1 Building Blocks
[σ, a] = Hertz(r1,r2,r3,r4,tp,P,geometry,material) given a point loading and 5 design parameters, this function output the stress (principal stress as 1 by 3 vector)
at the center of contacting and contact radius. This function use equation 3-12 in the project
[σbend] = bendStressPolymer(tp, a, P, x, y) given a UHMWPE thickness, the point loading and the distance of load from the left end, this function output the
bending stress at (x,y), where x is the distance to the left end, y is the depth below the
UHMWPE surface. This function is almost the same function in project part A, but you also
need bending below the beam surface.
[σV M ] = stressVM(σ) given a principal stress (1 by 3 vector), this function output
the von Mises stress as a scalar.
2 Objective function
[σA, a] = stressA(r1,r2,r3,r4,tp) given only design parameter, for the regular
loading case, this function call Hertz and bendStressPolymer to get the principal
stress at A point (center at contact ares, on the surface). One thing to notice is this function
call bendStressPolymer twice since we have two loading (symmetric), also the bending
stress from bendStressPolymer should be appended to first component of contact stress
[σB] = stressB(σA,a,tp) given the stress state at A point and the contact radius,
and the thickness of polymer, this function calculate the stress state at B point (max shear).
This function use the contact stress at A point with the scale to get the contact stress at
B point, also append the bending stress at B point from bendStressPolymer to get
complete stress state. One critical thing to notice is the x component in σA includes bending
stress at A point, which means you cannot use the value of x component to scale. You can
only use y or z component of stress at A point to scale to get stress at B point.