An implicit finite element method for discrete dynamic fracture

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A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector ... continued below

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Medium: P; Size: 147 pages

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Gerken, Jobie M. December 1, 1999.

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This thesis or dissertation is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 13 times . More information about this document can be viewed below.

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  • Los Alamos National Laboratory
    Publisher Info: Los Alamos National Lab., Los Alamos, NM (United States)
    Place of Publication: Los Alamos, New Mexico

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Description

A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some error is expected.

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Medium: P; Size: 147 pages

Notes

OSTI as DE00751964

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  • Other Information: TH: Thesis (M.S.); Submitted to Colorado State Univ., Fort Collins, CO (US)

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  • Report No.: LA-13663-T
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 751964
  • Archival Resource Key: ark:/67531/metadc708988

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  • December 1, 1999

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • March 21, 2016, 10:50 p.m.

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Gerken, Jobie M. An implicit finite element method for discrete dynamic fracture, thesis or dissertation, December 1, 1999; Los Alamos, New Mexico. (digital.library.unt.edu/ark:/67531/metadc708988/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.