Category Archives: Engineering

Evolution and entropy

Some salt required.

Once born we slowly evolve physically by gaining tissues and bones. The food we eat is transformed into the machinaries of body. This indicates that the entropy or randomness decreases over time to create a useful thing. But once we cross certain age decay starts and the biological machinaries starts to disfunction. It seems decay and dissolution is the final destiny. And in long term degeneration is imenent.

If so how about the evolution theory? Why should a simple being evolve to a complex one? More natural way would be a complex being degenerate into simple ones. Because this is the way we observe, its easy to break things than to create one. May be we human too are degenerated form of more complex superhumans, not the complex form of monkeys.

Code aster tutorial for load varying with time and depth

Here I post two tutorial in code aster/ salome meca as follows:
1. Applying varying load
In this tutorial, simple vertical element is considered in which a vertically varying load is applied by defining a function.

2. Analysis of dam for varying water level
This is a typical analysis of dam where water level is assumed to fluctuate with time. Since two variables changes i.e. time and water depth, we need to make an external file to read the pressure (load). This tutorial will show how to do it.

Fractals in matlab/octave

Codes in matlab/octave for generating some popular fractals:

Mandelbrot

mandelbrot

function mandelbrotmain()
clear variables; clc;

maxit=200;
x=[-2,1];
y=[-1 1];

xpix=601;
ypix=401;

x=linspace(x(1),x(2),xpix);
y=linspace(y(1),y(2),ypix);
[xG, yG]=meshgrid(x,y);

c=mb(maxit,xG,yG);

figure
imagesc(x,y,c);
colormap([1 1 1;0 0 0]);
axis on;
grind on;

endfunction

function count=mb(maxItr,xG,yG)
c=xG+1i*yG;
count=ones(size(c));
z=c;

for n=1:maxItr
z=z.*z+c;
inside=abs(z)<=2;
count=count+inside;
endfor
endfunction

 

Sierpinski triangle
sierpinski

clc;
clear variables;
close windows;

clf

N=500;
x=zeros(1,N);y=x;r=x;
for a=2:N
c=randi([0 2]);
r(a)=c;
switch c
case 0
x(a)=0.5*x(a-1);
y(a)=0.5*y(a-1);
case 1
x(a)=0.5*x(a-1)+.25;
y(a)=0.5*y(a-1)+sqrt(3)/4;
case 2
x(a)=0.5*x(a-1)+.5;
y(a)=0.5*y(a-1);
end
end
plot(x,y,’o’)
title(‘Sierpinski’s triangle’)
legend(sprintf(‘N=%d Iterations’,N))

 

Fractal tree
fractaltrree

function treemain
tic
clear all;
depth = 7;
figure 1;
hold on;

drawTree2(0, 0, 90, depth);
toc;
endfunction

function drawTree2(x1, y1, angle, depth)
deg_to_rad = pi / 180.0;
rot=30; #degrees :: rotation from second iteration
branchLength=100*depth;
if (depth != 0)
x2 = x1 + cos(angle * deg_to_rad) * branchLength;
y2 = y1 + sin(angle * deg_to_rad) * branchLength ;
line([x1, x2], [y1, y2],’LineWidth’,depth);
drawTree2(x2, y2, angle – rot, depth – 1);
drawTree2(x2, y2, angle + rot, depth – 1);

endif
endfunction

 

A note on fractal (from HH Hardey):
There are upper and lower limits to describe natural objects by fractals. A figure may look like a fern leaf, but continued generation of the “leaf on larger and larger scales produces only a larger and larger fern leaf. A fern “plant” will never be produced. Similarly, there is a smallest scale to which a fractal description applies. As the overall fern leaf pattern is repeated on smaller and smaller scales, eventually the scale of a single fern plant cell will be reached. A single cell does not look like the overall shape.

Using Math Kernal Library (MKL) in visual studio with Fortran

First install MKL from intel website

To use intel MKL library inside visual studio do the followings:
1. Right click the project>Properties
2. In Property page>Fortran>Libraries set (a) Runtime library : Multithreaded and (b) Use Intel MKL: Sequential
mklsetting

Once this setting is done, you can compile the file in DEBUG mode. Repeat the same process (1-2) for RELEASE mode too once more.(Note exe of DEBUG mode is far slower than exe of RELEASE mode. The settings to set are listed below.

To do the same thing MANUALLY (which gives more insight to the code) do the following in each DEBUG and RELEASE mode.
1. Property page>Fortran>General>Additional Include Directories: C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.4.245\windows\mkl\include
2. Property page>Fortran>Preprocessor>Preprocess source file: Yes
3. Property page>Linker>General>Additional Library Directories:C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.4.245\windows\mkl\lib\ia32_win
4. Property page>Linker>Input>Additional Dependencies: mkl_intel_c.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib

The manual setting is described in the video as well:

For method to install Fortran in visual studio see this post.

Specific gravity of soil particles

Consider the following figure.
specific gravity
W1= weight of empty vessel
W2= Weight of vessel + weight of sample
W3=Weight of vessel + weight of sample+Water
W4=Weight of vessel + Water

Here,
Weight of solid = W2-W1

Similarly, from last two figures
W3-W4=Weight of solid- Weight of water
or, W3-W4= W2-W1 -Weight of water
or, Weight of water=(W2-W1)-(W3-W4)(= weight of equal volume of water as that of solid)

Now,
specific-gravity=\frac{weight of solid}{weight of equal volume of water}
i.e. \rho_s=\frac{(W2-W1)}{(W2-W1)-(W3-W4)}