CURVE FITTING

SHELL MESHING OF A INTERIOR PANEL SUBSTRATE FOR FINITE ELEMENT ANALYSIS     OBJECTIVE: Structural mesh is oftained for the complex interior panel plastics of a car for finite element analysis, by extracting mid surfaces with thickness elements using manual and auto generated methods.   ABSTRACT & PRE-REQUISITES:…

MESHING A BONNET FOR STRUCTURAL ANALYSIS USING ANSA   OBJECTIVE: The given CAD of a car bonnet is to be meshed for structural analysis with the required mesh parameters. ABSTRACT: To work with thin-walled solids, using a midsurface shell model can reduce the degrees of freedom in your model by factors of ten…

SURFACE WRAP OF AN ENGINE ASSEMBLY OBJECTIVE: To extract a surface wrap of a CAD model, thereby eliminating the control volumes from which the 3D structure of meshed elements have been obtained. PROJECT WALKTHROUGH:  Firstly, the topology of the CAD has to be taken care of, in order to eliminate any possibility of…

OBJECTIVE: The given CAD model of BMW M6 is to be eliminated from it\'s topological errors & render surface mesh, expel the errors occuring during the wholesome process. PREREQUISITES: CAD CLEAN UP & ITS USES: Meshing for FEA and CFD is simple: Just start with your CAD model, break it up into a bunch of small pieces,…

OBJECTIVE: The given CAD model of BMW M6 is to be eliminated from it's topological errors & render surface mesh, expel the errors occuring during the wholesome process. PREREQUISITES: CAD CLEAN UP & ITS USES: Meshing for FEA and CFD is simple: Just start with your CAD model, break it up into a bunch of small pieces,…

OBJECTIVE: Elimination of topological errors, intersecting & broken surfaces, to render surface mesh & extract volume mesh. ABSTRACT: Typical volume meshes in three dimensions are designed to conform to an underlying two-dimensional surfacemesh, with volume mesh element size growing larger away from the surface.…

OBJECTIVE: Elimination of topological errors, intersecting & broken surfaces, to render surface mesh & extract volume mesh. ABSTRACT: Typical volume meshes in three dimensions are designed to conform to an underlying two-dimensional surfacemesh, with volume mesh element size growing larger away from the surface.…

A brief explanation of Interpolation Schemes & Flux Limiters in Finite Volume Method; Some of the interpolation schemes used are Linear, quadratic ,etc interpolation schemes. These methods are used toget to more realistic results as the engineering problems basically uses the real world environment.Here in FVM the…

ABSTRACT: This project main objective is the numerical solution of a 1D Supersonic Nozzle Flow using the Macormack Method. Although analytically identical, the numerical solution of conservation and nonconservation forms of the governing equations is usually different. That is the reason why both ways are solved and compared…

ABSTRACT: The main objective of this challenge is to write a matlab code which calculates Eigen Values, Spectral radius of a matrix. As well it should be able to find Iterative matrix and solution for variables using Jacobian, Gauss Seidel and Successive over Relaxation method. Given matrix are: EIGEN VALUE CALCULATION:…

OBJECTIVE: To simulate Steady state & Transient state analysis. To Solve the 2D heat conduction equation by using the point iterative techniques by implementing the following methods; 1. Jacobi 2. Gauss-seidel 3. Successive over-relaxation The absolute error criteria is 1e-4 ABSTRACT: The main objective of this challenge…

Study of Effect of time Step on Solution Assumptions 1. Gridpoints n=80; 2. Time Step used are 1e-1, 1e-2, 1e-3, 1e-4. 3. Velocity Profile is compared at t = 0.4 seconds.   For time step 1e-1 due to the value of C*dt/dx being greater than 1, the solution blows off.  The time step 1e-2 is the closest in terms…

OBJECTIVE: To arrive a numerical solution to the wave equation, 1. Let us assume that the domain length is L = 1m. 2. The initial velocity profile is a step function. It is equal to 2m/s between x= 0.1 and 0.3 and 1m/s everywhere else. 3. Let us use first order forward differencing for the time derivative. 4. The let us…

OBJECTIVE: To Derive the following 4th order approximations of the second order derivative 1. Central difference 2. Skewed right sided difference 3. Skewed left sided difference Once this is done, we write a program in Matlab to evaluate the second order derivative of the analytical function exp(x)*cos(x) and compare it…

ABSTRACT: Curve fitting means to find a mathematical expression which represents a line or curve that fit the data the best. The best means with the minimum error or we can say it represents the best approximation for the data. Interpolation and least square methods are two of the most widely used techniques One of the…

ABSTRACT: A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by: The motion of a simple pendulum is like simple harmonic motion…

ABSTRACT: The Otto cycle was given by Dr. Nikolaus August Otto. It is a gas power cycle that is used in petrol engine for its working. The entire modern petrol engine works on Otto cycle. It consist of four processes, Two isentropic (reversible adiabatic) processes and two isochoric (constant volume) processes. It…

OBJECTIVE: The drag force exerted on the bicycle is to be computationally extracted and its effects posed; ABSTRACT: A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is the relative…

The code to plot the first, second & fourth order error for a range of dx is given below; MATLAB CODE: clear all close all clc % First order approximations of the first derivate against the exact solution % f(x) = sin(x)/x^3 x = pi/3 ; dx = linspace(pi/4,pi/4000,100); % Computing Analytical derivative Analytical_derivative…

An initial value problem is a differential equations problem in which you are given the the value of the function and sufficient of its derivatives at ONE VALUE OF X. Now, if you have a second order equation, you are given the value of the function and its first derivative at some value of x. (That value of x being the…

OBJECTIVE: In this project, the first order derivative is discretized to obtain the desired order of accuracy. It is then discretized with forward differencing scheme to compare the results. Formula for the fourth order approximation of the first derivative: THE MATLAB CODE: close all clear all clc %Given function sin(x)/x^3;…

In this project, an OCTAVE code was written to calculate the air-fuel ratio (stochiometric ratio, ar), for alkanes, alkenes and alkynes. The variation of 'ar' with number of Carbon atoms in alkanes, alkenes and alkynes were compared. THE MATLAB CODE: %Determination of Stiochiometric coeffecient for alkanes, alkenes and…

Kinematic viscosity is defined as the resistive flow property of a fluid with respect to gravitational forces and no other external force is applied to it. It is expressed as 'v' = m^2/s or (centiStokes-cSt) Dynamic viscosity is defined as the resistive flow property of a fluid when it is subjected to and external force.…

  A[1,2,3,4,5] is an array of matrix 5x1 with 5 coloumns and 1 row. B[1;2;3;4;5] is also an array of 1x5 matrix  where there is 1 coloumn and 5 rows. C = A*B' is not possible as it is in other words multiplying a 1x5 matrix to another 1x5 matrix. Whereas C = A*B is possible is because of multiplying a 1x5 matrix…