38. Magnification factor and phase angle versus frequency ratio for different damping ratios of single degree of freedom systems subject to harmonic excitation 82 Fig. 2.39. Transient response FEA of a cantilever beam subject to a harmonic excitation applied perpendicularly at its free end 86 Fig. 3.1. Cantilevered beam geometry 91 Fig. 3.2. Dimensional laser scan of a part overlayed on the actual CAD geometry. . 92 Fig. 3.3. Schematic representation of a two spring system 94 Fig. 3.4 Simple p element mesh 98 Fig. 3.5. Solid p element mesh 98 Fig. 4.1. Plane stress idealization of simply supported beam 117 Fig. 4.2. Plane stress model of plastic clip feature 118 Fig. 4.3. Plane stress model of cable retainer with multiple wall thicknesses 118 Fig. 4.4. Plane stress model of a spur gear mesh 119 Fig. 4.5. Equivalent solid model of the retainer 120 Fig. 4.6. Plane strain idealization of long pipe under constant pressure 121 Fig. 4.7. Axisymmetric model of a pressure vessel 122 Fig. 4.8. Axisymmetric model of the forming of a calculator battery assembly. 122 Fig. 4.9. Axisymmetric model of an engine valve stem 123 Fig. 4.10. Axisymmetric model of a hydraulic cylinder piston 123 Fig. 4.11. Solid CAD model of steel hole punch 124 Fig. 4.12. Axisymmetric analyses of hole punch (a) without hole feature and (b) with hole cutout 125 Fig. 4.13. CAD solid model of pressure vessel lid 126 Fig. 4.14. Four constraint conditions and resulting displacement plots for the pressure vessel lid 127 Fig. 4.15. Three symmetry planes for a domed pressure vessel with the section required for an internal pressure load 128 Fig. 4.16. GAD solid model of stamped flange 129 r Products with Finite Element Analysis Tig. 4.17. Fan blade and hub model 130 Fig. 4.18. Turbine blade model with cyclic symmetry instance exploded 130 Fig. 4.19. Flywheels undergo windup in the transient portion of start up and are good candidates for cyclic symmetry 130 Fig. 4.20. Cyclic symmetry can be used on an instance of a motor rotor 131 Fig. 4.21. Cyclic symmetry concepts can be simulated with planar symmetry in this press fit model 132 Fig. 4.22. An odd number of features in an otherwise symmetric model can be simulated with radial cut planes as long as the loading is radial 132 Fig. 4.23. Construction of anti symmetry results 133 Fig. 4.24. Ring under internal pressure with a point constraint at the bottom and symmetry constraints. The smaller internal ring is the undeformed model for reference 134 Fig. 4.25. Full shell model of stamped flange with symmetry constraints on the appropriate planes 135 Fig. 4.26. Schematic representation of a rod element 136 Fig. 4.27. Beam element coordinate system. 137 Fig. 4.28. Linear (a), quadratic (b), and p element (c) beam elements 138 Fig. 4.29. Stress recovery points for an I beam cross section in FEMAP 139 Fig. 4.30. A displacement plot showing the difference in torsional stiffness of a closed tube (a), and a split tube with the free end constrained to remain planar (b) 140 Fig. 4.31. The orientation of a section greatly affects its ability to carry a bending load. . 141 Fig. 4.32. Linear and quadratic shell element types 142 Fig. 4.33. Shell mid planes can be offset to better capture thickness variations or a stack of plates 143 Fig. 4.34. Tapered or drafted walls can be modeled with (i) tapered shell elements, (ii) a median thickness, or (iii) a stepped thickness reduction 143 Fig. 4.35. Normals of shell elements in this bottle model point inward 144 Fig. 4.36. If shell normals are not consistent, discontinuities in stress results may appear. 145 List of Figures Fig. 4.37. "Virtual" overlap of the shell geometry as interpreted by the solver. . 146 Fig. 4.38. Steps required to break an I beam cross section into a shell model 147 Fig. 4.39. Thick walled weldments may not be good shell model candidates 148 Fig. 4.40. Solid CAD model of a cast cross brace 148 Fig. 4.41. Stress results of a shell model of the cast cross brace 148 Fig. 4.42. Plane stress model of thin walled panel 149 Fig. 4.43. Solid model of thin walled panel. 149 Fig. 4.44. Shell model of thin walled panel. 150 Fig. 4.45. Local mesh refinement of shell model near cutout 151 Fig. 4.46. Chunky solid CAD models are likely candidates for solid FEA models 152 Fig. 4.47. Common solid element shapes. . 153 Fig. 4.48. Comparison of an automeshed valve stem to a revolved brick mesh 154 Fig. 4.49. Spring elements can be used in a simulation in the same way as they are used in the actual part 156 Fig. 4.50. Schematic representation of damper element 157 Fig. 4.51. Mass element tied to vertical plate with rigid links 157 Fig. 4.52. Pro/ENGINEER mass property listing for solid part 158 Fig. 4.53. Use rigid elements to distribute beam moments at the correct footprint on a shell model 159 Fig. 4.54. Rigid elements enable meshes of dissimilar densities to be quickly connected. 160 Fig. 4.55. Gap element orientation 161 Fig. 4.56. Gap elements ensure that the load transfer beyond the root of the weld is correct 162 Fig. 4.57. Gap elements enable shaft to transmit load to retaining bore 162 Fig. 4.58. Slide line contact regions required to model battery assembly 163 Fig. 4.59. Slide line elements allow spur gear teeth to load each other naturally 164 Fig. 4.60. This sliced hemisphere can contact the plate in three dimensions using radially oriented slide lines 165 XXIII Fig. 4.61. This automotive bumper can contact the pole correctly using parallel slide lines 165 Fig. 4.62. General 3D contact regions are required to model impact between crossing cylinders 166 Fig. 4.63. Schematic representation of friction correlation fixture 167 Fig. 4.64. Pulley and mount assembly 168 Fig. 4.65. Solid element analysis of shaft component 168 Fig. 4.66. Shaft loading will produce a 'Y1 moment and a 'Z' lateral shear load on the flange 169 Fig. 4.67. Load path to base causes moments in both 'V and 'Z' with the 'X' oriented lateral shear 170 Fig. 4.68. Special handling is required to transition solid shaft to shell flange mesh. 171 Fig. 4.69. Depending on its geometry, a single part may need to transition from one element type to another 172 Fig. 4.70. Pressure loading on the gusset will cause significantly different displacements if the shell solid transition is ignored (a) and correctly adjusted for load transfer (b). . 172 Fig. 4.71. Test model of transitioning mesh as a continuous solid can aid in results interpretation 173 Fig. 5.1. Potato shaped parts usually mesh cleanly and solve well with automeshed tetrahedrons 178 Fig. 5.2. Parts similar to this one must clearly be modeled with solid elements 181 Fig. 5.3. Designer's choice of feature size controls the creation of dirty geometry. . 182 Fig. 5.4. Short edges on large faces can cause highly distorted elements or a failed mesh. 182 Fig. 5.5. This short edge was created by the proximity of two nearly aligned surfaces. . 183 Fig. 5.6. Sloppy geometry creation often causes small cracks or gaps in faces that are difficult to visually detect 184 Fig. 5.7. These two cylindrical features are offset only slightly 184 Fig. 5.8. As the two curved edges approach each other, a surface dimension much smaller than any part feature is created. 185 xxiV Building Beth Fig. 5.9. More thought on aligning these two features would have eliminated the sliver surface 185 Fig. 5.10. Sliver surface caused by a slightly undersized fillet 186 Fig. 5.11. A fillet across this shallow angle has created a difficult meshing situation 186 Fig. 5.12. It is extremely easy to accidentally create voids in a solid model while designing a new part 187 Fig. 5.13. A p element mesher which maps the element definition to the geometry definition is highly sensitive to any type of inconsistency 188 Fie. 5.14. Always try to avoid fragile dimensions such as depicted here 190 Fig. 5.15 Distributing load across bolt head or washer diameter can be achieved with patches 195 Fig. 5.16. While the actual location of the supporting beam represented by the rectangular patch might be off the part edge by a wall thickness or two, this small adjustment should not affect the reliability of die shell model 195 Fig. 5.17. Proper orientation of split surfaces facilitates the application of loads 196 Fig. 5.18. The mounting tab on this connector can easily be decoupled for submodeling. 197 Fig. 5.19. Connecting rod can be divided into two separate studies due to uniaxial nature of loading 198 Fig. 5.20. Initial geometry can be coarser. . 199 Fig. 5.21. As behavior of part is clearer, fillets are added to ensure that the stress distribution captured is correct 199 Fig. 5.22. The final analysis can have a much tighter mesh because a considerable amount of detail was removed from areas with no structural concerns 200 Fig. 5.23. The overall size of this part is so large in comparison to its wall thickness that a mid plane model will behave nearly the same as a mesh on the outer surface 203 Fig. 5.24. The time spent developing a mid plane surface of this geometry would probably not pay off. 203 Fig. 5.25. This thick walled part is questionable from a shell modeling standpoint, but must certainly be modeled at mid plane in order to achieve any level of accuracy 204 w Products with Finite Element Analysis Fig. 5.26. Solid model corrupted by IGES transfer 206 Fig. 5.27. With corrupted surfaces removed and rebuilt, the part is ready to mesh. . . . 207 Fig. 5.28. One rib pattern may appear visually to provide the best stiffness 208 Fig. 5.29. However, a drastically different pattern might actually be the better choice 209 Fig. 5.30. A simple beam model can quickly allow you to evaluate options, whereas a solid model of the wire rack would be nearly impossible to mesh and solve 211 Fig. 5.31. This shell model can be modified quickly and easily in pusuit of an optimal design 211 Fig. 5.32. A simple representation of a solid can be meshed with brick elements for a quick and reliable study 212 Fig. 5.33. Use surface patches to aid in aligning assembly components 213 Fig. 5.34. New bracket design must have mounting features as shown and fit within the specified envelope 214 Fig. 5.35. Evaluate drastically different approaches independently instead of trying to develop a single model that can capture all possibilities 215 Fig. 5.36. Holes shown in configuration at left can "merge" to create the larger opening shown at right if dimensioned properly. . 215 Fig. 5.37. By making the rib height less than plate thickness, the rib can be made to "disappear" in an optimization study 216 Fig. 5.38. A simple plate with a rectangular hole may require more complex dimensioning for an optimization study than for detailing a single design 217 Fig. 5.39. Order of creation becomes important if an optimizer is allowed to adjust the position of overlapping features 218 Fig. 6.1. Examples of good (a) and not so good (b) habits for shell property entries in Pro/MECHANICA 220 Fig. 6.2. FEMAP material property entry window 223 Fig. 6.3. Plate with stiffeners 227 Fig. 6.4. Inertia modeling comparison: point mass model without MMOI input (a) versus the full model (b) 230 Fig. 7.1. Sketch of a sheet metal weldment. 243 List of Figures Fig. 7.2. Sample 244 Fig. 7.3. Sample 244 Fig. 7.4. Sample 244 Fig. 7.5. Sample 244 Fig. 7.6. Sample 244 Fig. 7.7. Initial mesh on model 245 Fig. 7.8. Plot showing edges of shell elements not connected to other elements 245 Fig. 7.9. Four element distortion types to be controlled in the model 246 Fig. 7.10. Trapezoid like surface illustrating meshing of irregular surface 247 Fig. 7.11. Rectangular surface mesh biased toward one corner (a), and revolved mesh biased toward axis of revolution (b) 248 Fig. 7.12. Mesh showing use of patches to transition from a tight to a loose mesh. . . 249 Fig. 7.13. Shell model of rubber boot (a), corrected shell model with normals all pointing out (b), and final solid mesh (c). 251 Fig. 7.14. Mesh sections illustrating mid side nodes on linear edge of element (a) and mid side nodes on the curvature of geometry (b) 253 Fig. 7.15. Model illustrating slave surface allowed to slide parallel to master 256 Fig. 7.16. Illustration of proper way to tie shell mesh to solid mesh with MPCs 257 Fig. 8.1. FEA of motorcycle wheel 260 Fig. 8.2. Simple FEA of seat portion of chair subject to central loading 262 Fig. 8.3. Revised FEM boundary condition scheme for chair seat 266 Fig. 8.4. Plane stress model of plate with coupled strain unrestricted (a) and with coupled strain restricted (b) 268 Fig. 8.5. FEM and results of joint member at end of long shaft in tension, using uniaxial constraint (a) and full constraint at the modeling cut (b) 268 Fig. 8.6. Comparison of a point load versus distributed counterpart in a plane stress model 272 Fig. 8.7. Bracketing the boundary conditions of a chair analysis, using (a) infinite friction and (b) no friction 275 Fig. 8.8. User coordinate system types supported by most analysis codes 278 XXV Fig. 8.9. Plane stress FEA results of lifting lever using "incorrect" Cartesian constraint (a) and "correct" cylindrical constraint (b). . 279 Fig. 8.10. FEA constraints and their geometric equivalent in classic beam calculations. . . 281 Fig. 8.11. FEMs and results of half symmetry (a) and quarter symmetry models (b) of joint member presented in Fig. 8.5 283 Fig. 8.12. Equivalent symmetry constraints for solid and shell models 285 Fig. 8.13. Enforced displacement fastener interface 286 Fig. 8.14. Symmetry FEM of shaft clamp with corresponding results 287 Fig. 8.15. Linear versus follower forces at end of cantilevered beam 292 Fig. 8.16. Plane stress FEMs of suspension coupler link using different boundary conditions 295 Fig. 8.17. Baseline: FEA von Mises stress results of Fig. 8.16(a). Deformation display scale factor =1 296 Fig. 8.18. FEA von Mises stress results of Figs. 8.16 (a), (b), and (c). Deformation display scale factor = 500 297 Fig. 8.19. FEA von Mises stress results of Figs. 8.16 (a), (d) and (e). Deformation display scale factor = 500 298 Fig. 8.20. FEA von Mises stress results of Figs. 8.16 (a), (f), and (g). Deformation display scale factor = 500 299 Fig. 9.1. Shell mesh of motor end cap 307 Fig. 9.2. Correct free edge plot of motor end cap (a), and incorrect free edge plot of motor end cap showing cracks between sections of the mesh (b) 307 Fig. 10.1. Rectangle method for determining the area under a curve 314 Fig. 10.2. Area estimate improves with the resolution of the rectangles 314 Fig. 10.3. As the number of nodes increases, the mesh can conform to the geometry more precisely 315 Fig. 10.4. Simple nodal error estimate 318 Fig. 10.5. Two stress conditions with seemingly conflicting error estimates. . .318 Fig. 10.6. Convergence of beam in pure bending 319 Fig. 10.7. Convergence of plate with a hole. 320 xxW Building Beth Fig. 10.8. Convergence plot and resultant mesh for a valve handle 321 Fig. 10.9. Convergence plot and resultant mesh for a parts bin 321 Fig. 10.10. P element mesh and convergence plot of valve handle 322 Fig. 10.11. P element mesh and convergence plot of parts bin 323 Fig. 11.1. Flowchart of recommended method for viewing results 326 Fig. 11.2. Pro/MECHANICA FEM of an axially loaded section of a suspension component (a), and resulting animation display (b) 327 Fig. 11.3. Pro/MECHANICA displacement fringe plot of suspension component section 329 Fig. 11.4. Pro/MECHANICA von Mises stress results of a tet element automesh (a) and a hex element hand mesh (b) of a suspension component section 330 Fig. 11.5. Stress results of an assembly (a), one of its members (b), and a cut section of the member (c). This was done using groups in Pro/MECHANICA 333 Fig. 11.6. Pro/MECHANICA min principal (a) versus max principal (b) versus von Mises (c) stress results of a lug analysis 337 Fig. 11.7. Axial (a) versus bending (b) versus total stress (c) for the same beam model solution 339 Fig. 11.8. Pro/MECHANICA von Mises stress results of an intentionally underconverged analysis of a drilled plate under tension: standard (a), averaged (b), and continuous tone (c) 343 Fig. 11.9. Isolines (a) and isosurfaces (b) of the same model solution 344 Fig. 11.10. Querying within a fringe plot. . .345 Fig. 11.11. Maximum principal stress vector plot 345 Fig. 11.12. Von Mises stress results for an analysis of a drilled plate: fringe plot (a), graph along shell edges following the hole definition curve (b), and maximum of the model as a function of polynomial order (c) 346 Fig. 12.1. Initial design of winch support machined from a block of steel 358 Fig. 12.2. First design option for casting the winch mount 359 r Products with Finite Element Analysis Fig. 12.3. Second design option for casting the winch mount 359 Fig. 12.4. Third design option for casting the winch mount 360 Fig. 12.5. A finite element model of the first design casting option 360 Fig. 12.6. A finite element model of the second design casting option 360 Fig. 12.7. A finite element model of the third design casting option 360 Fig. 12.8 Sensitivity plot for the part height of casting option 1 362 Fig. 12.9 Sensitivity plot for the nominal wall thickness of casting option 1 362 Fig. 12.10. Sensitivity plot for Young's modulus and density combined 362 Fig. 12.11. Global sensitivity plot of von Mises stress versus the angular position of the second hole in the plate appearing in Fig. 12.12. 364 Fig. 12.12. Plate with two holes used for the global sensitivity study 364 Fig. 12.13. Global sensitivity study of the first natural frequency versus part height of casting option 1 365 Fig. 12.14. Global sensitivity study of the first natural frequency versus nominal wall thickness of casting option 1 366 Fig. 12.15. Winch mount geometry suggested by Hyperstruct 370 Fig. 12.16. Cross section of Hyperstruct solution of the winch mount 370 Fig. 12.17. 3D parameter space for two parameters 372 Fig. 12.18. Pro/MECHANICA setup form for the winch mount optimization 373 Fig. 12.19. Weight versus optimization pass showing the weight improvement as features are adjusted. At pass 3, too much material was removed and a correction can be seen in the plot 374 Fig. 13.1. Two bolted housings under an axial tensile load. The narrow flanged part (a) can be coupled at the entire interface surface without any loss in model integrity. The wide flanged part (b) undergoes enough deflection in the flange to warrant some thought as to where to join the interface surface with its mating part 381 List of Figures Fig. 13.2. Shell model of housing assembly constructed with different nominal mesh sizes at the interface surface. If the interface can be assumed continuous, rigid links can bridge the two parts for proper load transfer. . 382 Fig. 13.3. Solid model of shaft in journal. . 383 Fig. 13.4. Beam/shell model of shaft in journal with rigid elements forcing in plane moment transfer between shaft and plate 384 Fig. 13.5. Two plate models pinned at bases and loaded with a uniform pressure on the left face. The assembly in (a) is modeled as if the coincident edges are welded and (b) is modeled as if they are hinged. The resulting deformation is noticeably different 385 Fig. 13.6. Two plates attached with a beam element representing a bolt. The load at the end of the bolt is transferred to the plates with a spider web of rigid elements to increase the effective surface area 386 Fig. 13.7. Plane stress model of fillet weld in which vertical plate was too thick for full penetration 392 Fig. 13.8. Stress distribution in welded section can be affected by contact conditions between unwelded surface areas. Case (a) shows a contact interface, and (b) shows the joint with no contact 393 Fig. 13.9. Fittings or mounting hardware can stiffen the interface of two beams. The additional stiffness of this coupling was modeled with two plate elements 399 Fig. 13.10. The thin plate in these models is attached to the stationary frame with a single fastener on each end (a) and four fasteners (b). As the number of fasteners increases, the interface behaves more as if it were continuous than jointed 401 Fig. 13.11. Symmetry model of pipe clamp with initial penetration of fastener. All contact regions noted in the figure are important to total system response 402 Fig. 13.12. Beam model of shaft tied to plate with rigid elements to induce moment on plate. 405 Fig. 13.13. Beam model of shaft tied to plate with stiff springs so that no moment is transferred to plate 405 Fig. 13.14. Solid model of shaft in journal with contact conditions between shaft and ends of bore 406 xxvii Fig. 13.15. Solid model of shaft in journal with stiff springs coupling shaft and ends of bore around entire perimeter of shaft 406 Fig. 13.16. Solid model of shaft in journal with stiff springs only coupling portions of interface expected to be in compression. .406 Fig. 14.1. Sample parts intended to work in extremely hot or cold conditions 412 Fig. 14.2. Plane stress model of two fillet welds and stress fields calculated by thermal contraction of beads 416 Fig. 14.3. Tray modeled with isotropic properties, uniform wall thickness, and no draft 417 Fig. 14.4. Displacement results of tray modeled as shell 417 Fig. 14.5. Stress plot for a plane stress model of plate containing an unrestricted hole. .418 Fig. 14.6. Stress results for a model cooled with hole radius fixed using a radial constraint on a cylindrical coordinate system 419 Fig. 14.7. Desired radial press fit of 0.001. . .420 Fig. 14.8. Motor end cap 421 Fig. 14.9. First approach 422 Fig. 14.10. Second approach 422 Fig. 15.1. Newton Raphson method for stiffness updates 436 Fig. 15.2. Modified Newton Raphson method can fail when hard 437 Fig. 15.3. Modified Newton Raphson method can fail when hardening is involved 438 Fig. 15.4. Bilinear material model 441 Fig. 15.5. Trilinear material model 442 Fig. 15.6. Multilinear stress strain curve and data points that generated the curve. 443 Fig. 15.7. Stress strain curves offset by temperature and strain rate 443 Fig. 15.8. Flat plate under uniform pressure with two constraint cases: pinned guided (a) and pinned pinned (b) 445 Fig. 15.9. Plots of nonlinearity for two constraint cases described above 446 Fig. 15.10. Rubber and elastomeric parts require a hyperelastic solution for accurate simulation 448 Fig. 15.11. Initially distorting elements can ensure that the final shape will be valid. . 459 xxviii Building Bette Fig. 15.12. Pressure versus displacement of uniformly loaded flat plate linear and nonlinear. 461 Fig. 16.1. Simplified soda can with a 2001b person standing squarely on top of it. . . . 468 Fig. 16.2. Beam FEA model of the can, and results of its first buckling mode 470 Fig. 16.3. Shell FEA model of the can, and results of its first buckling mode 472 Fig. 16.4. 20" soda can, first buckling mode results of beam FEA and shell FEA 473 Fig. 16.5. 65" and 100" soda can, first buckling mode results of beam FEA and shell FEA. 474 Fig. 17.1. Simple cantilevered beam model. 478 Fig. 17.2. FEA results of simple beam model.479 Fig. 17.3. Longitudinal mode shape of a ultrasonic welding horn 481 Fig. 17.4. Stepped cylinder for modal study. 482 r Products with Finite Element Analysis Fig. 17.5. Schematic representation of two vibratory modes of free and constrained cylinder 483 Fig. 17.6. Flat steel disk for symmetry study. 485 Fig. 18.1. Basic components of a dynamic response analysis 490 Fig. 18.2. Typical frequency versus amplitude plot 491 Fig. 18.3. Combining static and dynamic results to produce a nonzero mean output 493 Fig. 18.4. 1994 Nordiridge earthquake data in time history format (a) and as a power spectral density format overlaid on the Uniform Building Code (UBC) PSD standard for eardiquake design (b) 497 Fig. 18.5. Response amplification at various damping values as the operating frequency approaches the first natural frequency. . 501 Table 2.1. Converting principal strain values to principal stress 40 Table 2.2 Maximum shear stress formulas for selected standard cross sections 44 Table 2.3. Representative damping ratios. .83 Table 8.1. Boundary'condition singularities for each element type 273 Table 8.2. Equivalent degrees of freedom in common coordinate system types 278 Table 8.3. Consistent set of units for standard steel in I P S and mm N S unit schemes . .288 Table 8.4. Commonly used conversion factors '. 289 Table 12.1. Summary of casting design option preliminary analysis results 361 Table 12.2. Range of parameter values used in full parameter response study 365 Table 13.1. Typical friction factors for calculating bolt loading 403 Table 14.1. Representative thermal expansion coefficients for commonly used materials .413 Table 16.1. Analytical buckling results of a fixed free soda can subject to a coaxial 2001b compressive load applied to its free rim . 472 Table 17.1. Modal results for a thin disk using various combinations of symmetry. .486 Table 18.1. Modal method versus direct method comparison 499 Table 18.2. Representative damping ratios as percent of critical damping 500 Table 19.1. Overview of selected industry preprocessors 512 Table 19.2. Overview of selected industry solvers 525 Table 19.3. Overview of selected industry postprocessors 527 Table 20.1. Information for evaluating required FEA solution types and modeling methods supported by your preprocessor 537
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spelling	Adams, Vince 1963- Verfasser (DE-588)1146215606 aut Building better products with finite element analysis Vince Adams and Abraham Askenazi Finite element analysis 1st. edition Santa Fe, NM Onword Press 1999 xxxii, 587 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Produktentwicklung (DE-588)4139402-1 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf CAD (DE-588)4069794-0 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 Produktentwicklung (DE-588)4139402-1 s Askenazi, Abraham Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008482851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Adams, Vince 1963- Askenazi, Abraham Building better products with finite element analysis Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd Produktentwicklung (DE-588)4139402-1 gnd CAD (DE-588)4069794-0 gnd
subject_GND	(DE-588)4017233-8 (DE-588)4139402-1 (DE-588)4069794-0
title	Building better products with finite element analysis
title_alt	Finite element analysis
title_auth	Building better products with finite element analysis
title_exact_search	Building better products with finite element analysis
title_full	Building better products with finite element analysis Vince Adams and Abraham Askenazi
title_fullStr	Building better products with finite element analysis Vince Adams and Abraham Askenazi
title_full_unstemmed	Building better products with finite element analysis Vince Adams and Abraham Askenazi
title_short	Building better products with finite element analysis
title_sort	building better products with finite element analysis
topic	Finite element method Finite-Elemente-Methode (DE-588)4017233-8 gnd Produktentwicklung (DE-588)4139402-1 gnd CAD (DE-588)4069794-0 gnd
topic_facet	Finite element method Finite-Elemente-Methode Produktentwicklung CAD
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008482851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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