User:Eas4200c.f08/HW report table/The best of HW5

 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 11:11, 10 November 2008 (UTC)


 * classnotes graded over 100%
 * torsional analysis (cont'd)
 * strain-stress relation for isotropic linear 3-D elasticity in Voigt notation
 * stress-strain relation:
 * inverse of block-diagonal matrix
 * inversion of strain-stress relation
 * deduce the 4 zero stress components from the 4 zero strain components due to kinematic relations using stress-strain relation
 * equilibrium equation for stresses
 * uniform stress field vs non-uniform stress field: 1-D case as example
 * derivation of 1-D equation of equilibrium with distributed axial load
 * 3-D equation of equilibrium in indicial notation
 * derivation for x direction
 * deduce equation of equilibrium in terms shear stresses for torsional analysis
 * bidirectional bending
 * definition of bending moments in terms of normal stress and cross-sectional coordinates
 * components of moment of inertia tensor for cross section
 * normal bending stress in terms of bending moments and moments of inertia
 * neutral axis, definition, formula


 * matlab problem graded over 100%: develop matlab codes to analyze the bending behavior of the NACA 2415 airfoil reinforced with stringers. Best overall solution: Team VQCrew, complete description of the problem with figures, complete matlab codes, figures describing the results, narrative on the results, comparison of the results of Part I and Part II in table form; but it is not clear why Team VQCrew chose not to use their rear stringers with L brackets. NOTE: Team ZYX (with annotations) did not do this problem.  Team Aero_(Eelman) (with annotations), there are a lot of problems to be fixed in this wiki page.  Team Aeris (with annotations).
 * description of the problem
 * Part I: neglect bending resistance from skin and spar webs
 * location of centroid of stringers
 * components of moments of inertia tensor
 * slope of neutral axis
 * highest normal bending stress and its location
 * ultimate bending moments, assuming stringers made of 300 M steel
 * a figure and a narrative explaining the above results
 * Results: $$\displaystyle I_{22}, I_{33}, I_{23}, \beta$$ in $$\displaystyle m^4, m^4, m^4, rad \ {\rm or} \ ^\circ$$; $$\displaystyle M_y^{ult}, M_z^{ult}$$ in $$\displaystyle Nm$$
 * Team VQCrew $$\displaystyle 6.6875E-007, 3.4375E-005, 9.3322E-007, 0.0345 \,rad = 1.219^\circ$$; Moments $$\displaystyle 28355, -11342$$.


 * Team Radsam $$\displaystyle 6.3403E-007, 3.6111E-005, -2.8043E-007, 0.7694$$. Later corrected in Team Radsam Fixed to $$\displaystyle 6.8320E-007, 8.1250E-005, 4.7132E-007, 1.3690^\circ$$ (Results in close agreement with Team VQCrew for $$\displaystyle \beta$$, except for $$\displaystyle I_{22}$$); Moments $$\displaystyle -41013, 16405$$ (Results NOT in agreement with Team VQCrew, likely incorrect)
 * Team Carbon $$\displaystyle 6.3913E-007, 8.3333E-006, -7.6055E-008, ???$$, $$\displaystyle \beta$$ not given ($$\displaystyle I_{22}$$ agreed with Team VQCrew and Team Radsam, but not other moments of inertia); Moments $$\displaystyle -7176, 2870$$ (Too small, likely incorrect).
 * Team Gator $$\displaystyle 8.7409E-007, 1.6664E-005, -6.4413E-007, -3.3609$$ (Results did not agree with VQCrew, Radsam; likely incorrect); $$\displaystyle -8087, -3235$$ (Results likely incorrect).


 * Part II: with bending resistance from skin and spar webs, and with detailed geometry of stringers
 * location of centroid of stringers
 * components of moments of inertia tensor
 * slope of neutral axis
 * highest normal bending stress and its location
 * now neglect bending contribution from the skin and spar webs
 * highest normal bending stress in any stringer
 * ultimate bending moments, assuming stringers made of 300 M steel
 * a figure and a narrative explaining the above results and a comparison with the results from Part I
 * Results
 * Team VQCrew $$\displaystyle 6.2884E-007, 1.4533E-004, 4.8673E-006, 0.0347$$ (Agreed with Part I of Team VQCrew); Moments $$\displaystyle 20970, -8388$$ (consistent with results in Part I; likely correct).
 * Team Radsam $$\displaystyle 7.4915E-005, 5.3120E-003, -9.6928E-003, 56.6522$$ !!! Later corrected in Team Radsam Fixed to $$\displaystyle 6.3373E-007, 1.4810E-004, 5.3883E-006, 2.2781$$; That's better, but still did not agree with Team VQCrew for $$\displaystyle \beta$$; Moments $$\displaystyle -24662, 9865$$ (closer to results of Team VQCrew, but signs seem incorrect)
 * Team Carbon $$\displaystyle 1.0893E-004, 1.7658E-004, -3.4076E-007, ???$$ ($$\displaystyle \beta$$ not given; results did not agree with Team VQCrew, Team Radsam; like not correct); Moments $$\displaystyle -490920, 196370$$ (too large, likely incorrect).
 * Team Gator $$\displaystyle 3.3178E-007, 1.4315E-004, 6.6650E-006, 2.6622$$ (Results did not agree with VQCrew; likely incorrect; $$\displaystyle \beta$$ switch from negative to positive); Moments $$\displaystyle 8630, 3452 $$ (magnitude did not agree with Team VQCrew; signs changed compared to Part I; results likely incorrect).

EML4500, The best of HW5