Transcription
Advanced CAE Applications for ProfessionalsSoftware that works — for you.SMUAI/NASTRAN User’s Guidefor Version 20.1UNIVERSAL ANALYTICS, INC.
Publication ND-002 1993-1999 UNIVERSAL ANALYTICS, INC.Torrance, California USAAll Rights ReservedFirst Edition, February 1991Second Edition, December 1992Third Edition, April 1994Fourth Edition, September 1995Fifth Edition, December 1997Sixth Edition, March 1999Restricted Rights Legend:The use, duplication, or disclosure of the information contained in this document is subject to therestrictions set forth in your Software License Agreement with Universal Analytics, Inc. Use, duplication, or disclosure by the Government of the United States is subject to the restrictions set forth inSubdivision (b)(3)(ii) of the Rights in Technical Data and Computer Software clause, 48 CFR252.227-7013.The concepts and examples contained herein are for educational purposes only and are not intended tobe exhaustive or to apply to any particular engineering problem or design. All information is subjectto change without notice. Universal Analytics Inc. does not warrant that this document is free oferrors or defects and assumes no liability or responsibility to any person or company for direct orindirect damages resulting from the use of any information contained herein.UNIVERSAL ANALYTICS, INC.3625 Del Amo Blvd., Suite 370Torrance, CA 90503Tel: (310) 214-2922FAX: (310) 214-3420
User’s GuideFOREWORDThe UAI/NASTRAN User’s Guide provides you with detailed information on the modelingand analytical disciplines of the system. It includes descriptions of finite elements, hints toimprove your modeling practices, examples of Bulk Data use and many sample problems andtheir solutions. It is strongly recommended that you review this guide thoroughly beforeusing a UAI/NASTRAN capability which is new to you.This manual includes thirty-one Chapters which are divided into five parts:INTRODUCTION1. FINITE ELEMENT MODELING2. ANALYSIS DISCIPLINES3. SPECIAL TOPICS4. GRAPHICSThe Introduction provides you with an overview of UAI/NASTRAN and an orientation to thesystem from both the software and engineering perspectives. Part I then describes the processof creating finite element models with UAI/NASTRAN. It describes not only the finite elementlibrary, but provides general information regarding boundary conditions, loads, and materialproperties. Part II of the manual provides you with detailed descriptions of the analyticaldisciplines available in the system. Special analysis techniques are discussed in Part III, and,finally, Part IV illustrates the use of the UAI/NASTRAN graphics capabilities and interfaceswith other software products.The companion to this volume is the UAI/NASTRAN User’s Reference Manual. The ReferenceManual provides you with detailed information on the modeling describing all of the inputdata used by the system.NASTRAN is a registered trademark of the National Aeronautics and Space AdministrationUAI/NASTRANi
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User’s GuideVERSION 20.1 RELEASE NOTESIn Version 20.1 of UAI/NASTRAN, there have been a number modifications to the User’s Guideto describe new features. These are summarized, by Chapter, in this section. In addition, therehave been many corrections and clarifications throughout the manual. Many of the datachanges required for new and enhanced analytic capabilities are found in the User’s ReferenceManual.ONLINE DOCUMENTATIONAs part of UAI’s ongoing modernization program, all UAI/NASTRAN manuals, as well as thosefor other UAI software products, continue to be delivered in Adobe Portable Document File(PDF) format. This allows them to be used online with any computer having the Adobe Acrobat Reader (Version 3.0 or later). This reader is also delivered with our software.To insure prompt updates to all documentation, any changes and enhancements may bedownloaded from UAI’s Web site at www.uai.com.DOCUMENTATION TRACKINGBeginning with Version 20.1, the documentation has been slightly modified so that each pageof specific commands and data entries has a revision date on it. The two forms are: New:V20.1, indicating that the page is new with the current release; and Rev: V20.1, which indicates that the page has been modified for the current release. In this manual, only the firstpage of new or revised Chapters is noted.Chapter 2. Orientation: The Software System Description of the additional FEMAP interface and changes to the SDRC IDEA-Sinterface.UAI/NASTRANRELEASE NOTES iii
User’s GuideChapter 5. The Finite Element Library Description of a new capability to compute equivalent Beam forces for sets of solidelements. Correction of solid element stress equations. Changes to the NLSTRAIN and NLSTRESS commands to add features missing fromearlier documentation.Chapter 6. Boundary Conditions and Equation Reduction Description of new capability to perform automatic reduction using the AUTOREDUCE command. Both Guyan reduction and Modal Reduction (including CraigBampton) may be performed using this feature. The reduced models may then beoutput, by using the new EXPORT command, on DMIG Bulk Data entries.Chapter 9. Dynamics Modeling Modified to include information on the automatic static and Modal reduction features (AUTOREDUCE).Chapter 10. Linear Static Analysis Expanded to include description of matrix conditioning checks for inertial reliefproblems.Chapter 16. Material Nonlinear Analysis Reflects the name change of the AUTOREDUCE command to NLREDUCE, and provides updated results for sample problems.Chapter 17. Geometric Nonlinear Analysis Typographic correctionsChapter 19. Substructuring Analysis Additional description of APP DMAP with substructuring.Chapter 25. Multidisciplinary Design Optimization Description of a new mode tracking feature used in the design of models withfrequency constraints, and the addition of modal damping as a design variable.iv RELEASE NOTESUAI/NASTRAN
User’s GuideTABLE OF CONTENTSFOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iRELEASE NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vLIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiLIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiChapter 1: OVERVIEW . . . . . . . . . . . .1.1THE DOCUMENTATION SUITE1.2FORMAT OF THIS MANUAL . .1.3REPORTING PROBLEMS . . .1-11-31-41-5Chapter 2: ORIENTATION: THE SOFTWARE SYSTEM . .2.1THE SYSTEM ARCHITECTURE . . . . . . . . .2.2THE UAI/NASTRAN INPUT DATA STREAM . .2.3CONTROL MECHANISMS FOR UAI/NASTRAN2.4DYNAMIC MEMORY MANAGEMENT . . . . . .2-12-22-32-52-62.52.62.72.8.THE eBase DATABASE . . . . . . . . . . . . . . . . . . . . . . . . 2-7The CHECKPOINT/RESTART Concept . . . . . . . . . . . . . . . . . . . . . 2-12WHAT IS A CONFIGURATION? . . . . . . . . . . . . . . . . . . . . . . . . . 2-15INTERFACING WITH OTHER PROGRAMS . . . . . . . . . . . . . . . . . . 2-20Chapter 3: ORIENTATION: THE ENGINEERING ANALYSIS SYSTEM . . . . .3.1OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2STANDARD UAI/NASTRAN STRUCTURAL ANALYSES . . . . . . .3.3SPECIAL UAI/NASTRAN CAPABILITIES . . . . . . . . . . . . . . .3.4PRACTICAL ASPECTS OF MODELING . . . . . . . . . . . . . . . . .3.5SPECIAL ALTERs FOR UAI/NASTRAN ENHANCED CAPABILITIESUAI/NASTRAN. 3-1. 3-2. 3-43-113-143-18TABLE OF CONTENTS v
User’s GuideChapter 4: THE FINITE ELEMENT IDEALIZATION4.1OVERVIEW . . . . . . . . . . . . . . . .4.2GRID POINTS AND OTHER DEGREES4.3FINITE ELEMENT CONVERGENCE . . . .OF. . . . . . . . . . . . . .FREEDOM. . . . . . . 4-1. 4-2. 4-34-14. 5-1. 5-2. 5-35-125-255-305-335-385-395-42Chapter 6: BOUNDARY CONDITIONS AND EQUATION REDUCTION6.1SYSTEM MATRIX ASSEMBLY . . . . . . . . . . . . . . . .6.2DIRECT MATRIX INPUT . . . . . . . . . . . . . . . . . . .6.3THE REPRESENTATION OF DISPLACEMENT SETS . . .6.4DEPENDENT DEGREES OF FREEDOM . . . . . . . . . .6.5FIXED AND ENFORCED MOTION . . . . . . . . . . . . . .6.6REDUCTION OF EQUATIONS OF MOTION . . . . . . . .6.7THE AUTOMATIC REDUCTION FEATURES . . . . . . . .6.8THE NLREDUCE FEATURE . . . . . . . . . . . . . . . . .6.9RETAINING a-set DEGREES OF FREEDOM . . . . . . . .6.10SOLVING FREE BODY MODELS . . . . . . . . . . . . . .6.11DYNAMIC RESPONSE MATRICES . . . . . . . . . . . . .6.12REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . 6-1. 6-2. 6-4. 6-5. 6-86-156-216-276-316-326-336-346-35Chapter 7: STRUCTURAL LOADS . . . . . . . .7.1SELECTING STATIC LOADS . . . . .7.2MECHANICAL LOADS . . . . . . . . .7.3INERTIAL LOADS . . . . . . . . . . .7.4ENFORCED DISPLACEMENTS . . .7.5INITIAL STRAINS . . . . . . . . . . .7.6THERMAL LOADS . . . . . . . . . . .7.7COMBINING LOADING CONDITIONS7.8NONLINEAR STATIC LOADS . . . . .7.9DYNAMIC LOADS . . . . . . . . . . . 7-1. 7-2. 7-3. 7-7. 7-97-107-117-137-147-15Chapter 5: THE FINITE ELEMENT LIBRARY . . . . . . . .5.1INPUT DATA REQUIREMENTS — GENERAL .5.2ONE-DIMENSIONAL ELEMENTS . . . . . . . .5.3TWO-DIMENSIONAL ELEMENTS . . . . . . . .5.4THREE-DIMENSIONAL ELEMENTS . . . . . . .5.5THE SCALAR ELEMENTS . . . . . . . . . . . .5.6SPECIALTY ELEMENTS . . . . . . . . . . . . .5.7THE ELEMENT MASS MATRIX FORMULATION5.8AUTOMATICALLY GENERATED DATA . . . . .5.9OUTPUT REQUESTS — GENERAL . . . . . . .vi TABLE OF CONTENTS.UAI/NASTRAN
User’s GuideChapter 8: MATERIAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . .8.1FINITE ELEMENTS AND MATERIAL PROPERTIES . . . . . . . . . . .8.2NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.3LINEAR MATERIALS — HOOKE’S LAW . . . . . . . . . . . . . . . . . .8.4HEAT TRANSFER MATERIAL PROPERTIES . . . . . . . . . . . . . . .8.5NONLINEAR MATERIAL PROPERTIES . . . . . . . . . . . . . . . . . .8.6COMPOSITE MATERIAL PROPERTIES . . . . . . . . . . . . . . . . . .8.7VISCOELASTIC MATERIAL PROPERTIES . . . . . . . . . . . . . . . . .8.8FREQUENCY DEPENDENT STIFFNESS AND DAMPING PROPERTIES. 8-1. 8-2. 8-4. 8-58-108-118-128-138-14Chapter 9: DYNAMICS MODELING . . . . . . . . . .9.1SUMMARY OF CAPABILITIES . . . . . .9.2MASS MODELING . . . . . . . . . . . . .9.3DAMPING MODELING . . . . . . . . . .9.4DIRECT MATRIX INPUT . . . . . . . . .9.5REDUCTIONS IN DYNAMIC ANALYSIS. 9-1. 9-2. 9-4. 9-89-129-14Chapter 10: LINEAR STATIC ANALYSIS . .10.1MATHEMATICAL BACKGROUND10.2THE STATIC ANALYSIS MODEL10.3INPUT DATA REQUIREMENTS .10.4SOLUTION RESULTS . . . . . . .10-110-210-410-510-10.Chapter 11: NORMAL MODES ANALYSIS . . .11.1MATHEMATICAL BACKGROUND . .11.2INPUT DATA REQUIREMENTS . . .11.3SOLUTION RESULTS . . . . . . . . .11.4METHOD SELECTION GUIDELINES. 11-1. 11-211-1011-1411-18Chapter 12: COMPLEX EIGENVALUE ANALYSIS12.1MATHEMATICAL BACKGROUND . . .12.2INPUT DATA REQUIREMENTS . . . .12.3SOLUTION RESULTS . . . . . . . . . .Chapter 13: FREQUENCY AND RANDOM RESPONSE ANALYSIS13.1MATHEMATICAL BACKGROUND . . . . . . . . . . . . .13.2FREQUENCY DOMAIN EXCITATIONS . . . . . . . . . .13.3INPUT DATA REQUIREMENTS . . . . . . . . . . . . . .13.4SOLUTION RESULTS . . . . . . . . . . . . . . . . . . .13.5MODELING GUIDELINES . . . . . . . . . . . . . . . . . .13.6EXAMPLE PROBLEMS . . . . . . . . . . . . . . . . . . . 13-1. 13-213-1213-1413-2013-2313-26Chapter 14: TRANSIENT RESPONSE ANALYSIS14.1MATHEMATICAL BACKGROUND . . .14.2TIME DOMAIN EXCITATIONS . . . . .14.3INPUT DATA REQUIREMENTS . . . .14.4SOLUTION RESULTS . . . . . . . . . .14.5MODELING GUIDELINES . . . . . . . .14.6EXAMPLE PROBLEM . . . . . . . . . . 14-1. 14-2. -8TABLE OF CONTENTS vii
User’s GuideChapter 15: RESPONSE SPECTRUM ANALYSIS15.1GENERAL APPROACH . . . . . . . .15.2MATHEMATICAL BACKGROUND . .15.3INPUT DATA REQUIREMENTS . . .15.4SOLUTION RESULTS . . . . . . . . .15.5EXAMPLE PROBLEM . . . . . . . . . 15-1. 15-2. 15-315-1015-1415-15. 16-1. 16-3. 16-416-1016-1116-2216-2916-3316-35Chapter 17: GEOMETRIC NONLINEAR ANALYSIS . . . . . . . . . . . . . . .17.1TERMINOLOGY AND CAPABILITIES . . . . . . . . . . . . . . . . .17.2MATHEMATICAL BACKGROUND - INTRODUCTION . . . . . . . .17.3MATH BACKGROUND - GEOMETRIC NONLINEAR ANALYSIS . .17.4MATH BACKGROUND - DIFFERENTIAL STIFFNESS APPROACH17.5INPUT DATA FOR GEOMETRIC NONLINEAR ANALYSIS . . . . .17.6EXAMPLE PROBLEMS - GEOMETRIC NONLINEAR ANALYSIS .17.7INPUT DATA - DIFFERENTIAL STIFFNESS APPROACH . . . . .17.8EXAMPLE PROBLEMS - DIFFERENTIAL STIFFNESS APPROACH17.9REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17.10 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 18: BUCKLING ANALYSIS . . . . . . . .18.1TERMINOLOGY . . . . . . . . . . . . .18.2MATHEMATICAL BACKGROUND . . .18.3INPUT DATA REQUIREMENTS . . . .18.4SOLUTION RESULTS . . . . . . . . . .18.5MODELING GUIDELINES . . . . . . . .18.6PERFORMING BUCKLING ANALYSESChapter 16: MATERIAL NONLINEAR ANALYSIS16.1TERMINOLOGY . . . . . . . . . . . .16.2MATHEMATICAL BACKGROUND . .16.3ELEMENT LIBRARY . . . . . . . . . .16.4NONLINEAR MATERIAL MODELS . .16.5INPUT DATA REQUIREMENTS . . .16.6SOLUTION RESULTS . . . . . . . . .16.7MODELING GUIDELINES . . . . . . .16.8EXAMPLE PROBLEMS . . . . . . . .Chapter 19: SUBSTRUCTURING ANALYSIS . . . . . . . . . . . . . . .19.1COMPARING SUBSTRUCTURING AND SUPERELEMENTS19.2BASIC CONCEPTS AND TERMINOLOGY . . . . . . . . . .19.3THE SUBSTRUCTURING OPERATIONS . . . . . . . . . . .19.4THE SOF DATABASE . . . . . . . . . . . . . . . . . . . . . .19.5INPUT DATA REQUIREMENTS . . . . . . . . . . . . . . . .19.6SOLUTION RESULTS . . . . . . . . . . . . . . . . . . . . . .19.7MODELING GUIDELINES . . . . . . . . . . . . . . . . . . . .19.8EXAMPLE PROBLEMS . . . . . . . . . . . . . . . . . . . . . 19-1. 19-3. 19-419-1019-1519-1819-4019-4319-45viii TABLE OF 17-4817-4918-118-218-318-418-518-618-7UAI/NASTRAN
User’s GuideChapter 20: AXISYMMETRIC HARMONIC MODELING20.1TERMINOLOGY . . . . . . . . . . . . . . . .20.2MATHEMATICAL BACKGROUND . . . . . .20.3INPUT DATA REQUIREMENTS . . . . . . .20.4SOLUTION RESULTS . . . . . . . . . . . . .20.5MODELING GUIDELINES . . . . . . . . . . .20.6EXAMPLE PROBLEM . . . . . . . . . . . . .20-120-220-320-520-1020-1220-13Chapter 21: AXISYMMETRIC RING MODELING21.1BACKGROUND . . . . . . . . . . . .21.2INPUT DATA REQUIREMENTS . . .21.3SOLUTION RESULTS . . . . . . . . .21.4MODELING GUIDELINES . . . . . . .21.5EXAMPLE PROBLEM . . . . . . . . .21-121-221-421-521-821-9Chapter 22: CYCLIC SYMMETRY ANALYSIS22.1TERMINOLOGY . . . . . . . . . .22.2MATHEMATICAL BACKGROUND22.3INPUT DATA REQUIREMENTS .22.4SOLUTION RESULTS . . . . . . .22.5MODELING GUIDELINES . . . . .22.6EXAMPLE PROBLEMS . . . . . .22-122-222-322-522-1122-1322-14INTERACTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-1. 23-223-1423-2023-2523-2623-28.Chapter 23: THREE DIMENSIONAL FLUID-STRUCTURE23.1MATHEMATICAL BACKGROUND . . . . . . .23.2THE FINITE ELEMENT IDEALIZATION . . . .23.3INPUT DATA REQUIREMENTS . . . . . . . .23.4MODELING GUIDELINES . . . . . . . . . . . .23.5EXAMPLE PROBLEM . . . . . . . . . . . . . .23.6REFERENCES . . . . . . . . . . . . . . . . . .Chapter 24: HEAT TRANSFER ANALYSIS . . . . . . . . . . . . . . .24.1TERMINOLOGY . . . . . . . . . . . . . . . . . . . . . . . .24.2MATHEMATICAL BACKGROUND . . . . . . . . . . . . . .24.3THE HEAT TRANSFER BOUNDARY ELEMENT . . . . . .24.4RADIATION EXCHANGE COEFFICIENT CALCULATIONS24.5INPUT DATA REQUIREMENTS . . . . . . . . . . . . . . .24.6SOLUTION RESULTS . . . . . . . . . . . . . . . . . . . . .24.7MODELING GUIDELINES . . . . . . . . . . . . . . . . . . .24.8EXAMPLE PROBLEMS . . . . . . . . . . . . . . . . . . . 15TABLE OF CONTENTS ix
User’s GuideChapter 25: MULTIDISCIPLINARY DESIGN OPTIMIZATION25.1WHAT IS MDO? . . . . . . . . . . . . . . . . . . .25.2THE DESIGN MODEL . . . . . . . . . . . . . . . .25.3MATHEMATICAL BACKGROUND . . . . . . . . .25.4INPUT DATA REQUIREMENTS . . . . . . . . . .25.5SOLUTION RESULTS . . . . . . . . . . . . . . . .25.6EXAMPLE PROBLEMS . . . . . . . . . . . . . . .25.7REFERENCES . . . . . . . . . . . . . . . . . . . .25-125-225-325-725-2525-4225-5125-80Chapter 26: SENSITIVITY ANALYSIS . . . . . . . . . . . .26.1CONSTRAINT DERIVATIVES . . . . . . . . . .26.2OPTIMIZATION: DESIGN VARIABLE SCALING26.3INPUT DATA REQUIREMENTS . . . . . . . . .26.4SOLUTION RESULTS . . . . . . . . . . . . . . .26.5EXAMPLE PROBLEMS . . . . . . . . . . . . . .26-126-226-326-526-726-11Chapter 27: MESH ERROR ESTIMATES . . .27.1TERMINOLOGY . . . . . . . . . .27.2MATHEMATICAL BACKGROUND27.3INPUT DATA REQUIREMENTS .27.4SOLUTION RESULTS . . . . . . .27.5EXAMPLE PROBLEMS . . . . . .27-127-227-327-627-827-9Chapter 28: AEROELASTIC FLUTTER . . . .28.1BACKGROUND . . . . . . . . . . .28.2THE AEROELASTIC MODEL AND28.3MATHEMATICAL BACKGROUND28.4INPUT DATA REQUIREMENTS .28.5SOLUTION RESULTS . . . . . . .28.6EXAMPLE PROBLEMS . . . . . .28.7REFERENCES . . . . . . . . . . . . . . . . . . . . . . .ANALYSIS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28-128-228-328-628-1728-2628-3128-50Chapter 29: STRUCTURAL PLOTTING . . . . . . . . . . . . .29.1STRUCTURAL PLOTTING TERMINOLOGY . . . .29.2STRUCTURAL PLOTTER DATA REQUIREMENTS29.3STRUCTURAL PLOT ELEMENTS . . . . . . . . . .29.4STRUCTURAL PLOTTER COMMANDS . . . . . . .29.5PLOTTING THE MODEL GEOMETRY . . . . . . . .29.6PLOTTING SOLUTION RESULTS . . . . . . . . . .29.7STRUCTURAL PLOTTER EXAMPLES . . . . . . .x TABLE OF STRAN
User’s GuideChapter 30: X-Y PLOTTING . . . . . . . . . . . . . . . . . . . . . . . . .30.1X-Y PLOTTING TERMINOLOGY . . . . . . . . . . . . . . . .30.2X-Y PLOTTER DATA REQUIREMENTS . . . . . . . . . . . .30.3THE X-Y PLOT ELEMENTS . . . . . . . . . . . . . . . . . .30.4X-Y PLOTTER COMMANDS . . . . . . . . . . . . . . . . . .30.5THE XYPLOT COMMAND . . . . . . . . . . . . . . . . . . .30.6THE XYPRINT COMMAND . . . . . . . . . . . . . . . . . . .30.7XYPUNCH — INTERFACING WITH POST-PROCESSORS30.8XYPEAK — DATA RANGE SCANNING . . . . . . . . . . . .30.9THE XYPAPER COMMAND . . . . . . . . . . . . . . . . . .30.10 X-Y PLOTTER EXAMPLES . . . . . . . . . . . . . . . . . . 0Chapter 31: INTERFACING WITH UAI/NASTRAN . . . . . . . . . . . . . . . . . . . . . 31-131.1THIRD-PARTY PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-231.2UAI PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31-6REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REF-1INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INDEX-1UAI/NASTRANTABLE OF CONTENTS xi
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User’s GuideLIST OF FIGURESChapter 2: ORIENTATION: THE SOFTWARE SYSTEM . . . .Figure 2-1. UAI/NASTRAN ARCHITECTURE . . . . . . . .Figure 2-2. eBase DIRECTORY HIERARCHY . . . . . . . .Figure 2-3. THE PHYSICAL DATABASE . . . . . . . . . . .Figure 2-4. IMPORTING BULK DATA FROM A DATABASEFigure 2-5. CHECKPOINT AND RESTART . . . . . . . . . . 2-1. 2-2. 2-82-102-112-13Chapter 4: THE FINITE ELEMENT IDEALIZATION . . . . . . . .Figure 4-1. THE FINITE ELEMENT DISCRETIZATION . . . .Figure 4-2. RECTANGULAR COORDINATE SYSTEM . . . .Figure 4-4. SPHERICAL COORDINATE SYSTEM . . . . . . .Figure 4-3. CYLINDRICAL COORDINATE SYSTEM . . . . .Figure 4-5. ELEMENT-ORIENTED GRID POINT FORCES . .Figure 4-6. MODELS FOR h-CONVERGENCE . . . . . . . .Figure 4-7. RATE OF CONVERGENCE FOR h-REFINEMENTFigure 4-8. RATE OF CONVERGENCE FOR p-REFINEMENT. 4-1. 4-2. 4-3. 4-4. 4-44-104-144-154-15Chapter 5: THE FINITE ELEMENT LIBRARY . . . . . . . . . . .Figure 5-1. ROD ELEMENT GEOMETRY . . . . . . . . . . . .Figure 5-2. BAR ELEMENT GEOMETRY . . . . . . . . . . . .Figure 5-3. BAR ELEMENT FORCES . . . . . . . . . . . . . .Figure 5-4. BEAM ELEMENT GEOMETRY . . . . . . . . . . .Figure 5-5. PILE ELEMENT GEOMETRY . . . . . . . . . . . .Figure 5-6. TRIA3 ELEMENT GEOMETRY . . . . . . . . . . .Figure 5-7. QUAD4 ELEMENT GEOMETRY . . . . . . . . . .Figure 5-8. PLATE ELEMENT FORCES . . . . . . . . . . . .Figure 5-9. QUAD8 ELEMENT GEOMETRY . . . . . . . . . .Figure 5-10. TRIA6 ELEMENT GEOMETRY . . . . . . . . . .Figure 5-11. USING LINEAR AND QUADRATIC ELEMENTSFigure 5-12. "DRILLING" DEGREES OF FREEDOM . . . . . 5-1. 5-3. 5-4. 5-5. 5-75-105-125-125-145-165-165-185-19UAI/NASTRANLIST OF FIGURES xiii
User’s 7.5-18.5-19.5-20.5-21.5-22.5-23.5-24.DEGREES OF FREEDOM FOR THE QUADRSHEAR AND TWIST GEOMETRY . . . . . .TWIST PANEL FORCES . . . . . . . . . . . .SHEAR PANEL FORCES . . . . . . . . . . .HEXA ELEMENT GEOMETRY . . . . . . . .PENTA ELEMENT GEOMETRY . . . . . . . .TETRA ELEMENT GEOMETRY . . . . . . . .GAP ELEMENT GEOMETRY . . . . . . . . .BUSH ELEMENT GEOMETRY . . . . . . . .BUSH ELEMENT COORDINATE SYSTEMSLAMINATED COMPOSITE ORIENTATION .STANDARD CROSS SECTIONS . . . . . . .AND. . . . . . . . . . . . . . . . . . . . . . .TRIAR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 6: BOUNDARY CONDITIONS AND EQUATION REDUCTIONFigure 6-1. RELATIONSHIP AMONG DISPLACEMENT SETS . . .Figure 6-2. USING THE RBE3: EXAMPLE 1 . . . . . . . . . . . . .Figure 6-3. USING THE RBE3: EXAMPLE 2 . . . . . . . . . . . . .Figure 6-4. USING THE RBE3: EXAMPLE 3 . . . . . . . . . . . . .Figure 6-5. USING THE RSPLINE ELEMENT . . . . . . . . . . . .5-195-235-235-235-255-255-255-355-355-365-395-40. 6-1. 6-66-106-116-116-12Chapter 7: STRUCTURAL LOADS . . . . . . . . . . . . . . . . . . . . .Figure 7-1. TYPES OF CONCENTRATED LOADS . . . . . . . . . . .Figure 7-2. DISTRIBUTED LOADS ON BARS AND BEAMS . . . . .Figure 7-3. DEFINING PRESSURE LOADS ON SOLID ELEMENTS.7-17-37-47-6Chapter 8: MATERIAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1Figure 8-1. TEMPERATURE DEPENDENT ELASTIC MODULUS . . . . . . . . . . . . 8-9Chapter 9: DYNAMICS MODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1Figure 9-1. GRID POINT WEIGHT AND BALANCE SUMMARY . . . . . . . . . . . . . 9-6Chapter 10: LINEAR STATIC ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1Figure 10-1. CASE CONTROL ORGANIZATION . . . . . . . . . . . . . . . . . . . . . 10-5Chapter 11: NORMAL MODES ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1Figure 11-1. GIVENS MEMORY REQUIREMENTS . . . . . . . . . . . . . . . . . . 11-19Chapter 12: COMPLEX EIGENVALUE ANALYSIS . . . . . . . . . . . . . . . . . . . . . 12-1Chapter 13: FREQUENCY AND RANDOM RESPONSE ANALYSIS . . . . . . . . . . . 13-1Figure 13-1. FINITE ELEMENT MODEL . . . . . . . . . . . . . . . . . . . . . . . . 13-27Figure 13-2. RESPONSE HISTORY . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-27Chapter 14: TRANSIENT RESPONSE ANALYSISFigure 14-1. TRANSIENT RESPONSE MODELFigure 14-3. ACCELERATION HISTOGRAM . .Figure 14-2. APPLIED LOAD HISTORY . . . . .xiv LIST OF FIGURES. 14-114-1914-2014-20UAI/NASTRAN
User’s GuideChapter 15: RESPONSE SPECTRUM ANALYSIS .Figure 15-1. SIMPLE SDOF STRUCTURE . . . .Figure 15-3. AVERAGE VELOCITY SPECTRUMFigure 15-2. TYPICAL RESPONSE SPECTRUMFigure 15-4. FRAME STRUCTURE MODEL . . .Figure 15-5. DESIGN SPECTRUM . . . . . . . .Chapter 16: MATERIAL NONLINEAR ANALYSIS . . . . . . . . . . . .Figure 16-1. STIFFNESS UPDATE METHODS . . . . . . . . . . . .Figure 16-2. NEGATIVE σ ε SLOPE . . . . . . . . . . . . . . . . . .Figure 16-3. ELASTO-PLASTIC MATERIAL . . . . . . . . . . . . . .Figure 16-4. ISOTROPIC AND KINEMATIC HARDENING . . . . . .Figure 16-5. COMBINED HARDENING . . . . . . . . . . . . . . . . .Figure 16-6. ISOTROPIC AND KINEMATIC HARDENING . . . . . .Figure 16-7. YIELD SURFACES AND HARDENING RULES . . . . .Figure 16-8. NONLINEAR INPUT FOR BILINEAR STRESS-STRAINFigure 16-9. NONCYCLIC HYSTERESIS . . . . . . . . . . . . . . . .Figure 16-10. CYCLIC HYSTERESIS . . . . . . . . . . . . . . . . . .Figure 16-11. NONLINEAR ELASTICITY . . . . . . . . . . . . . . . .Figure 16-12. STRESS COMPUTATION . . . . . . . . . . . . . . . .Figure 16-13. COMBINED MODEL . . . . . . . . . . . . . . . . . . .Figure 16-14. I-BEAM COLLAPSE MODEL . . . . . . . . . . . . . . .Figure 16-15. THREE-DIMENSIONAL PLASTIC MODEL . . . . . . .Figure 16-16. FINITE ELEMENT MODEL OF BEARING BLOCK . .Figure 16-17. NONLINEAR ELASTICITY . . . . . . . . . . . . . . . . 16-1. 16-5. 6-1916-2116-3516-3816-3916-40Chapter 17: GEOMETRIC NONLINEAR ANALYSIS . . . . . . . . .Figure 17-1. SOLUTION FOR UNSTABLE PROBLEM . . . . . .Figure 17-2. SNAP-THROUGH OF INCLINED ROD . . . . . . . .Figure 17-3. SOLUTION CURVE FOR INCLINED ROD . . . . .Figure 17-4. LARGE DEFORMATION OF CANTILEVER BEAM .Figure 17-5. BEAM SUBJECTED TO END MOMENT . . . . . . .Figure 17-6. DEFORMED SHAPE OF BEAM . . . . . . . . . . . .Figure 17-7. LARGE DEFLECTION OF SQUARE PLATE . . . .Figure 17-8. NONLINEAR SOLUTION FOR SQUARE PLATE . .Figure 17-9. CYLINDRICAL SHELL ROOF . . . . . . . . . . . . .Figure 17-10. NONLINEAR SOLUTION . . . . . . . . . . . . . . .Figure 17-11. DEFORMED SHAPE OF ELLIPTICAL CYLINDERFigure 17-12. STEEL PRESSURE VESSEL . . . . . . . . . . . .Figure 17-13. NONLINEAR SOLUTION . . . . . . . . . . . . . . .Figure 17-14. HANGING CABLE MODEL . . . . . . . . . . . . . .Figure 17-15. LINEAR SOLUTION . . . . . . . . . . . . . . . . .Figure 17-16. NONLINEAR SOLUTION . . . . . . . . . . . . . . .Figure 17-17. BEAM WITH A
Chapter 5. The Finite Element Library Description of a new capability to compute equivalent Beam forces for sets of solid elements. Correction of solid element stress equations. Changes to the NLSTRAIN and NLSTRESS commands to add features missing from earlier documentation. Chapter 6. Boundary Conditions and Equation Reduction Description of new capability to perform automatic reduction using .
