Algorytmy MES (1)

RoG@j 2005
11/14/2005
Opis algorytmu
Schematy blokowe
!
Algorytmy MES (1)
Block diagrams
read
Zapis algorytmu
Pseudokod
Szerokość półpasma
Allokacja
calculate
!
!
B
l
Falck rule:
Cij – product of
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A
!
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m
m
n
!
!
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row i in A
column j in B
External loops
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l
1
repeat … until
while … do
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!
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Smith diagrams
Matrix multiplication
C=AxB
A(m,l), B(l,n),
C(m,n)
i rows in A (C)
j colums in B (C)
Initialize variables and matrices
From i=1 to m
From j=1 to n
Sum=0
From k=1 to l
sum=sum+aki*bjk
cij=sum
Initialize variables
and matrices
For i=1 to m
For j=1 to n
Sum=0
For k=1 to l
Sum=sum+
a(k,i)*b(j,k)
i=1..m
j=1..n
Zagnieżdżona struktura
Pseudokod
Algorytmy MES (1)
for
Struktura zagnieżdżona
Opis Smith’a
Mnożenie macierzy
!
o
if
!
n
write
C(i,j)=sum
Struktura kodu MES
Read data and allocate arrays
Find problem size and bandwidth
Null matrices
For all elements
Find steering vector - allocation
Compute element matrices
Assemble global stiffness matrix
Factorize the matrix and solve equations
For all elements
Compute internal forces (tress recovery)
1
RoG@j 2005
11/14/2005
Zadanie praktyczne
Szerokość półpasma
!
Depends on maximum difference of nodal
numbers in all elements
For all elements
Find smallest and highest node number
Compute difference
Choose highest difference - bandwidth
Bandwidth
Sterowanie numeracją
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Local and global numbers
!
!
!
Band = 1
For i = 1 To NElem
Min = NNode
Max = 1
For j = 1 To MaxNode
If Elements(i, j) <
Then
If Elements(i, j) >
Then
Next j
MaxMin = (Max - Min +
If MaxMin > Band Then
Next i
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Assumption, that number of DOFs in each node is
the same
Kod allokacji
For i = 1 To Nelem
{elements loop}
ElemDOF = 1
{elem DOFs counter}
For j = 1 To MaxNode
{elem nodes loop}
NodeDOF = 1
{nod DOFs counter}
For k = 1 To MaxDOF {nod DOFs loop}
Nod = Elements(i, j)
Glob(ElemDOF) = (Nod - 1) * MaxDOF
+ NodeDOF
ElemDOF = ElemDOF + 1
NodeDOF = NodeDOF + 1
Next k
Next j
Next i
Algorytmy MES (1)
1) * MaxDof
Band = MaxMin
MaxDof – 3
Example
!
Easy rule: nodes on the list in the element are in
such a sequence as local numbers
DOFs numbering
{loop over elements}
{cannot be Min!!!}
{cannot be Max!!!}
{loop over nodes}
Min
Min = Elements(i, j)
Max
Max = Elements(i, j)
Numeracja stopni swobody
Node numbering
!
!
Numbers of nodes
Numbers of degrees of freedom
Kod
Szerokość półpasma
Local nodes 1
Global nodes 1
Local DOFs 1
Global DOFs 1
2
3
2
2
3
4
3
3
4
6 (Nod)
4 5 6 7 8 9 10 11 12
7 8 9…
Rule:
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Global=(Nod-1)*MaxDof+NodeDOF
Macierze elementowe
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Element
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Kind of element (plate or plane stress,
truss or frame…)
Materials (number of set)
Nodal coordinates
Allocation (in order to aggregate)
Two in one
!
Material set can say which kind of element and
which materials
2