Finite-Element Analysis Of Cracked Elastic Bodies Under Unsteady Translation And Rotation
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The broad objective of the investigations described in this report is the accurate finite element computation of stress intensity factors in cracked elastic bodies under steady or unsteady translational and rotational loads. Applications of interest include fatigue under adverse environments, such as stall in turbomachinery and critical speeds in elastic mechanisms. The enriched element formulation of Gifford and Hilton  has been extended to include inertial, centrifugal, Coriolis and angular acceleration effects, and to include Mode III (tearing), which is coupled to Modes I and II under unsteady rotation. The extension is based on the fact, which does not appear to be widely appreciated, that inertial effects near the crack tip are completely accounted for by the time dependence of the stress intensity factors. For Mode III, the Mindlin formulation for a plate in bending has been adopted in order to extend the enriched element formulation to torsion and bending effects. The centrifugal and angular acceleration effects are fully coupled to the displacements. A finite element code by Gifford and Hilton  for static problems in Modes I and II has been thoroughly rewritten and expanded to implement the dynamic features and Mode III. The code incorporates matrices and vectors representing translational, Coriolis, centrifugal and angular acceleration effects. It implements the Newmark method for time integration, and a non-symmetric 'wave front' solver. The elements are validated by comparison with several benchmark problems.
Gau, C. Y. and Nicholson, D. W., "Finite-Element Analysis Of Cracked Elastic Bodies Under Unsteady Translation And Rotation" (1993). Faculty Bibliography. 1755.