Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

NASA/TP 2004-207430 Integrated Force Method Solution to Indeterminate Structural Mechanics Problems Surya N. Patnaik Ohio Aerospace Institute, Brook Park, Ohio Dale A. Hopkins and Gary R. Halford Glenn Research Center, Cleveland, Ohio March 2004

The NASA STI Program Office... in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the Lead Center for NASA s scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA s institutional mechanism for disseminating the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types: TECHNICAL PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA s counterpart of peerreviewed formal professional papers but has less stringent limitations on manuscript length and extent of graphic presentations. TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. CONFERENCE PUBLICATION. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or cosponsored by NASA. SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and missions, often concerned with subjects having substantial public interest. TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and technical material pertinent to NASA s mission. Specialized services that complement the STI Program Office s diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results... even providing videos. For more information about the NASA STI Program Office, see the following: Access the NASA STI Program Home Page at http://www.sti.nasa.gov E-mail your question via the Internet to help@sti.nasa.gov Fax your question to the NASA Access Help Desk at 301 621 0134 Telephone the NASA Access Help Desk at 301 621 0390 Write to: NASA Access Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076

NASA/TP 2004-207430 Integrated Force Method Solution to Indeterminate Structural Mechanics Problems Surya N. Patnaik Ohio Aerospace Institute, Brook Park, Ohio Dale A. Hopkins and Gary R. Halford Glenn Research Center, Cleveland, Ohio National Aeronautics and Space Administration Glenn Research Center March 2004

Trade names or manufacturers names are used in this report for identification only. This usage does not constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space Administration. This work was sponsored by the Low Emissions Alternative Power Project of the Vehicle Systems Program at the NASA Glenn Research Center. Available from NASA Center for Aerospace Information 7121 Standard Drive Hanover, MD 21076 National Technical Information Service 5285 Port Royal Road Springfield, VA 22100 Available electronically at http://gltrs.grc.nasa.gov

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

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 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 this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 4. TITLE AND SUBTITLE 6. AUTHOR(S) March 2004 Integrated Force Method Solution to Indeterminate Structural Mechanics Problems Surya N. Patnaik, Dale A. Hopkins, and Gary R. Halford Technical Paper 5. FUNDING NUMBERS WBS 22 708 24 05 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration John H. Glenn Research Center at Lewis Field Cleveland, Ohio 44135 3191 8. PERFORMING ORGANIZATION REPORT NUMBER E 10681 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration Washington, DC 20546 0001 10. SPONSORING/MONITORING AGENCY REPORT NUMBER NASA TP 2004-207430 11. SUPPLEMENTARY NOTES Surya N. Patnaik, Ohio Aerospace Institute, Brook Park, Ohio and NASA Resident Research Associate at Glenn Research Center; and Dale A. Hopkins and Gary R. Halford, NASA Glenn Research Center. Responsible person, Surya N. Patnaik, organization code 5930, 216 433 5916. 12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified -Unlimited Subject Category: 39 Available electronically at http://gltrs.grc.nasa.gov This publication is available from the NASA Center for AeroSpace Information, 301 621 0390. 13. ABSTRACT (Maximum 200 words) 14. SUBJECT TERMS Equilibrium equation; Compatibility condition; Deformation displacement relation; Force deformation relation; Integrated Force Method; Dual Integrated Force Method; Truss; Beam; Shaft; Frame; Membrane structure 17. SECURITY CLASSIFICATION OF REPORT 18. SECURITY CLASSIFICATION OF THIS PAGE 19. SECURITY CLASSIFICATION OF ABSTRACT Unclassified Unclassified Distribution: Standard Unclassified 12b. DISTRIBUTION CODE Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, 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 examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems. 15. NUMBER OF PAGES 16. PRICE CODE 20. LIMITATION OF ABSTRACT NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102 180