User:Eml4500.f08/HW report table/The best of HW4

 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.) Eml4500.f08 13:46, 28 October 2008 (UTC)


 * 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 $$\displaystyle \tilde{\mathbf T} ^{(e)} _{4 \times 4}$$. Best overall explanation for method 2: Team Gravy (with an error on general inversion of block diagonal matrices; should not write the inverse of a matrix as $$\displaystyle \frac{1}{\underline{D}} = \underline{D}^{-1}$$) Team Echo
 * transformation of force components. Best explanation: Team Gravy
 * 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: $$\displaystyle {\tilde{\mathbf T} ^{(e)^{-1}}} = {\tilde{\mathbf T} ^{(e)^{T}}}$$. Best explanation: Team Echo
 * 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. Best explanation: Team Echo
 * 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. Best explanation: Team Jamama
 * principle of virtual work (PVW), the scalar case.

EAS 4200C, The best of HW4
 * matlab problem graded over 100%
 * 5-bar truss system
 * problem and matlab-code description. Best description: Team Bike. See also the matlab-code description of Team Ramrod
 * plot of underformed and deformed shapes with node numbers and element numbers. See Team Bike
 * 3-bar truss system
 * problem and matlab-code description. Best description: Team Bike. See also the matlab-code description of Team Ramrod
 * plot of underformed and deformed shapes with node numbers and element numbers. See Team Bike
 * 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 Echo (better plot of 2nd eigenmode; 3rd mode is pure mechanism) Team Delta_6 (plot of 2nd eigenmode may need small magnification factor) Team FEABBQ (plot of 2nd eigenmode may need small magnification factor)
 * rectangular truss system
 * problem description, matlab code description and results. See Team Bike, but this team did not plot the eigenmodes the right way (like deformed shapes). See Team Delta_6 for the 2-bar truss system above.
 * 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