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Enriched Space-Time Finite Element Methods for Structural Dynamics Applications

Alpert, David N
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451

Abstract Details

, PhD, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
Accurate prediction of structural responses under combined, extreme environments often involves a wide range of spatial and temporal scales. In the traditional analysis of structural response problems, time dependent problems are generally solved using a semi-discrete finite element method. These methods have difficulty simulating high frequency ranges, long time durations, and capturing sharp gradients and discontinuities. Some limitations include time step constraints or a lack of convergence. The space-time finite element method based on time-discontinuous formulation extends the discretization into the temporal domain and is able to address some of these concerns. The constraints on the time-step are relaxed and the method has had some success in accurately capturing sharp gradients and discontinuities. For applications featured by multiscale responses in both space and time, the regular space-time finite element method is unable to capture the full spectrum of the response. An enriched space-time finite element method is proposed based on a coupled space-time approximation. Enrichment is introduced into the space-time framework based on the extended finite element method (XFEM). The effects of continuous enrichment functions are explored for high frequency wave propagation. Previous works are based primarily on enrichment in time. Numerical solvers are developed and benchmarked for the space-time system on high-performance platform. The method’s robustness is demonstrated by convergence studies using energy error norms. Improvements are observed in terms of the convergence properties of the enriched space-time finite element method over the traditional space-time finite element method for problems with fine scale features. As a result, enrichment may be considered an alternative to mesh refinement. The numerical instability associated with the high condition number of the enriched space-time analogous stiffness matrices is studied. The factors affecting the condition numbers are explored and a Jacobi preconditioner is applied to reduce the condition numbers. Programs to model example problems are developed using Fortran. The computational expense for these programs is reduced by using advanced programming libraries utilizing GPGPU. It is concluded that the proposed formulation is robust and accurate but the high condition number of the system can pose difficulties for its implementation.
Dong Qian, Ph.D. (Committee Chair)
Thomas Eason, Ph.D. (Committee Member)
Randall Allemang, Ph.D. (Committee Member)
Yijun Liu, Ph.D. (Committee Member)
132 p.
Mechanical Engineering
Enriched Finite Element Method; Space Time Finite Element Method; Time Discontinuous Galerkin Method; Enrichment; XFEM; GPGPU

Recommended Citations

Citations

  • Alpert, D. N. (n.d.). Enriched Space-Time Finite Element Methods for Structural Dynamics Applications [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451

    APA Style (7th edition)

  • Alpert, David. Enriched Space-Time Finite Element Methods for Structural Dynamics Applications. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451.

    MLA Style (8th edition)

  • Alpert, David. "Enriched Space-Time Finite Element Methods for Structural Dynamics Applications." Doctoral dissertation, University of Cincinnati. Accessed APRIL 26, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1377870451

    Chicago Manual of Style (17th edition)

ucin1377870451
575
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This open access ETD is published by University of Cincinnati and OhioLINK.