An approximate method for dynamic plastic response of strain hardening beams

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Mode methods for rigid, perfectly plastic structures usually involve the definition of a basic mode having a fixed velocity or displacement profile and time-dependent amplitude and then the determination of an amplitude history, using momentum and energy principles, that gives a good approximation to the exact final displacement at some point of the structure. Because of the perfect plasticity assumption, the basic mode consists of stationary plastic hinges connected by rigid links. If the material strain-hardens, the deformation profile changes significantly during the response and the size of the plastically deforming region changes as the motion progresses. In the method ... continued below

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16 p.

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Youngdahl, C.K. November 1, 1994.

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Mode methods for rigid, perfectly plastic structures usually involve the definition of a basic mode having a fixed velocity or displacement profile and time-dependent amplitude and then the determination of an amplitude history, using momentum and energy principles, that gives a good approximation to the exact final displacement at some point of the structure. Because of the perfect plasticity assumption, the basic mode consists of stationary plastic hinges connected by rigid links. If the material strain-hardens, the deformation profile changes significantly during the response and the size of the plastically deforming region changes as the motion progresses. In the method presented here, polynomials in the spatial coordinates with time-dependent coefficients are used to represent the deformation in time-dependent plastic regions, which are connected by rigid links. Two stress fields are associated with the modal shape, one satisfying the dynamic relations and the other satisfying the constitutive equations. The application of suitable matching conditions results in a set of simultaneous differential equations for the time dependence of the plastic region sizes and the amplitude coefficients of the modal shape. Pulse shape effects are automatically taken into account, and the motion during the pulse is computed. The procedure can be made as accurate as desired by increasing the number of terms in the mode shape, with a corresponding increase in the number of matching conditions. This report gives a derivation of the mode solution for a strain-hardening, clamped beam. The analogous modes for the simply supported and cantilever beam can be obtained from this solution by eliminating the appropriate plastic region in the governing equations.

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16 p.

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OSTI as DE95014077

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  • Joint American Society of Mechanical Engineers (ASME)/Japan Society of Mechanical Engineers (JSME) pressure vessels and piping conference, Honolulu, HI (United States), 23-27 Jul 1995

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  • Other: DE95014077
  • Report No.: ANL/RE/CP--84716
  • Report No.: CONF-950740--79
  • Grant Number: W-31-109-ENG-38
  • Office of Scientific & Technical Information Report Number: 100270
  • Archival Resource Key: ark:/67531/metadc624546

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  • November 1, 1994

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • Dec. 16, 2015, 4:53 p.m.

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Youngdahl, C.K. An approximate method for dynamic plastic response of strain hardening beams, article, November 1, 1994; Illinois. (digital.library.unt.edu/ark:/67531/metadc624546/: accessed September 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.