Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

Transcription

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

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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

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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