Author
Gregory M. Hulbert
Other affiliations: General Motors
Bio: Gregory M. Hulbert is an academic researcher from University of Michigan. The author has contributed to research in topics: Finite element method & Vibration. The author has an hindex of 29, co-authored 92 publications receiving 5263 citations. Previous affiliations of Gregory M. Hulbert include General Motors.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, a new family of time integration algorithms is presented for solving structural dynamics problems, denoted as the generalized-α method, which possesses numerical dissipation that can be controlled by the user.
Abstract: A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.
2,094 citations
TL;DR: In this article, a generalized-α method was developed and analyzed for linear, first-order systems and extended to the filtered Navier-Stokes equations within the context of a stabilized finite element method.
735 citations
TL;DR: Space-time finite element methods are presented to accurately solve elastodynamics problems that include sharp gradients due to propagating waves in this paper, where linear stabilizing mechanisms are included which do not degrade the accuracy of the space time finite element formulation.
Abstract: Space-time finite element methods are presented to accurately solve elastodynamics problems that include sharp gradients due to propagating waves. The new methodology involves finite element discretization of the time domain as well as the usual finite element discretization of the spatial domain. Linear stabilizing mechanisms are included which do not degrade the accuracy of the space-time finite element formulation. Nonlinear discontinuity-capturing operators are used which result in more accurate capturing of steep fronts in transient solutions while maintaining the high-order accuracy of the underlying linear algorithm in smooth regions. The space-time finite element method possesses a firm mathematical foundation in that stability and convergence of the method have been proved. In addition, the formulation has been extended to structural dynamics problems and can be extended to higher-order hyperbolic systems.
310 citations
TL;DR: In this article, a predictor-corrector explicit time integration algorithm is presented for solving structural dynamics problems, which is based on the implicit generalized-α method developed by the authors.
233 citations
TL;DR: In this paper, the elastodynamics of 1D periodic materials and finite structures comprising these materials are studied with particular emphasis on correlating their frequency-dependent characteristics and elucidating their pass-band and stop-band behaviors.
196 citations
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TL;DR: In this paper, the authors describe photonic crystals as the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures, and the interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.
Abstract: The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.
2,722 citations
TL;DR: In this article, a general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is presented, showing how the exact theory represents a paradigm for subgrid-scale models and a posteriori error estimation.
1,578 citations
1,524 citations
TL;DR: It is shown that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.
1,260 citations
1,197 citations