User talk:Stress9/HW4

Templates: $$\displaystyle \clubsuit$$ Copyright violation / plagiarism: Completeness: Team contribution: Correctness: Artistic aspect: Comments: Overall rating:

 Note: The Overall rating: here is more of a "gut feeling" than a formal quantitative grading. Follow our list of criteria for formal grading and commenting. In case of a tie, let's favor new teams for the top-3 positions. Specific comments are given for a few teams, with a focus on the top teams to serve as a standard that other teams are measured against. You can now begin to do a quantitative grading of this HW. As you grade and see the best features in the HW reports, do not hesitate to add the teams with these best features to the wiki page "The best of HW4" for each course. Stress9 01:40, 6 November 2008 (UTC)

=EAS 4200C=

User:eas4200c.f08/HW_report_table

General comments for HW4

 * See also The best of HW4, which is also accessible at the bottom of the HW report table; most of the points made below in the general comments are reported in the above wiki page to inform the students where to look for the best features. In case I miss something, please do not hesitate to inform me; I don't have time to read through all HW reports like you do.  NOTE: The teams listed in The-best-of-HW_# are not necessarily the top teams, which are at the top because of the overall quality of their reports.


 * classnotes 60% + matlab problem 40% = 100%


 * classnotes graded over 100%
 * idealized single-cell airfoil (semi-circular leading edge, straight-line body), find $$\displaystyle J$$; need to complete the solution to find the numerical value of $$\displaystyle J$$. Some team went well beyond expectation and solved this problem by coding it up with matlab; give them extra points; see Team Aero6.
 * analytical result: $$\displaystyle J = 0.100 m^4$$ Team Aero, $$\displaystyle J = 0.1001 m^4$$ Team VQCrew
 * numerical result: $$\displaystyle J = 0.125 m^4$$ Team Aero6; the error compared to the analytical result was large; perhaps there was not enough accuracy in the quadrature.
 * idealized 2-cell airfoil (rectangular body), find $$\displaystyle J$$; need to complete the solution to find the numerical value of $$\displaystyle J$$ Some team went well beyond expectation and solved this problem by coding it up with matlab; give them extra points; see Team Aero6.
 * analytical result: $$\displaystyle J = 0.855 \times 10^{-4} m^4$$ Team VQCrew
 * numerical result: $$\displaystyle J = 0.855 \times 10^{+4} cm^4 = 0.855 \times 10^{-4} m^4$$ Team Aero6
 * engineering (ad-hoc) derivation of expression for $$\displaystyle \theta$$ in terms of $$\displaystyle (G, \bar{A}, q, t)$$. Best explanation: Team VQCrew
 * figure for the derivation. The figure in Team VQCrew is not exactly correct since the line $$\displaystyle \overline{PP^{\prime\prime}}$$ is not distinguishable from the tangent to the contour; see the more correct figure in Exam 2.
 * 3 ad-hoc aspects of engineering derivation. Best description: Team VQCrew
 * torsional analysis by elasticity theory (cont'd)
 * kinematic assumption (review from previous lecture)
 * 4 zero strain components for torsion problem
 * strain-stress relation for isotropic elasticity
 * inversion for stress-strain relation for isotropic elasticity
 * 4 zero stress components for torsion problem


 * matlab problem graded over 100%
 * problem description (a repeat of my wiki page Airfoil with figure describing the various variables defining the NACA airfoil). Best description: Team ZYX had matlab figure of the NACA airfoil with all of its geometric quantities presented.
 * figure showing various points on the NACA airfoil and method of area integration by triangles for each cell. Best figure: Team Aero_(Eelman) Team Aero
 * those who did not finish their matlab problem in HW3 should finish it in HW4:
 * computation of centroid coordinates and area $$\displaystyle \bar{A}$$ for single-cell airfoil
 * validate their code with circular airfoil with convergence plot(s)
 * validate their code with various observer points $$\displaystyle P_0$$
 * plot of circular airfoil
 * apply their code to NACA 2415 airfoil with $$\displaystyle c=0.5m$$ to find centroid location and area $$\displaystyle \bar{A}$$ with convergence plot(s)
 * plot of NACA airfoil and centroid at crosshair
 * grading standard:
 * if a team did NOT validate their code, but did NOT do correctly the computation of the torsional constant $$\displaystyle J$$ for both the single-cell and the 3-cell NACA 2415 airfoils: -50%
 * if a team did NOT validate their code, but did correctly the computation of the torsional constant $$\displaystyle J$$ for both the single-cell and the 3-cell NACA 2415 airfoils: No deduction, since the validation is included in the way the integration of the areas $$\displaystyle \bar{A}_i$$ for Cell i is done.
 * develop matlab code to find torsional constant $$\displaystyle J$$ of NACA airfoil
 * single-cell NACA 2415 airfoil, compute $$\displaystyle J$$
 * 3-cell NACA 2415 airfoil, compute $$\displaystyle J$$
 * quadrature by triangles at different points in the 3-cell NACA airfoil.
 * compute the area $$\displaystyle \bar{A}_i$$ for cell $$\displaystyle C_i$$, and sum them up to get total area $$\displaystyle \bar{A}$$; error must be within 1% of the area $$\displaystyle \bar{A}$$ for the single-cell NACA airfoil.
 * compare the numerical values of $$\displaystyle J$$ and draw some conclusion
 * best solution: Team Aero Team Aero_(Eelman) Team Aero6, figure showing the quadrature by triangles and selection of observer points $$\displaystyle P_0$$ in each cell; computed $$\displaystyle J_{1C}$$ for the single-cell NACA 2415 airfoil, and $$\displaystyle J_{3C}$$ for the 3-cell NACA 2415 airfoil, showing that $$\displaystyle J_{3C} \approx J_{1C}$$ (as noted in the textbook) even though they did not make this remark; Team VQCrew did make this remark, but they initially obtained $$\displaystyle J_{3C} \approx 2 J_{1C}$$, clearly not consistent with the remark; later, they updated their work to provide the correct result; see Team VQCrew Updated. See also Team ZYX, which did not have a figure to describe the quadrature by triangles and observer points $$\displaystyle P_0$$, but had a section describing the NACA airfoil geometry.
 * Team Aero: $$\displaystyle J_{1C} = 5.129 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.6884 \times 10^{-6} m^{4}$$
 * Team Aero_(Eelman): $$\displaystyle J_{1C} = 5.1163 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.5358 \times 10^{-6} m^{4}$$, relative difference $$\displaystyle 7\%$$.
 * Team Aero6: $$\displaystyle J_{1C} = 4.9978 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.4653 \times 10^{-6} m^{4}$$
 * Team ZYX: $$\displaystyle J_{1C} = 4.970 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.276 \times 10^{-6} m^{4}$$
 * Team VQCrew: $$\displaystyle J_{1C} = 4.7543 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 8.6086 \times 10^{-6} m^{4}$$, later corrected to $$\displaystyle J_{3C} = 5.250 \times 10^{-6} m^{4}$$ in Team VQCrew Updated.
 * the above 5 teams agreed more or less with the result for $$\displaystyle J_{1C}$$ and for $$\displaystyle J_{3C}$$, except for the value of $$\displaystyle J_{3C}$$ from Team VQCrew; as a result, it is likely that the value of $$\displaystyle J_{3C}$$ from Teams Aero, Aero_(Eelman), Aero6, ZYX is the correct one. After Team VQCrew updated their work, all 5 teams agreed on both $$\displaystyle J_{1C}$$ and $$\displaystyle J_{3C}$$.


 * matlab-code certification: some students signed this section, after having claimed not knowing how to code with matlab but did not report their matlab tutorial work (some of these students were from the two teams that were disbanded).


 * contributing team members: I noticed that not all team members contributed to HW4, e.g., Team Aero6. Non-contributing team members get zero HW4 grade. Please revisit HW1, HW2, HW3 to check on contributing team members; non-contributing team members should get zero HW grade.

Specific comments on team HW4 reports
$$\displaystyle \clubsuit$$ Team VQCrew Copyright violation / plagiarism: No. Completeness: Team contribution: Correctness: Artistic aspect: Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team Aero6 Copyright violation / plagiarism: No. Completeness: Team contribution: Correctness: Artistic aspect: Comments: Overall rating:

=EML 4500=

User:Eml4500.f08/HW_report_table

General comments for HW4

 * See also The best of HW4, which is also accessible at the bottom of the HW report table; most of the points made below in the general comments are reported in the above wiki page to inform the students where to look for the best features. In case I miss something, please do not hesitate to inform me; I don't have time to read through all HW reports like you do.  NOTE: The teams listed in The-best-of-HW_# are not necessarily the top teams, which are at the top because of the overall quality of their reports.


 * classnotes 65% + matlab problem 35% = 100%


 * classnotes graded over 100%
 * 2-bar truss model problem
 * assembly of element stiffness matrices into global stiffness matrix: connectivity (conn) array and location matrix master (lmm) array
 * method 2 to derive element stiffness matrix $$\displaystyle \mathbf k ^{(e)} _{4 \times 4}$$ in global coordinates: transformation of element dofs $$\displaystyle \mathbf d ^{(e)} _{4 \times 1}$$ in global coordinates $$\displaystyle (x,y)$$ to expanded element dofs $$\displaystyle \tilde{\mathbf d} ^{(e)} _{4 \times 1}$$ in axial and transversal coordinates, square transformation matrix $$\displaystyle \tilde{\mathbf T} ^{(e)} _{4 \times 4}$$.
 * force-displacement relation for dofs $$\displaystyle \tilde{\mathbf d} ^{(e)} _{4 \times 1}$$, stiffness matrix $$\displaystyle \tilde{\mathbf k} ^{(e)} _{4 \times 4}$$.
 * inversion of $$\displaystyle \tilde{\mathbf T} ^{(e)} _{4 \times 4}$$, orthogonal matrix: $$\displaystyle {\tilde{\mathbf T} ^{(e)^{-1}}} = {\tilde{\mathbf T} ^{(e)^{T}}}$$
 * derivation of $$\displaystyle \mathbf k ^{(e)} _{4 \times 4} = {\tilde{\mathbf T} ^{(e)^{T}}} \tilde{\mathbf k} ^{(e)} \tilde{\mathbf T} ^{(e)}$$; verification of this expression as HW.
 * eigenvectors corresponding to zero eigenvalues as obtained from matlab are not pure, i.e., they may not appear as pure rigid-body modes or mechanisms, but as linear combinations of these pure modes.
 * justification of the assembly process; equilibrium of global node 2; assembly operation $$\displaystyle \mathbf K = \overset{e=nel}{\underset{e=1}{\mathbb A}} \mathbf k^{(e)}$$ where $$\displaystyle {\mathbb A}$$ is the assembly operator.
 * principle of virtual work (PVW), the scalar case.


 * matlab problem graded over 100%
 * 5-bar truss system
 * matlab code description
 * plot of underformed and deformed shapes with node numbers and element numbers
 * 3-bar truss system
 * matlab code description
 * plot of underformed and deformed shapes with node numbers and element numbers
 * detection of mechanisms: Eigenvalue problem, zero eigenvalues, eigenvectors as deformed shapes
 * 2-bar truss system
 * rerun the eigenvalue problem to show 4 zero eigenvalues (if not done in HW3)
 * matlab code description and results
 * plot the eigenvectors as deformed shapes to exhibit 3 rigid body modes and 1 mechanism. Best figures: Team Delta_6
 * rectangular truss system
 * problem description, matlab code description and results
 * case with mechanism: Plot of underformed and deformed shapes (eigenvector with zero eigenvalue) showing the mechanism
 * case without mechanism: Plot of underformed and deformed shapes (eigenvector with lowest non-zero eigenvalue) showing NO mechanism


 * contributing team members: Non-contributing team members get zero HW4 grade. Please revisit HW1, HW2, HW3 to check on contributing team members; non-contributing team members should get zero HW grade.

Specific comments on team HW4 reports
$$\displaystyle \clubsuit$$ Team Bike Copyright violation / plagiarism: No. Completeness: Not complete; almost, did not do the 2-bar truss eigenvalue problem. Team contribution: OK; nothing beyond lecture presentations and HW requirements. Correctness: Classnotes: Almost; there are errors/misprints, e.g., missing a superscript 2 (square) in the coefficient (1,1) of the matrix

$$\mathbf{R}^{(e)}\mathbf{R}^{(e)T}=\begin{bmatrix}l^{(e)} & m^{(e)} \\ -m^{(e)} & l^{(e)}\end{bmatrix}\begin{bmatrix}l^{(e)} & -m^{(e)} \\ m^{(e)} & l^{(e)}\end{bmatrix}=\begin{bmatrix}l^{(e)} + m^{(e)2}&0 \\ 0 & l^{(e)2} + m^{(e)2}\end{bmatrix}$$;

even though this misprint is minor; also did not explain that $$\displaystyle l^{(e)2} + m^{(e)2} = 1$$; also did not exactly verify the expression $$\displaystyle \mathbf k ^{(e)} _{4 \times 4} = {\tilde{\mathbf T} ^{(e)^{T}}} \tilde{\mathbf k} ^{(e)} \tilde{\mathbf T} ^{(e)}$$, only displayed the matrices, but did not multiply them out explicitly, two matrices at a time; other incorect math formula, e.g.,

$$\mathbf{k}_{nxn}=A\mathbf{k}_{n_{el}xn_{el}}^{(e)}$$

which should be written as

$$\displaystyle \mathbf K = \overset{e=nel}{\underset{e=1}{\mathbb A}} \mathbf k^{(e)}$$

where $$\displaystyle {\mathbb A}$$ is the assembly operator. Matlab problem: 5-bar truss system: Nice table showing properties of truss elements. Good matlab code presentation. Good plot of underformed and deformed shapes. 3-bar truss system: Nice table showing properties of truss elements. Good matlab code presentation. Good plot of underformed and deformed shapes. Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). 2-bar truss: Did not do this problem. Rectangular truss: Did not actually do as I intended the problem to be; perhaps misunderstand the problem statement; there is no need for the applied load. Only need to run the eigenvalue problem on the frame using the reduced stiffness matrix $$\displaystyle \overline{\mathbf K}$$ (i.e., boundary conditions already applied to eliminate rigid-body modes) to find the number of zero eigenvalues that correspond purely to the mechanisms; there should be only one zero eigenvalue in this truss without brace. Nice table showing properties of truss elements. Good matlab code presentation. Plotting the eigenvector does not mean plotting the matrix itself, but rather the eigenmode, or deformed shape corresponding to that eigenvector (treat the eigenvector as the displacement vector); this team plotted the matrix, not the eigenmode !! Artistic aspect: OK, nothing outstanding, but correct. Comments: Nice presentation of matlab codes: syntax highlighting, comments. Misunderstood the plot of an eigenmode, which should be like plotting a deformed shape, not plotting the matrix of the eigenvector. Overall rating:

$$\displaystyle \clubsuit$$ Team Bottle Copyright violation / plagiarism: Completeness: More incomplete than others; did not do the 2-bar truss and rectangular truss eigenvalue problems; see below. Team contribution: Correctness: Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). 2-bar truss: There is something wrong with their solution; they got only 3 zero eigenvalues; I suspect that their stiffness matrix was wrong; there should be 4 zero eigenvalues; see Team Delta_6 correct plots of eigenmodes, Team Ramrod incorrect plots of eigenmodes. Rectangular truss: Rectangular truss: Did NOT do this problem. Artistic aspect: Figures not nice. Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team A-Team Copyright violation / plagiarism: Completeness: More incomplete than others; did not do the 2-bar truss and rectangular truss eigenvalue problems; see below. Team contribution: Correctness: Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). 2-bar truss: Did NOT do this problem. Rectangular truss: Rectangular truss: Did NOT do this problem. Artistic aspect: Figures not nice. Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team ATeam (Tatiana) Copyright violation / plagiarism: Completeness: Not complete; did not do the rectangular truss eigenvalue problem; see below. Team contribution: Correctness: Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). 2-bar truss: Did not plot correctly eigenmodes with zero eigenvalues; plotted the eigenvector matrices instead !! Rectangular truss: Did not do this problem. Artistic aspect: Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team Delta_6 Copyright violation / plagiarism: Completeness: Team contribution: Correctness: Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). Plotted correctly the eigenmodes for the zero eigenvalues for the 2-bar truss system, but did not do correctly (eigenvalue analysis and plot mechanism) for the case of the rectangular truss system. Artistic aspect: Comments: Nice overall presentation of the HW report; nice figures; nice matlab work (but not right for the detection of mechanism problem at the end of the HW report). Overall rating:

$$\displaystyle \clubsuit$$ Team Echo Copyright violation / plagiarism: Completeness: Team contribution: Correctness: Detection of mechanisms: 2-bar truss system and rectangular truss system (with 3 and 4 bars). 2-bar truss: Plotted correctly the eigenmodes for the zero eigenvalues for the 2-bar truss system. Rectangular truss: Did the eigenvalue analysis, but did not eliminate the boundary conditions, and hence got 5 zero eigenvalues; did not plot correctly eigenmodes with zero eigenvalues. Artistic aspect: Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team ATeam(Sean) Copyright violation / plagiarism: Completeness: Team contribution: Correctness: Detection of mechanisms: Did not actually do as I intended the problem to be; perhaps misunderstand the problem statement; there is no need for the applied load. Only need to run the eigenvalue problem on the frame using the reduced stiffness matrix $$\displaystyle \overline{\mathbf K}$$ (i.e., boundary conditions already applied to eliminate rigid-body modes) to find the number of zero eigenvalues that correspond purely to the mechanisms; there should be only one zero eigenvalue in this truss without brace. Did not run the eigenvalue problem; only do static analysis. Artistic aspect: Comments: Overall rating:

$$\displaystyle \clubsuit$$ Team Wiki1 Copyright violation / plagiarism: Completeness: Not complete; did not do the problem of detection of mechanisms (eigenvalue problem). Team contribution: Correctness: Artistic aspect: Nice figures. Comments: Misunderstood the plot of an eigenmode, which should be like plotting the deformed shapes, not plotting the matrix of the eigenvector. Overall rating:

$$\displaystyle \clubsuit$$ Team Wiki Copyright violation / plagiarism: Completeness: Not complete; did not do the problem of detection of mechanisms (eigenvalue problem). Team contribution: Correctness: Artistic aspect: Nice figures. Comments: Overall rating: