The assigned material is Steel AISI-4340 and its properties are gathered from the materials database handout.

Factor of Safety

Surface area of plate surfae

Depth to which plate will be subjected

Figure 1: NESTA. (2012). Density of Ocean Water. Retrieved March 28, 2016, from http://www.windows2universe.org/earth/Water/density.htmlThe pressure at the operating depth is a combination of two regions as seen in Figure 1. The first is from the surface to 1000m where the density of the sea water becomes constant, the second is 1000m to 6000m which is a consistant density. This ends up being a simple equation of density*Depth*gravity=Pressure

Youngs Modulus

Yield Stress

Poissons RatioAllowable stress due to factor of safety

This For loop creates a matrix of values of a/b from 1 to 2 in 0.05 increments

These two equations solve for a and b so that surface area remains constant. At any value of a and b, ab=SA

a and b are defined here as a single integer value taken from the matrices for a and b

h has to be defined to so that the root() function has a starting point to work from, Note that the solution for h is discontinuous and results in an error when it cannot converge to a single value in the case of an asymptote. So by varying h the function gets into a region which does have a zero value.

Since their is a large pressure applied to the top surface of the plate this has some impact on the resultsAmplitude of deflection. Note that D is omitted as it cancels out in all the stress equations

max stress at edge of plate on y-axis

max stress at edge of plate on x-axis

Max stress at the center of the plate

Minimum Thickness of plate at y=b

Minimum Thickness of plate at x=a

Minimum Thickness of plate at x=y=0

Deflection at center of PlateFlexural Stiffness

global definition of i to determine value in matrices for a and b