Section 4: Implementation of Finite Element
Analysis Other Elements
1. Quadrilateral Elements
2. Higher Order Triangular Elements
3. Isoparametric Elements
Implementation of FEA:
Other Elements
-1-
Se
Environmental Science : Ecology
Centre for Oceans, Rivers, Atmosphere and Land sciences (CORAL) , I.I.T Kharagpur
Ecology and Life
Definition of Ecology: Ecology (from the Greek words oikos, house or
Syllabus
Ecology
Water Pollution
Water and Wastewater Treatment
Solid and Hazardous Waste Management
Air Pollution
Soil Pollution
Noise Pollution
Waste Minimization and Cleaner Production
Environmenta
Groundwater
Hydrologic Cycle
Rainfall can:
flow into rivers and streams,
return to the atmosphere by evaporation or transpiration
seep into the ground to become part of the subsurface water.
Aquife
Soil Erosion
Soil erosion from rainfall
A single drop does not have a great effect on soil, but when all the raindrops in an inch of rain are
combined over an area of 1 acre, they weigh 10.38 kg.
Thes
National Ambient Air Quality Standards
National Ambient Air Quality Standards, as of 18 Nov 2009
Concentration in Ambient Air
Time
Weighted
Average
Pollutant
Annual*
SO2, g/m3
24 hours*
Annual*
NO2, g
MINE CLOSURE PLAN
Mineral conservation and development rules 1988
All coal/metalliferrous mine owners shall adopt a mine closure plan
23A. Mine Closure Plan- All mine shall have Mine Closure Plan.
The
Noise Pollution
Defined as objectionable or unwanted sound.
Sound is produced by a source causing vibrations in the medium surrounding it. Sound is
defined as any pressure variation that the human ear
WATER TREATMENT SYSTEMS
Water Treatment process: Theory and application
The purpose of a water treatment system is to bring raw water up to drinking water quality.
The type of treatment will depend on
Mine Reclamation
Ref: Environmental Impact of Mining (1977), Down and Stocks, Applied Science Publishers Ltd.
Mining land has passed through a cycle of land use which can be summarized as:
The exploi
Use of Various Types
12 The
ofNMR and IR Spectroscopy
for Structural Characterization
of Chitin and Chitosan
Mohammad Reza Kasaai
Contents
12.1 Introduction. 149
12.2 Description of Different Techni
Activity
15 Antimicrobial
ofChitin, Chitosan,
andTheirOligosaccharides
Joydeep Dutta and Pradip Kumar Dutta
Contents
15.1 Introduction. 196
15.2 Chitin, Chitosan, and Their Oligosaccharides versus O
Modifications
13 Chemical
of Chitosan Intended for
Biomedical Applications
Mani Prabaharan and Ashutosh Tiwari
Contents
13.1 Introduction. 173
13.2 In Drug Delivery. 174
13.2.1 Thiolated Chitosan D
~
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR
Date:
(FN/AN)
No. of Students: 175
Subject No: EV20001
2nd Year B. Tech.: GG, CY, EE, HS, ME
Full Mark.;: 50
Time: 3 hrs.
Spring End Semester Examination, 2
Boot Strapping and Bagging
Need for a Diverse Dataset
If we had access to a classifier with perfect generalization performance, there would be no need to resort
to ensemble techniques. The realities o
CE208: Numerical Methods for Civil and Infrastructure Engineering
Assignment#1 (Error Analysis)
1. Problem on truncation error:
Use Taylor series expansion with n = 0 to 2 to approximate f(x) =
tan(x)
MA231, Tutorial Sheet: Numerical Analysis
Numerical Methods for Solving Nonlinear Equations
(1) Find a real root of the equation f (x) = x3 x 1 = 0.
(2) Find the real root of the equation x2 + 4 sin x
1. Find the root of x * cos[(x)/ (x-2)]=0
The graph of this equation is given in the figure.
Let a = 1 and b = 1.5
Iteration
No.
1
2
3
4
5
6
a
b
c
f(a) * f(c)
1 1.51.133 0.159 (+ve)
1.1331.51.194 0.03
Module
for
Pivoting Methods
Background
In the Gauss-Jordan module we saw an algorithm for solving a general linear
system of equations
consisting of n equations and n unknowns where it is
assumed that
Indeterminate Analysis
Force Method1
The force (flexibility) method
expresses the relationships
between displacements and
forces that exist in a structure.
Primary objective of the force
method is t
Numerical Analysis
Chapter 4
4.1
Goal
Interpolation and Approximation
Polynomial Interpolation
Given n + 1 data points
(x0 , y0), (x1, y1 ), (xn , yn ),
to nd the polynomial of degree less than or equ
Solutions to Problems
on the Newton-Raphson Method
These solutions are not as brief as they should be: it takes work to
be brief. There will, almost inevitably, be some numerical errors. Please
inform
Gerschgorin Circle Theorem
Eigenvalues
In linear algebra Eigenvalues are defined for a square matrix M. An Eigenvalue
for the matrix M is a scalar such that there is a non-zero vector x such that
Mx=x
Problem # 1
Given function:
True value of f(x)
f (x) x
x+1
x
f (100) = 4.98756211208899
f (1) = 0.414213562373095
f (10) = 1.5434713018702
f (10000) = 49.9987500624854
f (1000) = 15.8074374289576
f (
CE208: Numerical Methods for Civil and Infrastructure Engineering
Assignment#2 (Finding Roots)
1. Find the root of the following equation correct up to 3 digits after
decimal point: x sin( x) 1 0 in [
2
1. There is no closed form solution for the error function
erf() =
2
0
Use the two-point Gauss quadrature approach to estimate erf(1.5). [The exact value is
0.966105.]
2. The depths of a river H
CE208: Numerical Methods for Civil and Infrastructure Engineering
Assignment#3 (Solution of Linear System)
Code all methods stated below in MATLAB to find solution of a well-conditioned linear system