User:Eas4200c.f08/HW report table/The best of HW6

 Under construction; not final (but close to being stable after a couple of weeks). The intention here is to document the best features in any HW report for the readers (including you); if you see excellent features in any HW report (including your team's) that I may have missed noticing, don't hesitate to let me know. I don't have time to read all HW reports in detail. In fact, due to time constraint, I only selectively looked at a few important features. On the other hand, I also added some annotations (e.g., related to errors) in the HW reports that I looked through for the benefit of everyone. Eml4500.f08 15:12, 22 November 2008 (UTC)


 * classnotes graded over 100%
 * user:eas4200c.f08/Plate buckling: lecture from my wiki page.
 * motivation: NACA airfoil
 * rectangular plate under compressive force
 * simply-supported boundary conditions
 * clamped boundary conditions
 * torsional analysis by elasticity theory (cont'd)
 * dimensional analysis of equilibrium equation for stresses
 * equation of equilibrium for shear stresses
 * Prandtl stress function, governing equation in terms of rate of twist angle
 * traction force in terms of stress tensor and normal to a facet
 * expression for $$\displaystyle t_y$$
 * expression for $$\displaystyle t_z$$
 * boundary condition for Prandtl stress function
 * torsion of uniform bar with circular cross section
 * Prandtl stress function $$\displaystyle \phi$$
 * verification with boundary condition for $$\displaystyle \phi$$
 * evaluation of free parameter using governing equation $$\displaystyle \phi$$
 * read and report from Sun [2006]. Most complete: Team Aero6, Team Blue
 * formal proof of zero warping by elasticity
 * zero boundary condition for axial displacement $$\displaystyle u_x (y,z)$$ at $$\displaystyle x=0$$
 * deduce zero axial displacement $$\displaystyle u_x (y,z)$$ throughout the bar, hence no warping. NOTE: Team VQCrew (with annotations), Team Aeris (with annotations) copyright violation / plagiarism -20%, Team Carbon Lecture Notes (with annotations), Team Aero (with annotations)
 * flexural shear flow in thin-walled cross sections
 * non-symmetrical cross sections
 * bending normal stress
 * matrix form
 * particularization to symmetrical cross sections
 * shear flow
 * matrix form


 * matlab problem graded over 100%: develop matlab codes to analyze the bending behavior of the NACA 2415 airfoil reinforced with stringers and buckling analysis of skin panels under compressive loads.
 * figure of simply-supported rectangular plate under distributed compressive load
 * figure of buckling modes with $$\displaystyle m=n=1$$ and $$\displaystyle (m=2, n=1)$$ in perspective. Best figures: Team Aero (with annotations). NOTE: Many teams did not plot the perspective view of the buckling mode shapes, but only the plot of a sine function in these buckling modes, e.g., Team VQCrew (with annotations).
 * bending normal stress along the top and bottom skin panels of NACA airfoil
 * plot of $$\displaystyle \sigma_{xx}$$ vs $$\displaystyle y$$ coordinate
 * plot of average $$\displaystyle \sigma_{xx}$$
 * Results for average compressive $$\displaystyle \sigma_{xx}$$:
 * Team VQCrew (with annotations) -59 MPa on panel FB; seems more reliable than most, but not sure about correctness; at least the result is consistent with their previous result for maximum compressive bending stress of -81 MPa in Team VQCrew HW5. Later, in Team VQCrew HW6 Fixed (with annotations), the average compressive stresss was corrected to about -3 MPa, with the maximum compressive bending stress about -4 MPa; need to verify with "back-of-the-envelope" calculation.
 * Team Aero (with annotations) -26.5 MPa on panel FB, -32.1 MPa on panel EH (both compressive !?), something is wrong; see also my comments regarding the plot.
 * Team Aero_Eelman Lectures HW6 Did not provide the result in numerical value; from the figures, negative (compressive) stress about -44 MPa on panel EH; something is wrong.
 * Team Aeris (with annotations) About -19 MPa on panel FB from the figure; much lower than Team VQCrew; likely incorrect.
 * Team Carbon Matlab code About -1 MPa on panel FB; seems too low; likely incorrect. Also, the neutral axis has too steep angle; looks incorrect.
 * theoretical buckling stress for rectangular plate under compressive load
 * simply-supported boundary conditions
 * figure of $$\displaystyle k_c$$ versus aspect ratio $$\displaystyle a/b$$
 * clamped boundary conditions
 * figure showing lowest critical buckling stress for both boundary conditions versus aspect ratio $$\displaystyle a/b$$
 * comparison with computed stress of NACA skin panel
 * Results:
 * Team VQCrew (with annotations). The figure shows the critical buckling stress for the simply supported boundary conditions is higher than that for the clamped boundary conditions; should be the other way around; something is wrong; likely incorrect. See also my comments in Team VQCrew HW6 Fixed (with annotations).
 * Team Aero (with annotations): Ditto, same remark as for Team VQCrew; why critical buckling stress for clamped boundary conditions lower than that for simply supported boundary conditions.
 * Team Radsam did not provide this figure.

EML 4500, The best of HW6