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Explain why the functions diag, dim, length, and names can be assigned new values (as in diag(m)=pi).
Using the Orange dataset that monitors tree growth versus age for five orange trees, represent the dataset using the command xyplot.
Compare both of the generators in part a. with rnorm.
Calculate the strain at position x = aw/4, y = af /2 for the case of a longitudinal tensile load Nx = 5 N/mm using the bending-restrained model.
Optimum values for these geometric ratios could be obtained by analyzing the buckling modes of the beam.
The maximum deflection should not exceed 1/800 of the span. Use the carpet plots for E-glass-polyester with Vf = 0.5.
Determine the maximum tip load P that can be applied to the beam of Example 1.
Compute the torsional stiffness (GJR) of the beam designed in Example 1.
Data has been obtained experimentally for a composite based on an unidirectional carbon-epoxy prepreg
Redesign the dome in Example 1 for the case of added internal pressure p = 2 kP a. Use the carpet plots for E-glass-polyester.
Find the values of shift ns in weaves defines by 6/ns/1, 8/ns/1, and 9/ns/1, that feature the same property as 4/2/1 in Problem .
Use solid modeling software such as ProE(TM) to draw to scale the RUC's for sample type 2 in Table.
Calculate the mesoscale tow volume fraction Vmeso and the tow fiber volume fraction V f f iber = V w f iber of the weave type 5.
Compute the curvature of the bimetallic in Problem 2 when it is subjected to a change of temperature ?T = 10 ?C.
All laminae are 1.0 mm thick. Comment on the coupling of the constitutive equations for each case.
Calculate the strength ratio R for a unidirectional lamina of glass-epoxy.
Compute the mean, standard deviation, and coefficient of variance. Plot the histogram. Plot the normal probability density function.
A tensile test specimen of the material in Problem 1 is 10 mm wide, 2 mm thick, and 150 mm long and it subjected to an axial force of 200 N.
What is the detrimental effect of an incompletely cured thermoset matrix on the life of a PMC?
Same as Problem 1 but you are required to use a thermoplastic matrix. What additional considerations must be accounted for in this case?
Write a definition for Representative Volume Element. Draw a set of fibers in an hexagonal array: six fibers at the vertices of an hexagon plus one.
Consider the following material called carbon-epoxy with a fiber volume fraction of 70% and E= = 379 GPa, ?f = 0.22, Em= 3.3 GPa, and ?= = 0.35.
The amount of fibers in a composite sample can be determined by a burn-out test.
Assume that the standard deviation of fiber misalignment remains constant at the production value of 1.41 degrees.
Give an approximate value for the compressive strength of an Al-Boron composite with Vf = 0.4. Aluminum 2024 has E = 71GPa.