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| ' Programs in this module are based on Fortran programs taken from "Prgramming The Finite Element Method"
' by IM Smith ans D.V. Griffiths, published by John Wiley & Sons
Sub BoEF(beamA As Array, LoadA As Array, FixedNodeA As Object, NIP As Long, ByRef resa(,) As Double)
Dim nels As Long, neq As Long, nn As Long, nband As Long, nr As Long
Dim iel As Long, i As Long, j As Long, k As Long, l As Long
Dim loaded_nodes As Long, fixed_nodes As Long, FixedCols As Long, Sense As Long, Value As Double, Node As Long
Dim fs As Double, fs0 As Double, fs1 As Double, x As Double, samp_pt As Double, EI0 As Double, EI1 As Double, EI As Double
Dim Loads() As Double
Dim action As Object
Dim no() As Long
Dim n As Long
Const nod As Long = 2, nodof As Long = 2, ndof As Long = 4, ndim As Long = 1
Const element As String = "line"
loaded_nodes = UBound(LoadA)
nels = UBound(beamA) - 1
If NIP < 2 Then NIP = 2
If NIP > 6 Then NIP = 6
nn = nels + 1
Dim nf As Array = Array.CreateInstance(GetType(Long), {nodof, nn}, {1, 1})
Dim km As Array = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
Dim coord As Array = Array.CreateInstance(GetType(Double), {nod, ndim}, {1, 1})
Dim g_coord As Array = Array.CreateInstance(GetType(Double), {ndim, nn}, {1, 1})
Dim eld As Array = Array.CreateInstance(GetType(Double), {ndof}, {1})
Dim g_num As Array = Array.CreateInstance(GetType(Long), {nod, nels}, {1, 1})
Dim num As Array = Array.CreateInstance(GetType(Long), {nod}, {1})
Dim g As Array = Array.CreateInstance(GetType(Long), {ndof}, {1})
Dim g_g As Array = Array.CreateInstance(GetType(Long), {ndof, nels}, {1, 1})
Dim mm As Array = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
Dim ftf As Array = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
Dim ell As Array = Array.CreateInstance(GetType(Double), {nels}, {1})
Dim dtd As Array = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
Dim store_km As Array = Array.CreateInstance(GetType(Double), {ndof, ndof, nels}, {1, 1, 1})
Dim der2 As Array = Array.CreateInstance(GetType(Double), {ndof}, {1})
Dim fun As Array = Array.CreateInstance(GetType(Double), {ndof}, {1})
Dim mom As Array = Array.CreateInstance(GetType(Double), {nn}, {1})
Dim points As Array = Array.CreateInstance(GetType(Double), {NIP, ndim}, {1, 1})
Dim weights As Array = Array.CreateInstance(GetType(Double), {NIP}, {1})
Dim etype As Array = Array.CreateInstance(GetType(Long), {nels}, {1})
fs0 = beamA(1, 3)
fs1 = beamA(2, 3)
EI = beamA(1, 2)
For i = 1 To nels
ell(i) = beamA(i + 1, 1) - beamA(i, 1)
etype(i) = 1
Next i
nr = 0
For i = 1 To nodof
For j = 1 To nn
nf(i, j) = 1
Next j
Next i
If nr > 0 Then
'read(10,*)(k,nf(:,k),i=1,nr)
End If
Call formnf(nf)
neq = WorksheetMax(nf)
'!--------------loop the elements to find global array sizes--------------------
nband = 0
For iel = 1 To nels
Call geometry_2l(iel, ell(iel), coord, num)
Call num_to_g(num, nf, g, ndof)
For i = 1 To nod
g_num(i, iel) = num(i)
Next i
For j = 1 To nod
g_coord(1, num(j)) = coord(j, 1)
Next j
For i = 1 To ndof
g_g(i, iel) = g(i)
Next i
If nband < bandwidth(g) Then nband = bandwidth(g)
Next iel
Dim kv As Array = Array.CreateInstance(GetType(Double), {neq * (nband + 1)}, {1})
Loads = Array.CreateInstance(GetType(Double), {neq + 1}, {0})
Call sample(element, points, weights)
x = 0#
For iel = 1 To nels
km = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
mm = Array.CreateInstance(GetType(Double), {ndof, ndof}, {1, 1})
For i = 1 To ndof
g(i) = g_g(i, iel)
Next i
fs0 = beamA(iel, 3)
fs1 = beamA(iel + 1, 3)
EI0 = beamA(iel, 2)
EI1 = beamA(iel + 1, 2)
For i = 1 To NIP
samp_pt = ell(iel) * 0.5 * (points(i, 1) + 1.0#)
fs = samp_pt / (ell(iel)) * (fs1 - fs0) + fs0
EI = samp_pt / (ell(iel)) * (EI1 - EI0) + EI0
Call fmbeam(der2, fun, points, i, ell(iel))
For k = 1 To ndof
For l = 1 To ndof
ftf(k, l) = fun(k) * fun(l) * weights(i) * 0.5 * ell(iel) * fs
dtd(k, l) = der2(k) * der2(l) * weights(i) * 8.0# * EI / (ell(iel) ^ 3)
mm(k, l) = mm(k, l) + ftf(k, l)
km(k, l) = km(k, l) + dtd(k, l)
Next l
Next k
Next i
For i = 1 To ndof
For j = 1 To ndof
km(i, j) = km(i, j) + mm(i, j)
store_km(i, j, iel) = km(i, j)
Next j
Next i
x = beamA(iel, 1)
Call formkv(kv, km, g, neq, iel)
Next iel
'!-----------------------------read loads---------------------------------------
If loaded_nodes <> 0 Then
'
For i = 1 To loaded_nodes
k = LoadA(i, 1)
For j = 1 To nodof
Loads(nf(j, k)) = LoadA(i, j + 1)
Next j
Next i
End If
'read (10,*)fixed_nodes
If IsArray(FixedNodeA) = True Then
fixed_nodes = UBound(FixedNodeA)
FixedCols = UBound(FixedNodeA, 2)
Else
fixed_nodes = 0
End If
If fixed_nodes <> 0 Then
For i = 1 To fixed_nodes
Node = FixedNodeA(i, 1)
Sense = 0
If FixedNodeA(i, 2) = 1 Then Sense = 1
If FixedNodeA(i, 3) = 1 Then Sense = Sense + 2
If Sense = 1 Or Sense = 3 Then
If FixedCols > 3 Then Value = FixedNodeA(i, 4) Else Value = 0
n = nf(1, Node)
kv(n) = kv(n) + 1.0E+20
Loads(n) = kv(n) * Value
Sense = Sense - 1
End If
If Sense = 2 Then
If FixedCols > 4 Then Value = FixedNodeA(i, 5) Else Value = 0
n = nf(2, Node)
kv(n) = kv(n) + 1.0E+20
Loads(n) = kv(n) * Value
End If
Next i
End If
'!-----------------------------equation solution -------------------------------
Call banred(kv, neq)
Call bacsub(kv, Loads)
'!-----------------------retrieve element end actions---------------------------
For iel = 1 To nels
For i = 1 To ndof
For j = 1 To ndof
km(i, j) = store_km(i, j, iel)
Next j
g(i) = g_g(i, iel)
eld(i) = Loads(g(i))
Next i
action = MATMUL(km, eld)
resa(iel, 3) = -action(2)
resa(iel, 4) = action(1)
Next iel
resa(iel, 3) = -action(4)
resa(iel, 4) = -action(3)
For i = 1 To nn
resa(i, 1) = beamA(i, 1)
resa(i, 2) = Loads(2 * i - 1)
Next i
End Sub
Sub formnf(nf)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' ! reform nf
Dim i As Long, j As Long, M As Long
M = 0
For j = 1 To UBound(nf, 2)
For i = 1 To UBound(nf, 1)
If (nf(i, j) <> 0) Then
M = M + 1
nf(i, j) = M
End If
Next i
Next j
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
'!----------------Node to freedom number conversion ----------------------------
Sub num_to_g(num, nf, g, ndof)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' !finds the g vector from num and nf
Dim i As Long, j As Long, k As Long, nod As Long, nodof As Long
nod = UBound(num, 1)
nodof = UBound(nf, 1)
For i = 1 To nod
k = i * nodof
For j = 1 To nodof
g(k - nodof + j) = nf(j, num(i))
Next j
Next i
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
' !-------------------------------- Lines --------------------------------------
Sub geometry_2l(iel, ell, coord, num)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' ! node numbers, nodal coordinates and steering vectors for
' ! a line of (nonuniform) beam elements
num(1) = iel
num(2) = iel + 1
If (iel = 1) Then
coord(1, 1) = 0#
coord(2, 1) = ell
Else
coord(1, 1) = coord(2, 1)
coord(2, 1) = coord(2, 1) + ell
End If
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Sub rod_km(km, ea, Length)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
Dim Stiff As Double
Stiff = ea / Length
km(1, 1) = Stiff
km(2, 2) = Stiff
km(1, 2) = -Stiff
km(2, 1) = -Stiff
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Sub formkv(bk, km, g, n, iel)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' !global stiffness matrix stored as a vector (upper triangle)
Dim idof As Long, i As Long, j As Long, icd As Long, ival As Long
idof = UBound(km, 1) - LBound(km, 1) + 1
For i = 1 To idof
If (g(i) <> 0) Then
For j = 1 To idof
If (g(j) <> 0) Then
icd = g(j) - g(i) + 1
If (icd - 1 >= 0) Then
ival = n * (icd - 1) + g(i)
bk(ival) = bk(ival) + km(i, j)
End If
End If
Next j
End If
Next i
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
' Return
End Sub
Sub banred(bk, n)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' ! gaussian reduction on a vector stored as an upper triangle
Dim i As Long, il1 As Long, kbl As Long, j As Long, ij As Long, nkb As Long, M As Long, ni As Long, nj As Long, iw As Long
Dim sum As Double
iw = UBound(bk, 1) / n - 1
For i = 2 To n
il1 = i - 1
kbl = il1 + iw + 1
If (kbl - n > 0) Then kbl = n
For j = i To kbl
ij = (j - i) * n + i
sum = bk(ij)
nkb = j - iw
If (nkb <= 0) Then nkb = 1
If (nkb - il1 <= 0) Then
For M = nkb To il1
ni = (i - M) * n + M
nj = (j - M) * n + M
sum = sum - bk(ni) * bk(nj) / bk(M)
Next M
End If
bk(ij) = sum
Next j
Next i
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Sub bacsub(bk, Loads)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' ! performs the complete gaussian backsubstitution
Dim nkb As Long, k As Long, i As Long, jn As Long, jj As Long, i1 As Long, n As Long, iw As Long
Dim sum As Double
n = UBound(Loads, 1)
iw = UBound(bk, 1) / n - 1
Loads(1) = Loads(1) / bk(1)
For i = 2 To n
sum = Loads(i)
i1 = i - 1
nkb = i - iw
If (nkb <= 0) Then nkb = 1
For k = nkb To i1
jn = (i - k) * n + k
sum = sum - bk(jn) * Loads(k)
Next k
Loads(i) = sum / bk(i)
Next i
For jj = 2 To n
i = n - jj + 1
sum = 0#
i1 = i + 1
nkb = i + iw
If (nkb - n > 0) Then nkb = n
For k = i1 To nkb
jn = (k - i) * n + i
sum = sum + bk(jn) * Loads(k)
Next k
Loads(i) = Loads(i) - sum / bk(i)
Next jj
' Return
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Function MATMUL(A, b)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' PRODUCT OF TWO MATRICES
'
Dim i As Long, j As Long, k As Long, x As Double, l As Long, n As Long
l = UBound(A, 2)
n = UBound(A)
Dim Mat = Array.CreateInstance(GetType(Double), {l}, {1})
For i = 1 To l
For j = 1 To n
x = 0#
For k = 1 To l
x = x + A(i, k) * b(k)
Next k
Mat(i) = x
Next j
Next i
MATMUL = Mat
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Function
'
Sub MATRAN(A, IA, b, IB, M, n)
'
' FORMS THE TRANSPOSE OF A MATRIX
'
' REAL A(IA,*),B(IB,*)
' DO 1 I = 1,M
' DO 1 J = 1,N
' A(j, i) = B(i, j)
End Sub
Sub MSMULT(A, IA, c, M, n)
'
' MULTIPLIES A MATRIX BY A SCALAR
'
' REAL A(IA,*)
' DO 1 I = 1,M
' DO 1 J = 1,N
' A(i, j) = A(i, j) * c
End Sub
Sub MVMULT(M, v, k, l, y)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' MULTIPLIES A MATRIX BY A VECTOR
Dim i As Long, j As Long, x As Double
' ReDim Preserve M(k, l), V(l), Y(k)
ReDim y(k)
For i = 1 To k
x = 0#
For j = 1 To l
x = x + M(i, j) * v(j)
Next j
y(i) = x
Next i
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Function bandwidth(g)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
'! finds the element bandwidth from g
If WorksheetMin(g) > 0 Then
bandwidth = WorksheetMax(g) - WorksheetMin(g)
Else
bandwidth = 0
End If
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Function
Sub sample(element, s, wt)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' ! returns the local coordinates of the integrating points
' **** Edited for line element only *****
Dim NIP As Long, root3 As Double, R15 As Double
Dim w = Array.CreateInstance(GetType(Double), {3}, {1})
Dim v = Array.CreateInstance(GetType(Double), {9}, {1})
Dim b As Double, c As Double, i As Long
root3 = 1.0# / (3.0#) ^ 0.5
R15 = 0.2 * (15.0#) ^ 0.5
NIP = UBound(s, 1)
w(1) = 5.0# / 9.0#
w(2) = 8.0# / 9.0#
w(3) = 5.0# / 9.0#
For i = 1 To 7 Step 3
v(i) = 5.0# / 9.0# * w(1)
v(i + 1) = 8.0# / 9.0# * w(2)
v(i + 2) = 5.0# / 9.0# * w(3)
Next i
Select Case element
Case "line"
Select Case (NIP)
Case (1)
s(1, 1) = 0#
wt(1) = 2.0#
Case (2)
s(1, 1) = root3
s(2, 1) = -s(1, 1)
wt(1) = 1.0#
wt(2) = 1.0#
Case (3)
s(1, 1) = R15
s(2, 1) = 0#
s(3, 1) = -s(1, 1)
wt = w
Case (4)
s(1, 1) = 0.861136311594053
s(2, 1) = 0.339981043584856
s(3, 1) = -s(2, 1)
s(4, 1) = -s(1, 1)
wt(1) = 0.347854845137454
wt(2) = 0.652145154862546
wt(3) = wt(2)
wt(4) = wt(1)
Case (5)
s(1, 1) = 0.906179845938664
s(2, 1) = 0.538469310105683
s(3, 1) = 0#
s(4, 1) = -s(2, 1)
s(5, 1) = -s(1, 1)
wt(1) = 0.236926885056189
wt(2) = 0.478628670499366
wt(3) = 0.568888888888889
wt(4) = wt(2)
wt(5) = wt(1)
Case (6)
s(1, 1) = 0.932469514203152
s(2, 1) = 0.661209386466265
s(3, 1) = 0.238619186083197
s(4, 1) = -s(3, 1)
s(5, 1) = -s(2, 1)
s(6, 1) = -s(1, 1)
wt(1) = 0.17132449237917
wt(2) = 0.360761573048139
wt(3) = 0.467913934572691
wt(4) = wt(3)
wt(5) = wt(2)
wt(6) = wt(1)
End Select
End Select
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Sub fmbeam(der2, fun, points, i, ell)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
' !
' ! this subroutine forms the beam shape functions
' ! and their 2nd derivatives in local coordinates
' !
Dim xi As Double, xi2 As Double, xi3
xi = points(i, 1)
xi2 = xi * xi
xi3 = xi2 * xi
fun(1) = 0.25 * (xi3 - 3.0# * xi + 2.0#)
fun(2) = 0.125 * ell * (xi3 - xi2 - xi + 1.0#)
fun(3) = 0.25 * (-xi3 + 3.0# * xi + 2.0#)
fun(4) = 0.125 * ell * (xi3 + xi2 - xi - 1.0#)
der2(1) = 1.5 * xi
der2(2) = 0.25 * ell * (3.0# * xi - 1.0#)
der2(3) = -1.5 * xi
der2(4) = 0.25 * ell * (3.0# * xi + 1.0#)
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Sub
Function WorksheetMax(tr As Object, Optional InitialRowNumber As Integer = 0, Optional InitialColumnNumber As Integer = 0)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
WorksheetMax = Nothing
For Each element In tr
If IsNumeric(element) Then
If IsNothing(WorksheetMax) Then
WorksheetMax = element
Else
If element > WorksheetMax Then WorksheetMax = element
End If
End If
Next
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Function
Function WorksheetMin(tr As Object, Optional InitialRowNumber As Integer = 0, Optional InitialColumnNumber As Integer = 0)
Static TimeofFunction
Dim Stopwatch1 As Stopwatch = Stopwatch.StartNew()
WorksheetMin = Nothing
For Each element In tr
If IsNumeric(element) Then
If IsNothing(WorksheetMin) Then
WorksheetMin = element
Else
If element < WorksheetMin Then WorksheetMin = element
End If
End If
Next
Stopwatch1.Stop()
TimeofFunction = TimeofFunction + Stopwatch1.Elapsed
End Function |
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