Formulating the Applied Element Method: Linear 2D (Part I)

I first came to know about the Applied Element Method (AEM) during the one day seminar on "Geotechnics and Geo hazards" 2012 held in Nepal. Ramesh Guragain had mentioned this method in his presentation on the study of collapse of masonry structures (and something to do with fragility functions I believe). The results he showed using AEM were really compelling. I wanted to learn more about this method.

Here I discuss the basic procedures that I have followed to develop an AEM program on Python that can solve Linear 2D structural problems. Poisson's ratio is not considered here. All of the procedures discussed below are based on Meguro and Tagel-Den (2000). The developed program is then used to solve a classic cantilever beam problem. The displacement values obtained using AEM are compared with corresponding theoretical values and values obtained from Finite Element Method (FEM) for plane stress condition. AEM performs better compared to FEM even when the number of elements is small.

Introduction

AEM is modeled by dividing the structure into rigid elements connected with pairs of normal and shear springs as shown in figure 1. The stiffness values of each pair of springs represent the material property of certain area of both the elements as shown in figure 1 b. The stiffness values are determined as shown below:

where E and G are Young's and shear modulus, d is the distance between springs, T is the thickness of the element and a is the length of representative area.

Simple 2D simulation of the Phailin Cyclone

It was the time of Dashain festival here at Nepal in 2013, which falls during the autumn season. The rainy season was supposed to have ended by then, but it had been raining for a couple of days and it was mainly because of the Tropical Cyclone Phailin that had hit the south eastern coast of India. No, the cyclone didn't reach Nepal, but it did send clouds here.

Source: Cooperative Institute for Meteorological Satellite Studies

Here is my simplified 2D simulation of the Phailin Cyclone I did using the instantaneous vorticity data as initial condition. I mainly solve the 2D Navier-Stokes equation using a forth order finite difference scheme in MATLAB.

Video link: https://youtu.be/Fwew6RCIt9A

A scar on Annapurna that had caused the Seti Flood of 2012

I had been going through different articles and papers about the Seti Flash Flood of 2012 and, I wanted to try out something for myself.

On May 5th of 2012, a flash flood full of debris, triggered in the Seti river, had devastated different parts of Pokhara with an estimated 71 people killed. A unique thing about this flood was that, it was probably triggered by an avalanche near the Annapurna range. This triggering of the avalanche was actually captured in tape by a Russian pilot who was flying over the same area at the time of avalanche, and about 40 minutes after the avalanche, the devastating  flood hit Pokhara. One of the most comprehensive reports on the cause of the flood should be the report prepared by Dr. NP Bhandary, Dr. RK Dahal and Prof. M Okamura based on their field visit (Bhandary et al. 2012).

Initial speculations on what might had caused the flood ranged from intensive rainfall-cloudburst flood, possible GLOF (Glacial lake outburst flood) as well as LDOF (Landslide Dam Outburst Flood). But no significant evidences supporting the latter two were found in the field. Also, the flood had occurred way before the monsoon, reducing the possibility of cloudburst flood . Looking at the devastation and magnitude of the flood, initiation of such a flood would require a huge source of water (millions of cubic meters) and these speculations couldn't properly explain the source of such a huge quantity of water.