integrated force method solution to indeterminate structural mechanics … ·  ·...

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

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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.