AERO4630-Project 2 Solved

Problem 1: Conducting a tensile test
Let’s try to recreate the tensile test we did in class. We are recreating the experiment done by the Instron machine.The idea is to take a beam of rectangular cross section, clamp it on one end and provide a displacement on theother. , and just like in class. Let’s say we are working We are clamping the left facewith steel. This makes the densityAssume we have a beam of lengthρ and providing a displacement= 7800kgmand−3, the Young’s modulusfrom and . on the right faceE = 200GPa and the Poisson ratio. ν = 0.3.

                                                                      L = 150mm W = 25m              H = 25mm

(1a)         Compute the Lame’ parameters,x = 0                                              δ                                   x = L

δ = 1.0mm
(1b)   Modify the code to perform a tensile test for a given displacementCompute the average stressbyto plot the normal stress. Using paraview, obtain the total forceon the face, perform an area integral, and get the total force on that face.λ     µ                                                                                                                 whereE is the area of the face.ν on the right face . The average strain is given. To do this you need

εavg = δ/L                                                                                                           Fright                                                          x = L

                                                                   = F              A         A
(1c) Repeat the above for multiple displacements and plot a stress-strain curveof the stress-strain curve.Hint: Features like weighted area integral and slicing might be useful                                                                                              . Compute the slope

σavg −εavg

Note the units of the problem. Any code starts to behave weird if you have really large values (like GPa) and really small values (like mm) at the same time. It might be wise to non-dimensionalize your equations. You can nondimensionalize an equation in many different ways.

Problem 2: Applying force on a beam clamped at both ends
Let’s modify our problem. Imagine a beam of length L, width W and height H clamped at x = 0 and x = L.

y

 

more and more concentrated on a smaller and smaller region.(2The beam is subjected to a total forcea)     Assume the dimensions of the beam and material properties are the same as previous question. Let’spointpick a total force             . Remember that you need traction (force per unit area) for the code.andF spread on the top face as shown in the figure. As. Simulate this force and obtain the vertical displacement of thea increases, the force is

                                                      F = 10N             a = L/4

(L/2,W,H/2)
Hint: To get the displacement at a point from Fenics, read the tutorial ft02_poisson_membrane.py on the website. Line 61 might give you a hint.

(2b) Repeat these simulations forIf you are curious, try to see if you can makea = L/N, where N = 6work !,5,4,3 and plot the vertical displacement of (L/2,W,H/2).