What happens in a state of uniform dilatation

Assignment Help Mechanical Engineering
Reference no: EM131226438

Multiaxial States

The computing project Multiaxial States concerns the analysis of strain and stress at a point in a solid body. The goal is to write a MATLAB program that will allow the computation of the strain associated with a prescribed motion and the stress associated with that strain through Hooke's Law. We will compute principal values, maxima, and graphically represent the state by mapping the motion both in the (x,y)  coordinates and in the principal coordinates.

Finally, we will produce Mohr's circle to represent the state.

The theory needed to execute this project is contained in the Course Notes entitled Multiaxial Strain.

The general steps are as follows:

1. Specify the components of the deformation tensor (matrix) F and use it to compute strain tensor E. The tensor F is the mapping matrix. We can use it to compute the deformed location of points that we identify in the undeformed configuration (e.g., the vertices of the initial square of material).

2. Develop code to plot both the undeformed square and the deformed version of it. Establish the vertices of the square with the points (0,0), (1,0), (0,1), and (1,1).

Compute the deformed positions of those points using F.

3. Compute the angle for the principal directions along with the principal values of strain. Develop code to plot the undeformed and deformed square defined in the coordinate system associated with the principal directions (i.e., take the initial square to have its sides along those directions and map the vertices to find the deformed body.

4. Compute the stresses associated with the strains by virtue of Hooke's law for plane strain.

5. Solve the problem of finding principal values using the eigenvalue solver (the "eig" command) in MATLAB. Output the principal values of stress, the maximum shear stress, and plot Mohr's circle for the stress state. Do the same for the strain.

6. Examine the implications of different states of strain. For example:

a. What happens in a state of uniform dilatation (elongation without shearing)?

b. Verify that pure shear has principal directions at 45 degrees from the original orientation of the block.

c. Show that the principal directions for stress and strain are the same. Is this due to the nature of Hooke's Law? Do you expect it to be true for all material models?

d. Explore any other feature of the problem that you find interesting.

e. Extend the code to do three dimensional states of strain for an extra nice project. Note that this step is not required but you are encouraged to do it to earn top marks. The visualization plots (especially the deformed and undeformed cube need to be rendered in 3D).

Write a report documenting your work and the results (in accord with the specification given in the document Guidelines for Doing Computing Projects). Post it to the Critviz website prior to the deadline.

Please consult the document Evaluation of Computing Projects to see how your project will be evaluated to make sure that you can get full marks. Note that there is no peer review process for reports in this course.

Reference no: EM131226438

Ratio of the density of the outside

The temperature outside a house is -20-C and inside it is 20-C. What is the ratio of the density of the outside air to the density of the inside air? Would in?ltration, whic

Estimate the rotating bending endurance limit

Estimate the rotating bending endurance limit and also the 103 -cycle fatigue strength for standard R. R. Moore test specimens made of steels having Brinell hard nesses of 1

Estimate the amount of pumping power required

What is the loss in available energy associated with this flow? If this same amount of loss is associated with pumping the fluid from the lower lake to the higher one at the

Estimate the thermal efficiency and the refrigerant

Cooling water is available at 208C. Specify the preliminary design of the cycle and estimate the thermal efficiency and the refrigerant and cooling water flow rates, in kg/h

What is the present worth of this project

Assume that all cash flows take place at year-end. Consider the present to be the end of 2010/beginning of 2011. Assume that there is no salvage value at the end of year 205

Calculations for the cooling effect

A reversible heat engine operates between 875 K and 310 K and drives a reversible refrigerator operating between 310 K and 225 K. the engine receives 2000 kJ of heat and the

Larger tank for settling and aeration

A water purification plant uses one tank for chemical sterilization and a second, larger tank for settling and aeration. Each tank is equipped with two sensors that measure

Uncertainty influence the decisions that managers make

Explain how risk, certainty, and uncertainty influence the decisions that managers make.  giving examples, or expressing opinions for your answer, and write the conclusion. Th


Write a Review

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd