Week 3 - Solving second order ODEs

Objective: To model spot weld for the given assembly of parts and perform crash test using LS DYNA software. Introduction: Weight reduction is one of the main parameters to be considered in Automobile industries for better fuel efficiency and performance. To replace the heavy structures in automobiles, high strength steel…

Crash Box Simulation Aim: To simulate the crash box of different thickness 1.2mm and 1.5mm crashing under the rigid wall using LS Dyna software. Introduction: Crash box is an energy absorbing device that crashes on application of load and reduces impact on other components nearby. In this work a simple rectangular crash…

Introduction: A drop test is a test designed to examine the structural integrity of a product. Drop tests usually involve an object being dropped from a predefined height onto a floor or surface. The object being tested can be either the dropped object or the object/surface that an object is being dropped on to. In this…

Aim To develop a python code that can perform Data visualization, compatibility check, and perform the basic calculations. 1.Data Visualization: "Matplotlib" is used to perform plotting operations. "numpy" is used to perform array operations.  A function "def datavisvualizer():" is defined to perform repetitive…

Introduction: Curve fitting is the process of specifying the model that provides the best fit to the specific curves in the dataset. Curve fitting can involve either interpolation where an exact fit to the data is required, or smoothing in which a "smooth" function is constructed that approximately fits the data. In this…

Objective: To write a python program that simulates the motion between 0-20 sec, for angular displacement=0, angular velocity=3 rad/sec at time t=0. ODE for a motion of a  pendulum with damping where b= damping coefficient(kg/s) l= length of pendulum (m) m= mass of pendulum(kg) g= acceleration due to gravity(m/s2) b=0.05kg/s…

Aim: To plot PV diagram of an Otto cycle using python software To estimate the overall efficiency Otto Cycle: The Otto cycle is a set of processes used by spark-ignition internal combustion engines. These engines a) intake a mixture of fuel and air, b) compress it, c) heat addition to the mixture, d) expand the combustion…

Introduction:Explicit and Implicit Analysis                 Explicit and implicit methods are used in numerical analysis for obtaining numerical approximations to find solutions of time-dependent ordinary and partial differential equations which require computer simulations of physical…

Introduction A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. For example, a length is a physical quantity. A meter is a unit of length that represents a definite predetermined length.…

` Abstract The present work focuses on the analysis of two-dimensional flow past a circular cylinder and determining the variation in the coefficient of lift and drag over the cylinder at Reynolds number 10,100,1000,10000,100000. In addition to this, the Strouhal Number is calculated to describe the oscillating flow mechanism…

Simulation of flow through the pipe in OpenFOAM Objectives: To determine the hydrodynamic length. To validate the fully developed flow velocity profile with its analytical results. To calculate pressure drop along the length of the pipe. To calculate the shear stress distribution. Hagen Poiseuille's Law: Hagen Poiseuille's…

Introduction: Open FOAM stands for Open source Field Operation And Manipulation used for developing numerical solvers and finding solutions for continuum mechanics problems including computational fluid dynamics. This work focusses on the transient simulation of an incompressible laminar viscous flow through the backwards-facing…

Introduction:      Tee value is used in the air conditioning system to regulate the room temperature. It works on the principle that by maintaining the mass flow rate of the cold fluid inlet the outlet fluid temperature can be controlled. Aim: To compare the mixing effectiveness of longer and shorter mixing…

Finite volume method           Finite volume method is similar to the finite difference method in which the domain is divided into very small elements of geometrically similar shapes. This method is based on the fact that many physical laws are conservation laws. I.e. what goes into one cell on…

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Objective To solve the 2D conduction equations using Transient solver and Steady-state solver using iterative techniques Jacobi, Gauss seidal and SOR. Assumptions made The 2D model is assumed to be a perfect square  nx=ny The initial temperature is assumed to be 298K(@ normal atmospheric temperature) Error=9e9 Boundary…

ODE for a motion of a  pendulum with damping where b= damping coefficient(kg/s) l= length of pendulum (m) m= mass of pendulum(kg) g= acceleration due to gravity(m/s2) b=0.05kg/s l=1m m=1kg g=9.81m/s^2   Reduction of Order In order to solve the equation of pendulum using Matlab first, we should convert second…