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The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability EquationsA new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
Document ID
19790002290
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Hannah, S. R. (Air Force Inst. of Tech. Wright-Patterson AFB, OH, United States)
Palazotto, A. N. (Air Force Inst. of Tech. Wright-Patterson AFB, OH, United States)
Date Acquired
August 10, 2013
Publication Date
October 1, 1978
Publication Information
Publication: NASA. Langley Res. Center Res. in Computerized Structural Analysis and Syn.,
Subject Category
Structural Mechanics
Accession Number
79N10461
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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IDRelationTitle19790002277Collected WorksResearch in computerized structural analysis and synthesis
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