integrated force method solution to indeterminate structural mechanics … · ·...
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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
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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
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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
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This work was sponsored by the Low Emissions AlternativePower Project of the Vehicle Systems Program at the
NASA Glenn Research Center.
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NASA TP—2004-207430
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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.