In this paper, a finite element (FE)-based model that efficiently evaluates the dynamic behavior of damreservoir-foundation interaction (DRFI) problem was proposed including the radiation of waves to the unbounded rock and reservoir domains. Lagrangian fluid elements were used to discretize the near-field reservoir domain, while the presented infinite fluid elements were used to discretize the far-field reservoir domain. The fully coupled equation of motion for DRFI problem was solved by direct method. A twodimensional (2D) plane-strain FE formulation of the problem is written in FORTRAN 90 programming language. Investigations were conducted on the effect of near-field domain size (length and depth) on the dynamic behavior of DRFI, dam-foundation interaction (DFI), and dam-reservoir interaction (DRI) problems. The results of this study demonstrate that the proposed model outperforms many other models that have been evolved in the literature in terms of accuracy and speed. The reflected hydrodynamic pressures at the far-field reservoir domain were efficiently absorbed by the suggested infinite fluid elements. The near-field domains size has a noticeable impact on the dynamic behavior of the dam. Making an exact choice about the size is more challenging. However, it was observed that the size of 1.5H is the physically appropriate response.

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A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.

The effective numerical model that examines the seismic behavior of concrete gravity dams in the Laplace domain-Finite Element (FE) approach is presented. Further research on the potential damage levels and seismic performance of the dam body is done considering the simultaneous effect of horizontal (H) and vertical (V) components of six different earthquake loads. The time durations of the selected earthquakes vary from 10 sec to 80 sec with the magnitude range from 6.5 to 7.62 Mw. The Lagrangian fluid finite elements are utilized to model the near-field water domain. On the other hand, the fluid infinite elements are utilized to model the far-field water domain considering the rigid base rock foundation condition. The two-dimensional (2D) model is developed in FORTRAN 90 and MATLAB programming languages. The findings of this study suggest that the seismic behavior of concrete gravity dam affects not only with the seismic severity; the length and significant time duration of the earthquake are also important factor. The evaluation of the obtained results revealed that the longer length of significant earthquake duration leads to the high deformations, the high stress excursions and high probability of damages in the dam. 20.9% and 18.8% of the selected dam cross section experiences overstress condition under the H and H+V components of the Chi-Chi earthquake loads, respectively; which result the dam failure.