Hey guys! I have a pretty simple MATLAB assignment here, due at 11pm (Central Standard Time) Sunday Nov. 20th!

Let me know if you have any questions!

 

Week 13 Application ActivityME219 Computer Programming for EngineersThis week we will be revisiting our problem from Week 8, with a few key differences:a.Stress calculations will be done over a range of distances beneath the surfaceb.Maximal shear stress will be calculated (see equation 4)c.Major program operations will be handled by function filesConsider the diagram below, which depicts two cylinders being held in contact by a force (ܨ) that isuniformly distributed along the length (ܮ) of the cylinders. The resulting stress distribution will beelliptical in shape, such that the maximum stress occurs along the line of contact whereݕൌݖൌ0.We are interested in calculating the magnitude of the principal normal stresses (ߪ௫,ߪ௫,ߪ௫) andmaximum principal shear stress (߬௠௔௫) in the larger cylinder for points beneath its surface, i.e. forincreasing values ofݖ. These may be calculated as follows1:ߪ௫ൌെ2ߥଶ݌௠௔௫ቆට1൅௭మ௕మെ௭௕ቇ(1)ߪ௬ൌെ݌௠௔௫ቈቆ2 െଵଵା೥మ್మቇ ට1൅௭మ௕మെ2௭௕቉(2)ߪ௭ൌି௣೘ೌೣටଵା೥మ್మ(3)߬௠௔௫ൌఙ೥ିఙ೤ଶ(4)zyxFFLd2d1zy2b

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whereܾis the half‐width of the elliptical distribution, given byܾൌ ටଶிగ௅൫ଵିఔభమ൯ாభ⁄ା൫ଵିఔమమ൯ாమ⁄ଵௗభ⁄ାଵ ௗమ⁄(5)and݌௠௔௫is the maximum pressure, given by݌௠௔௫ൌଶிగ௕௅(6)The following table summarizes the properties of the cylinders we’re interested in evaluating.SymbolDescriptionValueݒଵ,ߥଶPoisson’s Ratios for bothcylinders0.3(both)ܧଵ,ܧଶYoung’s Modulus for bothcylinders206 ൈ 10ଽܰ݉ଶ⁄݀ଵDiameter of top cylinder38 ݉݉݀ଶDiameter of bottom cylinder70 ݉݉ܮLength of both cylinders50 ݉݉ܨCompressive force450 ܰݖDistance below surface ofbottom cylinder0 െ 0.15 ݉݉Please follow the instructions below to complete this problem.1.Open MATLAB, navigate to the directory where you want to save your work, and create a newscript file called “W13.m”.2.PART 1: create variables for the constants in the table above. Note thatݖwill be a vectorranging from 0 to 1.5 mm. Be sure to select an appropriate step size when creating this vector –I suggest 0.001 mm.3.PART 2: Create a function file named “stresscalc.m” to handle your stress calculations. Theinputs to this function should include the nine variables listed in the table above; the outputsshould include the 4 stresses calculated using equations (1)‐(4). In your function file: do thefollowing:a.Using equations (5) and (6), calculateܾand݌௠௔௫, respectively, and assign them toappropriate variables.b.Calculate the following intermediate variables, which will simplify the process ofcalculating your principal stresses:ܽଵൌ௭௕ܽଶൌ ට1൅௭మ௕మ(7) (8)

Attachments:

• 1494234261-Week 13 Application Activity.pdf