Surya N. PatnaikOhio Aerospace Institute, Brook Park, Ohio
Dale A. Hopkins and Gary R. HalfordGlenn Research Center, Cleveland, Ohio
Integrated Force Method Solution toIndeterminate Structural Mechanics Problems
NASA/TP—2004-207430
March 2004
https://ntrs.nasa.gov/search.jsp?R=20040045162 2018-07-01T23:23:42+00:00Z
The NASA STI Program Office . . . in Profile
Since its founding, NASA has been dedicated tothe advancement of aeronautics and spacescience. The NASA Scientific and TechnicalInformation (STI) Program Office plays a key partin helping NASA maintain this important role.
The NASA STI Program Office is operated byLangley Research Center, the Lead Center forNASA’s scientific and technical information. TheNASA STI Program Office provides access to theNASA STI Database, the largest collection ofaeronautical and space science STI in the world.The Program Office is also NASA’s institutionalmechanism for disseminating the results of itsresearch and development activities. These resultsare published by NASA in the NASA STI ReportSeries, which includes the following report types:
• TECHNICAL PUBLICATION. Reports ofcompleted research or a major significantphase of research that present the results ofNASA programs and include extensive dataor theoretical analysis. Includes compilationsof significant scientific and technical data andinformation deemed to be of continuingreference value. NASA’s counterpart of peer-reviewed formal professional papers buthas less stringent limitations on manuscriptlength and extent of graphic presentations.
• TECHNICAL MEMORANDUM. Scientificand technical findings that are preliminary orof specialized interest, e.g., quick releasereports, working papers, and bibliographiesthat contain minimal annotation. Does notcontain extensive analysis.
• CONTRACTOR REPORT. Scientific andtechnical findings by NASA-sponsoredcontractors and grantees.
• CONFERENCE PUBLICATION. Collectedpapers from scientific and technicalconferences, symposia, seminars, or othermeetings sponsored or cosponsored byNASA.
• SPECIAL PUBLICATION. Scientific,technical, or historical information fromNASA programs, projects, and missions,often concerned with subjects havingsubstantial public interest.
• TECHNICAL TRANSLATION. English-language translations of foreign scientificand technical material pertinent to NASA’smission.
Specialized services that complement the STIProgram Office’s diverse offerings includecreating custom thesauri, building customizeddatabases, organizing and publishing researchresults . . . even providing videos.
For more information about the NASA STIProgram Office, see the following:
• Access the NASA STI Program Home Pageat http://www.sti.nasa.gov
• E-mail your question via the Internet [email protected]
• Fax your question to the NASA AccessHelp Desk at 301–621–0134
• Telephone the NASA Access Help Desk at301–621–0390
• Write to: NASA Access Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076
Surya N. PatnaikOhio Aerospace Institute, Brook Park, Ohio
Dale A. Hopkins and Gary R. HalfordGlenn Research Center, Cleveland, Ohio
Integrated Force Method Solution toIndeterminate Structural Mechanics Problems
NASA/TP—2004-207430
March 2004
National Aeronautics andSpace Administration
Glenn Research Center
Available from
NASA Center for Aerospace Information7121 Standard DriveHanover, MD 21076
National Technical Information Service5285 Port Royal RoadSpringfield, VA 22100
Trade names or manufacturers’ names are used in this report foridentification only. This usage does not constitute an officialendorsement, either expressed or implied, by the National
Aeronautics and Space Administration.
Available electronically at http://gltrs.grc.nasa.gov
This work was sponsored by the Low Emissions AlternativePower Project of the Vehicle Systems Program at the
NASA Glenn Research Center.
NASA/TP—2004-207430 iii
NASA/TP—2004-207430 iv
NASA/TP—2004-207430 v
NASA/TP—2004-207430 vi
NASA/TP—2004-207430 vii
NASA/TP—2004-207430 viii
NASA/TP—2004-207430 ix
NASA/TP—2004-207430 x
NASA/TP—2004-207430 1
NASA/TP—2004-207430 2
NASA/TP—2004-207430 3
NASA/TP—2004-207430 4
NASA/TP—2004-207430 5
NASA/TP—2004-207430 6
NASA/TP—2004-207430 7
NASA/TP—2004-207430 8
NASA/TP—2004-207430 9
NASA/TP—2004-207430 10
NASA/TP—2004-207430 11
NASA/TP—2004-207430 12
NASA/TP—2004-207430 13
NASA/TP—2004-207430 14
NASA/TP—2004-207430 15
NASA/TP—2004-207430 16
NASA/TP—2004-207430 17
NASA/TP—2004-207430 18
NASA/TP—2004-207430 19
NASA/TP—2004-207430 20
NASA/TP—2004-207430 21
NASA/TP—2004-207430 22
NASA/TP—2004-207430 23
NASA/TP—2004-207430 24
NASA/TP—2004-207430 25
NASA/TP—2004-207430 26
NASA/TP—2004-207430 27
NASA/TP—2004-207430 28
NASA/TP—2004-207430 29
NASA/TP—2004-207430 30
NASA/TP—2004-207430 31
NASA/TP—2004-207430 32
NASA/TP—2004-207430 33
NASA/TP—2004-207430 34
NASA/TP—2004-207430 35
NASA/TP—2004-207430 36
NASA/TP—2004-207430 37
NASA/TP—2004-207430 38
NASA/TP—2004-207430 39
NASA/TP—2004-207430 40
NASA/TP—2004-207430 41
NASA/TP—2004-207430 42
NASA/TP—2004-207430 43
NASA/TP—2004-207430 44
NASA/TP—2004-207430 45
NASA/TP—2004-207430 46
NASA/TP—2004-207430 47
NASA/TP—2004-207430 48
NASA/TP—2004-207430 49
NASA/TP—2004-207430 50
NASA/TP—2004-207430 51
NASA/TP—2004-207430 52
NASA/TP—2004-207430 53
NASA/TP—2004-207430 54
NASA/TP—2004-207430 55
NASA/TP—2004-207430 56
NASA/TP—2004-207430 57
NASA/TP—2004-207430 58
NASA/TP—2004-207430 59
NASA/TP—2004-207430 60
NASA/TP—2004-207430 61
NASA/TP—2004-207430 62
NASA/TP—2004-207430 63
NASA/TP—2004-207430 64
NASA/TP—2004-207430 65
NASA/TP—2004-207430 66
NASA/TP—2004-207430 67
NASA/TP—2004-207430 68
NASA/TP—2004-207430 69
NASA/TP—2004-207430 70
NASA/TP—2004-207430 71
NASA/TP—2004-207430 72
NASA/TP—2004-207430 73
NASA/TP—2004-207430 74
NASA/TP—2004-207430 75
NASA/TP—2004-207430 76
NASA/TP—2004-207430 77
NASA/TP—2004-207430 78
NASA/TP—2004-207430 79
NASA/TP—2004-207430 80
NASA/TP—2004-207430 81
NASA/TP—2004-207430 82
NASA/TP—2004-207430 83
NASA/TP—2004-207430 84
NASA/TP—2004-207430 85
NASA/TP—2004-207430 86
NASA/TP—2004-207430 87
NASA/TP—2004-207430 88
NASA/TP—2004-207430 89
NASA/TP—2004-207430 90
NASA/TP—2004-207430 91
NASA/TP—2004-207430 92
NASA/TP—2004-207430 93
NASA/TP—2004-207430 94
NASA/TP—2004-207430 95
NASA/TP—2004-207430 96
NASA/TP—2004-207430 97
NASA/TP—2004-207430 98
NASA/TP—2004-207430 99
NASA/TP—2004-207430 100
NASA/TP—2004-207430 101
NASA/TP—2004-207430 102
NASA/TP—2004-207430 103
NASA/TP—2004-207430 104
NASA/TP—2004-207430 105
NASA/TP—2004-207430 106
NASA/TP—2004-207430 107
NASA/TP—2004-207430 108
NASA/TP—2004-207430 109
NASA/TP—2004-207430 110
NASA/TP—2004-207430 111
NASA/TP—2004-207430 112
NASA/TP—2004-207430 113
NASA/TP—2004-207430 114
NASA/TP—2004-207430 115
NASA/TP—2004-207430 116
NASA/TP—2004-207430 117
NASA/TP—2004-207430 118
NASA/TP—2004-207430 119
NASA/TP—2004-207430 120
NASA/TP—2004-207430 121
NASA/TP—2004-207430 122
NASA/TP—2004-207430 123
NASA/TP—2004-207430 124
NASA/TP—2004-207430 125
NASA/TP—2004-207430 126
NASA/TP—2004-207430 127
NASA/TP—2004-207430 128
NASA/TP—2004-207430 129
NASA/TP—2004-207430 130
NASA/TP—2004-207430 131
NASA/TP—2004-207430 132
NASA/TP—2004-207430 133
NASA/TP—2004-207430 134
NASA/TP—2004-207430 135
NASA/TP—2004-207430 136
NASA/TP—2004-207430 137
NASA/TP—2004-207430 138
NASA/TP—2004-207430 139
NASA/TP—2004-207430 140
NASA/TP—2004-207430 141
NASA/TP—2004-207430 142
NASA/TP—2004-207430 143
NASA/TP—2004-207430 144
NASA/TP—2004-207430 145
NASA/TP—2004-207430 147
NASA/TP—2004-207430 148
NASA/TP—2004-207430 149
NASA/TP—2004-207430 150
NASA/TP—2004-207430 151
NASA/TP—2004-207430 152
NASA/TP—2004-207430 153
NASA/TP—2004-207430 154
NASA/TP—2004-207430 155
NASA/TP—2004-207430 156
NASA/TP—2004-207430 157
NASA/TP—2004-207430 158
NASA/TP—2004-207430 159
NASA/TP—2004-207430 161
NASA/TP—2004-207430 162
NASA/TP—2004-207430 163
NASA/TP—2004-207430 164
NASA/TP—2004-207430 165
NASA/TP—2004-207430 166
NASA/TP—2004-207430 167
NASA/TP—2004-207430 168
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.
REPORT DOCUMENTATION PAGE
2. REPORT DATE
19. SECURITY CLASSIFICATION OF ABSTRACT
18. SECURITY CLASSIFICATION OF THIS PAGE
Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 JeffersonDavis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102
Form Approved
OMB No. 0704-0188
12b. DISTRIBUTION CODE
8. PERFORMING ORGANIZATION REPORT NUMBER
5. FUNDING NUMBERS
3. REPORT TYPE AND DATES COVERED
4. TITLE AND SUBTITLE
6. AUTHOR(S)
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
11. SUPPLEMENTARY NOTES
12a. DISTRIBUTION/AVAILABILITY STATEMENT
13. ABSTRACT (Maximum 200 words)
14. SUBJECT TERMS
17. SECURITY CLASSIFICATION OF REPORT
16. PRICE CODE
15. NUMBER OF PAGES
20. LIMITATION OF ABSTRACT
Unclassified Unclassified
Technical Paper
Unclassified
National Aeronautics and Space AdministrationJohn H. Glenn Research Center at Lewis FieldCleveland, Ohio 44135–3191
1. AGENCY USE ONLY (Leave blank)
10. SPONSORING/MONITORING AGENCY REPORT NUMBER
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space AdministrationWashington, DC 20546–0001
Available electronically at http://gltrs.grc.nasa.gov
March 2004
NASA TP—2004-207430
E–10681
WBS–22–708–24–05
180
Integrated Force Method Solution to Indeterminate StructuralMechanics Problems
Surya N. Patnaik, Dale A. Hopkins, and Gary R. Halford
Equilibrium equation; Compatibility condition; Deformation displacement relation; Forcedeformation relation; Integrated Force Method; Dual Integrated Force Method; Truss; Beam;Shaft; Frame; Membrane structure
Unclassified -UnlimitedSubject Category: 39 Distribution: Standard
Surya N. Patnaik, Ohio Aerospace Institute, Brook Park, Ohio and NASA Resident Research Associate at GlennResearch Center; and Dale A. Hopkins and Gary R. Halford, NASA Glenn Research Center. Responsible person,Surya N. Patnaik, organization code 5930, 216–433–5916.
Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysisprimarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additionalcompatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated bymanipulating the equilibrium concept, either by rewriting in the displacement variables or through the ‘cutting and closinggap’ technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authorshave researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilib-rium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primaryunknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the DualIntegrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. Thesubject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibriumequation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load,temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examplesillustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.
