Class notes

CE3330: Computer Methods in Civil Engineering Detailed Classnotes

12 views 0 purchase

Course
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...

[Show more]

Preview 4 out of 48 pages

View example

Uploaded on July 3, 2023
Number of pages 48
Written in 2022/2023
Type Class notes
Professor(s) Subhadeep banerjee
Contains All classes

newman boundary condition
gauss elimination method
lu decomposition
pivoting
norm
dirichlet boundary condition
essential forced boundary condition
natural boundary condition
jacobi method of iteration

Institution
Indian Institute Of Technology Madras
Course
CE3330: Computer Methods in Civil Engineering (CE3330)

CA$11.50

Added

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

, firstorder differential equation
: aytg(u); t= fy)

second differential equation
convert
=- ky;my"+ by'+ky=f(t)
Natural phenomenon mathematical model solves
post-processing
- >
-> ->

Validation
->
Force balance

Continuity (mass continuity, etc...)
continuity, valume
->

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

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller nirjarabongurala. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$11.50. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

75759 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling