In this project, I am working on the propagation of elastic waves in heterogeneous media. The study focuses on nearsurface and neartopography effects. Hence, we truncate the physical domain at distances much closer to the surface. Consequently, we need an absorbing boundary. A recently developed stable time domain Perfectly Matched Layers model (PML) is used to properly account for truncation surfaces embedded within a heterogeneous medium. In addition, an unstructured mesh is used for both the topographic surface features, as well as the underlying soil. Due to the cost of computations, we have to resort to a parallel code. We develop a parallel code built on top of PETSc to conduct largescale numerical simulations. We simulated at fairly large scales the propagation of waves through arbitrarily heterogeneous and geometrically irregular halfspaces. Finally, we plan to investigate the effects of topography on the amplification and deamplification of earthquake waves. Support for this work provided by the US National Science Foundation. SVwave propagation in a flat twodimensional homogeneous domain
SVwave propagation in a flat threedimensional homogeneous domain
Reflection of a plane shear wave in a semicircular alluvial valley
SVwave propagation at the critical angle in a flat twodimensional homogeneous domain
Double couple seismic source simulation Reflection of a plane shear wave by a valley (total displacement) Twodimensional shear wave diffraction by a hill Wave propagation in a threedimensional pyramid Wave propagation in a typical levee Master Research: Dynamic Analysis of Concrete Dams[My thesis(in Persian) is available upon request] Growing energy and food demand at the beginning of 20th century led to the construction of large dams. Rockfill dams alongside the concrete dams play a significant role in irrigation and hydropower energy. Years later after the construction of dams, they need to be carefully inspected for probable damage. Moreover, this industry is still active in some parts of the world. Numerical simulation of concrete dams is very expensive due to the size of the structure and complexity of items need to be considered in calculations. To obtain an accurate analysis, reservoir and foundation are also need to be simulated, which makes the cost of calculations even more. Hence, using a direct approach might be inefficient. In order to reduce the cost, one can use a modal approach which is much cheaper in comparison with the direct approach. The purpose of this study was investigating the efficiency of coupled and decoupled modal approaches and compare it with the results of a direct method. Dam body and water domain are discretized by finite elements. The material of the dam body is assumed to be isotropic and homogeneous with linear viscoelastic behavior. The foundation is assumed to be rigid. However, the effects of wave absorption in sediments are included. Water in the reservoir is considered as an irrotational, inviscid and compressible fluid. Furthermore, Sommerfeld boundary condition is imposed for the upstream boundary of the reservoir. Pressure and nodal displacements degrees of freedom are used for the water in the reservoir and dam body, respectively. This selection of degrees of freedom leads to a coupled equation of the damreservoir system with unsymmetric mass and stiffness matrices. A computer code is developed in FORTRAN to perform numerical 2D and 3D analysis of dam–reservoir systems with first and second order finite elements. Direct Approach
To verify the results of the modal approach, an exact direct approach is required. As mentioned before, global matrices of the damreservoir system are unsymmetric, which are very expensive to solve. To avoid unsymmetric solvers, a direct method called "pseudosymmetric technique" is used so that the final matrices are all symmetric. Thus, Gauss Elimination, which is an efficient symmetric solver, can be used to solve the system.
Modal Approach As mention in the introduction, pressure and nodal displacements degrees of freedom are used for the water in the reservoir and dam body, respectively. This selection of degrees of freedom leads to a coupled equation of the damreservoir system with unsymmetric mass and stiffness matrices. Therefore, an unsymmetric eigenproblem should be solved to obtain the mode shapes of the system, which requires a complicated computer programming. Decoupled modal approach is used as an alternative to avoid this problem. In this method, a symmetric eigenproblem is solved which is obtained by eliminating the unsymmetric terms of the initial eigenproblem. Thus, a series of mode shapes are calculated that can be used for the analysis of the coupled system. By increasing the number of mode shapes utilized, results of this approach converges to the exact response of the system. Moreover, unsymmetric eigenproblem is also studied for comparison purposes. As already mentioned, this unsymmetric eigenproblem is difficult to solve and a special technique is utilized for calculating mode shapes of the system. Results of the coupled modal approach are compared with the decoupled method and it is observed that the former technique gives good results with a relatively low number of modes.
FluidStructure Interaction in AnsysAs the project of the fluidstructure interaction course, a short survey is done over the simulation of dam and reservoir in Ansys. There are a couple movies in this presentation. In order to see the movies, one must have Camtasia or related codec installed on the system.
