Computational engineering: SHELLS
Budget: €30 – €250 EUR
Open the file A03 - Shells.zip to read the activity and see documentation attached.
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Consider a squared clamped plate of thickness h = 0.005 m and side length ? = 1.5 m, subjected to a uniformly distributed surface load ? = −1.5 × 105 N/m2. The plate is made of an isotropic material with Young’s modulus ? = 69 GPa, Poisson’s ratio ??= 0.3.
(See figures in the document attached)
The following is asked:
(a) Create a Matlab function that obtains the mesh information of the plate discretization with 4-noded rectangular elements, for a given number of elements ? (in each direction) as input. The function should return:
- Nodal coordinates matrix [?]
- Nodal connectivities matrix [?n]
- Fixed degrees of freedom matrix [?p]. Reminder: Clamped conditions imply prescribed displacements and rotations on all boundary nodes.
- Distributed loads matrix [?e].
Plot the resulting meshes for ?? = {4, 8, 16, 32}.
(b) Solve the static system of equations for ?? = {4, 8, 16, 32} and plot the deformed plate. For each case, obtain the maximum vertical displacement ?_?max and plot them versus ??.
(c) Compute the Von Mises stress at each Gauss point and plot the results for ?? = 32.
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Consider a squared clamped plate of thickness h = 0.005 m and side length ? = 1.5 m, subjected to a uniformly distributed surface load ? = −1.5 × 105 N/m2. The plate is made of an isotropic material with Young’s modulus ? = 69 GPa, Poisson’s ratio ??= 0.3.
(See figures in the document attached)
The following is asked:
(a) Create a Matlab function that obtains the mesh information of the plate discretization with 4-noded rectangular elements, for a given number of elements ? (in each direction) as input. The function should return:
- Nodal coordinates matrix [?]
- Nodal connectivities matrix [?n]
- Fixed degrees of freedom matrix [?p]. Reminder: Clamped conditions imply prescribed displacements and rotations on all boundary nodes.
- Distributed loads matrix [?e].
Plot the resulting meshes for ?? = {4, 8, 16, 32}.
(b) Solve the static system of equations for ?? = {4, 8, 16, 32} and plot the deformed plate. For each case, obtain the maximum vertical displacement ?_?max and plot them versus ??.
(c) Compute the Von Mises stress at each Gauss point and plot the results for ?? = 32.