User:Eml4500.f08.group/HW5/Matlab

=Constant Element Properties=

Below is the code for analysis and plotting of the 6-Bar truss with equivalent elements.

Additional Fuctions
The book's code divides up the work load on the FEA analysis among a a number of functions. The three functions called upon in the above code are shown below.

Results
The Results obtained were identical to the results in the book.



K =

85355       35355       -50000            0            0            0            0            0       -35355       -35355        35355        35355            0            0            0            0            0            0       -35355       -35355       -50000            0        85355       -35355            0            0            0            0       -35355        35355            0            0       -35355  1.0202e+005            0            0            0       -66667        35355       -35355 0           0            0            0        71554       -35777            0            0       -71554        35777            0            0            0            0       -35777        17889            0            0        35777       -17889            0            0            0            0            0            0        71554        35777       -71554       -35777            0            0            0       -66667            0            0        35777        84555       -35777       -17889       -35355       -35355       -35355        35355       -71554        35777       -71554       -35777  2.1382e+005            0 -35355      -35355        35355       -35355        35777       -17889       -35777       -17889            0  1.0649e+005

R (Loading N)=

0           0        10000        17321            0            0            0            0            0            0

d (displacement)=

d1          0 d2          0 d3    0.21311 d4    0.24998 d5          0 d6          0 d7          0 d8          0 d9 -0.0060971 d10  0.012242

reactions (N) =

F1     -10873 F2    -217.27 F5     874.27 F6    -437.13 F7    -1.7279 F8     -16666

results = Stress (MPA)  Axial Forces (N) 5.3276e-005      10.655        10655 -4.6334e-006    -0.92669      -926.69 -4.8873e-006    -0.97746      -977.46 -8.3326e-005     -16.665       -16665 1.5363e-006     0.30727       307.27 -9.659e-009  -0.0019318      -1.9318

=Variable Element Properties=

Below is the code for analysis and plotting of the 6-Bar truss with varying elements properties.

Results
The Variation of the element properties has a minor effect on the displace and reactions, but it isn't very noticeable. This is because Elements 2 and 4, which are working the most against the applied load were in one case left unchanged, and in the other changed to a slightly lower E of 180 GPa instead of 200 GPa.



K =

76391       38891       -37500            0            0            0            0            0       -38891       -38891        38891        38891            0            0            0            0            0            0       -38891       -38891       -37500            0        69320       -31820            0            0            0            0       -31820        31820            0            0       -31820        98486            0            0            0       -66667        31820       -31820            0            0            0            0        71554       -35777            0            0       -71554        35777            0            0            0            0       -35777        17889            0            0        35777       -17889            0            0            0            0            0            0        89443        44721       -89443       -44721            0            0            0       -66667            0            0        44721        89027       -44721       -22361       -38891       -38891       -31820        31820       -71554        35777       -89443       -44721  2.3171e+005        16015 -38891      -38891        31820       -31820        35777       -17889       -44721       -22361        16015  1.1096e+005

R (Loading in N) =

0           0        10000        17321            0            0            0            0            0            0

d (displacement) =

d1          0 d2          0 d3    0.26485 d4    0.26083 d5          0 d6          0 d7          0 d8          0 d9 0.00063864 d10 -0.001246

reactions (N) =

F1    -9908.3 F2     23.619 F5    -90.274 F6     45.137 F7    -1.4008 F8     -17389

results = Stress (MPA)  Axial Forces (N) 6.6213e-005      9.9319       9931.9 5.347e-007    0.096245       96.245 5.0465e-007     0.10093       100.93 -8.6943e-005     -17.389       -17389 -1.5183e-007   -0.033402      -33.402 -6.2645e-009  -0.0015661      -1.5661

=3D Trusses=

Additional Fuctions
The book's code divides up the work load on the FEA analysis among a a number of functions. The three functions called upon in the above code are shown below.

Results
This three bar truss is statically indeterminate. See other three bar trusses

conn =

1    4     2     4     3     4

lmm =

1    2     3    10    11    12     4     5     6    10    11    12     7     8     9    10    11    12

d =

d1     0 d2     0 d3     0 d4     0 d5     0 d6     0 d7     0 d8     0 d9     0 d10   -0.18705 d11   -2.592 d12   -0.3858

reactions (N) =

F1     6666.7 F2      13333 F3     -13889 F4    -6666.7 F5     6666.7 F6    -9259.3 F7          0 F8          0 F9      23148

results = Stress (MPA)  Axial Forces (N) 0.00050936      101.87        20375   0.00033036       66.072        13214   -0.0001929       -38.58       -23148

Plots