Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

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1 NASA/TP 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

2 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 your question via the Internet to Fax your question to the NASA Access Help Desk at Telephone the NASA Access Help Desk at Write to: NASA Access Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076

3 NASA/TP 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

4 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 National Technical Information Service 5285 Port Royal Road Springfield, VA Available electronically at

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181 REPORT DOCUMENTATION PAGE Form Approved OMB No 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 , and to the Office of Management and Budget, Paperwork Reduction Project ( ), Washington, DC 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 PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration John H. Glenn Research Center at Lewis Field Cleveland, Ohio PERFORMING ORGANIZATION REPORT NUMBER E SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) National Aeronautics and Space Administration Washington, DC SPONSORING/MONITORING AGENCY REPORT NUMBER NASA TP 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, a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified -Unlimited Subject Category: 39 Available electronically at This publication is available from the NASA Center for AeroSpace Information, 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 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z

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