Browsing by Author "Vernon C. Matzen, Committee Member"

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Equivalent Damping in Support of Direct Displacement-Based Design with Applications to Multi-Span Bridges
(2004-12-16) Dwairi, Hazim Mustafa; Vernon C. Matzen, Committee Member; Jame M. Nau, Committee Co-Chair; Mervyn J. Kowalsky, Committee Chair; Paul Zia, Committee Member
This dissertation aimed at contributing to the advancement of Direct Displacement-Based Seismic Design (DDBD) method in order to ensure its wider acceptance and to enable its implementation in future codes. The concept of equivalent linearization of nonlinear system response as applied to DDBD for single-degree-of freedom (SDOF) structures was evaluated. The evaluation process revealed significant errors in approximating maximum inelastic displacements due to overestimation of the equivalent damping values in the intermediate to long period range. Conversely, underestimation of the equivalent damping led to overestimation of displacements in the short period range. Earthquake characteristics had a significant effect on the equivalent damping, resulting in a scatter in estimating peak inelastic displacements between 20% and 40% as a function of displacement ductility. New equivalent damping relationships for 4 structural systems, based upon nonlinear system ductility and maximum inelastic displacement were proposed. The accuracy of the new equivalent damping relations was assessed, yielding a significant reduction of the error in predicting peak inelastic displacements. Furthermore, a simplified approach was proposed to select target displaced shapes for continuous bridges based on the relative stiffness between the superstructure and the substructure. The approach, in some cases, minimizes the effort and time needed to design multi-span bridge structures because it eliminates the need for the iterative approach in selecting target profiles.
Novel Finite Element Methods for Wave Propagation Modeling
(2004-10-12) Yue, Bin; Murthy N. Guddati, Committee Chair; Fuh-Gwo Yuan, Committee Member; G. Kumar Mahinthakumar, Committee Member; Vernon C. Matzen, Committee Member; M. Shamimur Rahman, Committee Member
The phenomenon of wave propagation is encountered in various engineering problems related to earthquake engineering, nondestructive evaluation and acoustics. Due to the complex material and geometrical features, many of these wave propagation problems are modeled using numerical methods such as the finite element method. Most numerical methods, due to their approximate nature, incur errors in the solution. In the context of wave propagation, these errors can be classified as amplitude and dispersion errors. Of these, dispersion error tends to have more severe effect on the accuracy due to its accumulative nature. Although it is possible to reduce the dispersion error by mesh refinement, such refinement imposes unrealistic computational cost even for medium-sized problems. In light of this, researchers have long sought efficient methods that reduce the dispersion error without any mesh refinement, but such efforts have only been partially successful. This dissertation develops efficient finite element methods for simulation of time-harmonic as well as transient wave propagation. For time harmonic waves, most existing dispersion reducing methods are limited to square meshes and homogeneous acoustic media. This dissertation develops two novel finite element methods that are applicable to unstructured meshes, as well as to heterogeneous media. They are the Local mesh-dependent augmented Galerkin finite element methods and the modified integration rules. Compared with existing methods, the proposed methods have higher convergence rate while maintaining low computational cost. When applied to elastic waves, the modified integration rules can reduce the dispersion error for either longitudinal or transverse wave, but not both. In the context of transient wave propagation, the spatial error of dispersion is coupled with temporal error resulting from time discretization. This dissertation focuses on reducing these errors by utilizing the modified integration rules and a modified time integration scheme. All the existing methods have second order convergence rates, while that of the proposed method has fourth order convergence. Numerical examples are utilized to illustrate the accuracy of the proposed method.