Research


Postdoc Research: Improving the efficiency of the EPANET software


PhD Research: Numerical Simulation of Wave Propagation in Heterogeneous Media

In this project, I am working on the propagation of elastic waves in heterogeneous media. The study focuses on near-surface and near-topography 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 large-scale 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 de-amplification of earthquake waves. Support for this work provided by the US National Science Foundation. 

SV-wave propagation in a flat two-dimensional homogeneous domain

 

YouTube Video

Displacement in the x-direction
 

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Displacement in the y-direction


SV-wave propagation in a flat three-dimensional homogeneous domain

 

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Displacement in the x-direction
 

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Displacement in the y-direction


Reflection of a plane shear wave in a semi-circular alluvial valley

YouTube Video

Displacement in the x-direction

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Displacement in the y-direction


SV-wave propagation at the critical angle in a flat two-dimensional homogeneous domain

YouTube Video


Displacement in the x-direction

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Displacement in the y-direction


Double couple seismic source simulation

YouTube Video



Reflection of a plane shear wave by a valley (total displacement)

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Two-dimensional shear wave diffraction by a hill

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Wave propagation in a three-dimensional pyramid

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Wave propagation in a typical levee

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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 dam-reservoir 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 dam-reservoir system are unsymmetric, which are very expensive to solve. To avoid unsymmetric solvers, a direct method called "pseudo-symmetric 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. 

  • Analysis of Arch Dams
Shahid Rajaee concrete dam is selected as the case study for 3D numerical analysis of dams. This dam is 138m high and is located in Mazandaran, Iran. This figure shows the envelope of maximum principal compressive and tensile stresses of downstream under Friuli-Tolmezzo record.
Plots are drawn by the post processor of MAP-76 software. 

 Envelope of Maximum Principal Tensile stresses
Envelope of Maximum Principal Compressive stresses


  • Analysis of Gravity dams
Pine Flat concrete gravity dam is used for 2D cases. This dam has been investigated by many scientists; therefore,  analytical and numerical solutions are available to verify the results. This figure shows the envelope of maximum principal compressive and tensile stresses under Taft record.
Plots are drawn by the post processor of MAP-76 software.

Envelope of Maximum Principal Tensile stresses
 
Envelope of Max. Principal Compressive stresses

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 dam-reservoir 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.

  • Coupled Modal Approach (UnSymmetric Eigen-Value Problem)

Inverse iteration method is used to obtain the mode shapes of coupled system of dam and reservoir. This is a slow iterative algorithm, though can solve eigenproblem of unsymmetric matrices. This method calculates the eigenvector corresponding to the smallest eigenvalue, in the absolute value.
Thus, to obtain each eigenpair, a shifting is required. The cost of solving the eigenproblem increases as the mode number increases. This figure shows the first two eigenvectors of the coupled system of dam and reservoir.

Plots are drawn by the post processor of MAP-76 software.
First coupled mode shape of dam and reservoir
Second coupled mode shape of dam and reservoir

  • DeCoupled Modal Approach (Symmetric Eigen-Value Problem)
In the decoupled method, we use the mode shapes of dam and reservoir, separately, to calculate the response of the system. Hence, all matrices are symmetric. The sub-space method is used to compute the mode shapes of the dam and the reservoir. This method is an efficient algorithm to solve the eigenproblems for symmetric matrices. This figure shows the first two mode shapes of the dam and the reservoir for Shahid Rajaee concrete arch dam.

Plots are drawn by the post processor of MAP-76 software.

First decoupled mode shapes of dam & reservoir 
Second decoupled mode shapes of dam & reservoir 


Fluid-Structure Interaction in Ansys

As the project of the fluid-structure 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. 

Lateral-Torsion Study of Thin Wall Beams with Cut-out in Web

The effects of different parameters in lateral-torsion buckling of plate girders are investigated. Lateral-torsion buckling loads of more than 700 plate girders are calculated with openings in different shapes, dimensions, and locations by Ansys5.4. The study is performed using numerical approach and the results are compared with the analytical solution. Three kinds of cut-outs including square, circular and hexagonal are selected. An extensive parametric study is conducted to study the influence of cut-out dimensions, thickness, area, location and distribution along the beam length. Finally, optimum scheme is obtained in order to have better estimation load carrying capacity of the open-section beam.

Mode I 
Mode I
 Mode II