## Constraint Minimization of Equation using lagrange's method

OBJECTIVE

The main objective is to Minimize the given equation with respect to the given constraint.

Problem:

This function f(x,y) = 5-(x-2)^2 -2(y-1)^2 is subject to the following constraint x + 4y = 3

Solution:

Make a new function as g(x,y) = f(x,y) + lamda (x+4y-3)

g(x,y) = (5-(x-2)^2 -2(y-1)^2) + lamda (x+4y-3)

g(x,y) = 5-(x^2 - 4x + 4 ) - 2(y^2 - 2y +1 ) + lamda (x+4y-3)

g(x,y) = -x^2 +4x - 2 y^2 +4y -1 + lamda (x+4y-3)

Perform partial differential equation on this g(x,y) function w.r.t. x, y & lamda

(del g)/(del x) = 0

-2x + 4+ lamda = 0   ---------------> Eq. 1

(del g)/(del y) = 0

-4y + 4+ 4lamda =0

lamda - y+1 =0

lamda = y-1              ---------------> Eq. 2

(del g)/(del lamda) = 0

x+4y-3=0                ---------------> Eq. 3

Put eq. 2 into eq. 1, we get

-2x+4+y-1=0

-2x+y+3=0              ---------------> Eq. 4

multiply eq. 3 with 2 and solve with eq. 4, we get

9y-3=0

y=1/3

put value of y in eq. 2, we get lamda

lamda = -2/3

put value of y in eq. 3, we get  value of x

x = 5/3

CONLUSION

We get the value of x , y and lamda

x = 5/3 , y=1/3 , lamda = -2/3

### Comparison of Simulation results and Improve Shell Property of rail model using Hypermesh RADIOSS Jitesh Sahjwani · 2019-09-20 14:57:35

OBJECTIVE Using the crash beam file, Comparison of simulation results of the base setup and improved shell element properties. Questions: 1.Using the crash beam file and change the run time to 55 ms. 2. Change the number of animation steps during simulation to a min Read more

### Crash Worthiness Analysis of Housing and Arm Bracket using Hypermesh Radioss Jitesh Sahjwani · 2019-09-20 04:21:10

Crash Worthiness analysis of housing and arm bracket using Radioss Hypermesh OBJECTIVE The key objective is to create the 2D and 3D meshing for the given models and solve the following questions PROCEDURE & Answers 1. Material property for steel we can ch Read more

### Geometry Cleanup and Mesh on 2D SHELL Elements Using Hypermesh Radioss Jitesh Sahjwani · 2019-09-17 07:48:47

Google drive link for Hypermesh files: https://drive.google.com/open?id=1MDhngswNUUJFrXmWwMTR4jfR0R9T6PKd   OBJECTIVE The key objective is to carry out the geometry cleanup operation & ignore holes less than dia 5mm, extract mid surface and create a 2D mesh Read more

### Data analysis File parsing script using Python Jitesh Sahjwani · 2019-09-14 04:40:04

Google drive link for the \'Engine_data.out\' file: https://drive.google.com/open?id=1lIh6RdUZRex9klgtDhpQ0tmtRTBY11YC   OBJECTIVE The primary aim is to create a data visualizer tool using python and perform certain things by this code is: The scri Read more

### Curve Fitting for Temperature and specific heat values using Python Jitesh Sahjwani · 2019-09-13 18:38:15

OBJECTIVE The key objective of writing this program is to perform curve fitting with the help of a linear and cubic polynomial for the Temp. & Cp data. #1. What does popt and pcov mean? #2. What does np.array(temperature) do? #3. What does the * in *popt Read more

### Breaking Ice with Air cushion Vehicle - Find minimum pressure with Newton-Raphson method Using Python Jitesh Sahjwani · 2019-09-11 05:44:38

OBJECTIVE The key objective is to determine the minimum cushion pressure needed to break a given thickness of the ice using an air-cushion vehicle. Solve the equation by using the Newton Raphson method and Write a Python code. Methodology that we use; Whole ide Read more

### Transient behavior of a simple pendulum using python Jitesh Sahjwani · 2019-09-10 15:38:28

OBJECTIVE  The key objective is to write a program that solves the following ODE and simulate & create an animation of the transient behavior of a simple pendulum using python. 2nd Order Equation given (d^2theta)/dt^2 + b/m (d theta)/dt +g/l sin theta = 0 Read more

### Simulation of the forward kinematics for 2R Robotic Arm Using Python Jitesh Sahjwani · 2019-09-10 04:21:22

OBJECTIVE The main aim of this program in python to simulate the forward kinematics of a 2R Robotic Arm and also make animations of the plotted graph. 2R robotic arm contains two links and two rotational joints. Workspace refers to the possible locations that th Read more

### Simulation of Otto Cycle with P-V curve plotting using Python Jitesh Sahjwani · 2019-09-10 04:09:38

OBJECTIVE The key objective of this program is to make OTTO cycle simulator.Calculate the unknown pressure & temperature and plot the PV diagram using thermal equations and find the thermal efficiency with the help of Python scripting. Otto cycle: The air-standard Read more