Ask MATLAB Expert

Root-Finding Techniques: Application to Stress Analysis

In mechanics, stress is a measure of the internal forces acting within a de-formable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are produced between the particles in the body as a reaction to external forces applied on the body. In materials without microstructure (these are materials whose microstructure does not play an important role in the mechanical deformation), these internal forces are distributed continuously within the volume of the material body, and result in deformation of the body's shape. Beyond certain limits of material strength, this can lead to a permanent change of shape or physical failure. The dimension of stress is that of pressure, and therefore the SI unit for stress is the pascal (Pa).

A three-dimensional stress eld in a material can be represented as a symmetric matrix of the following form:

677_3 dimensional stress field.jpg

where the diagonal terms represent tensile or compressive stresses and the off -diagonal terms represent shear stresses.

At every point in a stressed body there are at least three planes, called principal planes, with normal vectors called principal directions, where there are no normal shear stresses. The three stresses normal to these principal planes are called principal stresses and they are the eigenvalues of matrix (1). To find the principal stresses, it is necessary to construct the the following algebraic equation:

1190_algebraic equation.jpg

Are known as the stress invariants. The roots of equation (2), σ1, σ2, σ3, are the principal stresses.

We consider now a homogeneous material whose stress field (in MPa) has been found experimentally to be:

1493_stress field.jpg

We are interested in nding the principal stresses σ1, σ2, σ3, corresponding to the given stress eld.

problem 1: Find σ1, σ2, σ3 using the following root- nding techniques for solving equation (2): bisection, Newton-Raphson and secant.

problem 2: Show the pseudocode and flowchart for one of the methods.

problem 3: prepare a C++ program(s) for all three methods and compare the results.

MATLAB, Engineering

  • Category:- MATLAB
  • Reference No.:- M9699

Have any Question?


Related Questions in MATLAB

Assignment - matlab programmingusing appropriate matlab

Assignment - MatLab Programming Using appropriate MatLab syntax, write the code required to analyse and display the data as per the problem description. The order of the MatLab Program should be as follows: Variables and ...

Assignment details -need to write a code for connecting

Assignment Details - Need to write a code for connecting segments (Lines) a special case of TSP. The problem is to connect lines in 2d/ 3d space with path obstructions. Can you help me write the code for this? Hope you m ...

Assignment -we have daily gridded rainfall data of 40 years

Assignment - We have daily gridded rainfall data of 40 years and structure of the dataset is like below; Lat = [6.5:0.25:38.5]; Lon = [66.5:0.25:100]; Rainfall (135x129x365x40) (Lon, Lat, days, years). Now, we looking fo ...

Question a safe prime is a prime number that can be written

Question : A safe prime is a prime number that can be written in the form 2p + 1 where p is also a prime number. Write a MATLAB script file that finds and displays all safe primes between 1 and 1000.

Question - verify the attached paper with matlab and get

Question - Verify the attached paper with matlab and get all the results in the paper and explain step by step the matlab code. Paper - Improving Massive MIMO Belief Propagation Detector with Deep Neural Network. Attachm ...

Assignment -data is given on which want to do computational

Assignment - Data is given on which want to do computational production planning using Metaheuristic MATLAB Programming: 1) Ant Colony Algorithm on both Partial and Total Flexible Problem. 2) Bee Algorithm on both Partia ...

What comparison of means test was used to answer the

What comparison of means test was used to answer the question

Question 1 manipulate spectral imagehyperspectral images

Question 1. Manipulate spectral image Hyperspectral images can be seen as a generalisation of normal colour images such as RGB images. In a normal RGB colour image, there are 3 channels, i.e. channels for red colour, gre ...

Assignment -matlab codes and simulated model in

Assignment - Matlab codes and simulated model in simulink/matlab and truetime. 1. Matlab codes and simulink model for pid controller optimization using particle swarm optimization (PSO) my plant is integer order 1000/(s^ ...

Assignment matlab programmingusing appropriate matlab

Assignment: MatLab Programming Using appropriate MatLab syntax, write the code required to analyse and display the data as per the problem description. The order of the MatLab Program should be as follows: Variables and ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As