Automatic Mesh Function for Heterosis Fem with Modular-Filter Technique (update:31-07-07)

English Description:

Generally, in finite element models degree-of-freedom of all nodes be equals. But, a Heterosis finite element model has each of the corners are assumed to possess three degree-of-freedom (one displacement two rotation w,Qxx,Qyy) and centroidal node has two degree-of-freedom (two rotation Qxx,Qyy). In this matlab sub-function application have produced automatic mesh function, position matrix, reology matrix and this matrix components (R and Re matrix) with modular-filter-technique.

Turkish Description:

Genellikle, sonlu eleman modellerinin tüm dügümlerinde esdeger serbetlik derecesi vardir. Fakat, bir Heterosis sonlu eleman modelinin, her bir kösesinde üç adet serbetlik derecesine (bir deplasman, iki dönme w,Qxx,Qyy) ve merkezi dügüm noktasinda iki adet serbestlige (Qxx,Qyy) sahiptir. Bu Matlab alt-program uygulamasinda otomatik ag fonksiyonu, konum matrisi ve reoloji matrisi ve bu matrisin bilesenleri (R ve Re matrisi) modüler filtreleme teknigi ile türetilmistir.

Syntax:
mesh_x = "x" axis direction total mesh value.
mesh_y = "y" axis direction total mesh value.
total_x = "x" axis direction total length.
total_y = "y" axis direction total width.

Cor = In global cartesian system all nodes coordinates (xi,yi)
Pos = All nodes position matrisi for each finite element
R,Re = Reology matrix components.
freedom = System total degree-of-freedom.

Example:

[A,B,C,D]=Heterosis(2,3,1,0.5) <----|


A =
-0.5000 -0.2500
0 -0.2500
0.5000 -0.2500
1.0000 -0.2500
1.5000 -0.2500
-0.5000 -0.0833
..... ...... ......
0.5000 0.7500
1.0000 0.7500
1.5000 0.7500

B =
1 3 13 11 2 8 12 6 7
3 5 15 13 4 10 14 8 9
11 13 23 21 12 18 22 16 17
13 15 25 23 14 20 24 18 19
21 23 33 31 22 28 32 26 27
23 25 35 33 24 30 34 28 29

C = size(6x27)

Columns 22 through 27

... 16 17 18 19 20 NaN
... 21 22 23 24 25 NaN
... 44 45 46 47 48 NaN
... 49 50 51 52 53 NaN
... 72 73 74 75 76 NaN
... 77 78 79 80 81 NaN

D =
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17 18
19 20 NaN
21 22 23
24 25 NaN
26 27 28
29 30 31
32 33 34
35 36 37
38 39 40
41 42 43
44 45 46
47 48 NaN
49 50 51
52 53 NaN
54 55 56
57 58 59
60 61 62
63 64 65
66 67 68
69 70 71
72 73 74
75 76 NaN
77 78 79
80 81 NaN
82 83 84
85 86 87
88 89 90
91 92 93
94 95 96
97 98 99

Run-Times:

tic;[A,B,C,D]=Heterosis (2,2,1,0.5);toc Elapsed time is 0.012970 s.
tic;[A,B,C,D]=Heterosis(10,10,1,0.5);toc Elapsed time is 0.007256 s.
tic;[A,B,C,D]=Heterosis(50,50,1,0.5);toc Elapsed time is 2.262299 s.
tic;[A,B,C,D]=Heterosis(100,100,1,0.5);toc Elapsed time is 89.255372 s.