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Mixed mode fracture analysis of rectilinear anisotropic plates by high order finite elements (1981)

Heppler, Glenn ; Hansen, Jorn S.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 17 (1981), S. 445-464

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ISSN: 0029-5981

Keywords: Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics , Technology

Notes: A singular finite element is developed for direct calculation of combined modes I and II stress intensity factors for planar rectilinear anisotropic structures subject to arbitrary loading. Twelve-node conventional elements are used in conjunction with a linear elastic fracture mechanics enrichment of the same element which is formed into a four-element macro-element. Example problems show this formulation to be exceptionally accurate and results are presented for a variety of modern fibre-reinforced composites in simple mode I extension and in mixed mode I and II situations. In addition, it is shown that the meshes for accurate results are relatively coarse and thus calculations are quite economical.

Additional Material: 5 Ill.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/nme.1620170311

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Dynamics of a Flexible Cantilever Beam Carrying a Moving Mass (1998)

Siddiqui, Sultan A. Q. ; Golnaraghi, M. Farid ; Heppler, Glenn R.

Springer

Nonlinear dynamics 15 (1998), S. 137-154

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ISSN: 1573-269X

Keywords: Beam carrying a moving mass ; internal resonance ; kinematic nonlinearities

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The motion of a flexible cantilever beam carrying a moving spring-mass system is investigated. The beam is assumed to be an Euler–Bernouli beam. The motion of the system is described by a set of two nonlinear coupled partial differential equations where the coupling terms have to be evaluated at the position of the mass. The nonlinearities arise due to the coupling between the mass and the beam. Due to the nonlinearities the system exhibits internal resonance which is investigated in this work. The equations of motion are solved numerically using the Rayleigh–Ritz method and an automatic ODE solver. An approximate solution using the perturbation method of multiple scales is also obtained.