CE3330: Computer Methods in Civil Engineering (CE3330)
Lecture notes
CE3330: Computer Methods in Civil Engineering Detailed Classnotes
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Module
CE3330: Computer Methods in Civil Engineering (CE3330)
Institution
Indian Institute Of Technology Madras
These class notes consist of topics that were taught for the course "Computer Methods in Civil Engineering" by Prof. Subhadeep Banerjee. The topics that are covered in these notes are Dirichlet & Newman Condition (Essential Forced & Natural Boundary Condition), Gauss Elimination Method, LU Decompos...
Force displacement relations/contributive law
->
-
(AJ(u] (B]
- >
=
nxc
nxh nx1
solves
- >
1.
2.
condition
contract
11 10-8 preconditiones
I
so thatthey
->
are
(C)(A)(U) (CTT (B)
=
(D](u] (c] (B)
=
+
properly!
I I
solved preconditiones matrix [C]
10,3
-
13000
- >
huge difference, better ways to solve like pivoting
Post
Processing
->
fi(u) k
=
1.
Boundary condition
2. Initial condition I before solvingsolving!
not after
Validation
->
I should (not violate) nature
2. Validation follow againstmeasurement
, 3. Compare with existing
4. Compatibility to
existing languages
is Equilibrium problems
(ii) Propagation (ex: wave propagation in string (time-varying]]
(iii) Eigen problems (finding eigen functions and eigenvalues]
multiple solutions but
discrete, modes of
string ·im
ODE +
EI
= -
9
PDE-
crde det
·reta)--ai
How to
analyse PDE?
vibration of
de vibrating string
+
propagation
am + a + 0
=
(Laplace equationi
1.
memory allocation ->
space/ and time
Order
+(a) I
2.
3.
degree
order-z, degree-1
4 linearity before solving we
analyse
order to choose particul
n
x(x,y) B(x,y) in
=
+
r(u) 14x(x,y) B(x,y)]
=
+
-
al method appropriate
L(u) thatclass
1x(x,y)
=
B(x,y)
+
for
su:
+y d 0
=
Linearity
ua b
=
+
( yy)u ↓[a+ by 2(a) ((b) +
=
0
+ =
↓Sany = 2 d(u)
->
u
x(x,y) 3(x,y)
=
+
, ( +
y(y) (x(x,y) B(x,y) =
8y+y+y
+
+
0
=
+y +ye +
↓(x(x,y)) (((u,y)) 0 +
=
->
u cx(x,y) =
(En 3ty)n (En yzy) (((n,y)
+
+
au c22
=
= =>
+(5) y
((((x,y))
=
5.
Homogenity ->
non-zero
function
at a*8 e
the
directly giving
Domain, Boundary
->
conditions rates
give the values
-
bisichlet condition/essential forced boundaryatthe
ionos
of derivative Newman condition/natural boundary
-- condition
at the
boundary
PDE O12S) IPDE of order 2x5)
forced BC -
to (s-1) in derivative
natural BC -> s to (25-1) in derivative
Ex = -
1
4th older gives a dirichlet you would require newman condi
***
z(z)=- a -
tion a dirichlet B.C
014) -> s =2 - essential desivatives,
I,
In total, I would need is
boundary conditions
x 0,y 0;x
=
= 0,M/dx 0
=
=
x L, y
=
0
=
Natural derivatives
->
it -
(25-13th
n
2,d
=
=
0
-> no condition
for this
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