cven302 502
Download
Skip this Video
Download Presentation
CVEN302-502

Loading in 2 Seconds...

play fullscreen
1 / 15

CVEN302-502 - PowerPoint PPT Presentation


  • 61 Views
  • Uploaded on

CVEN302-502. Computer Applications in Engineering and Construction. Modeling is the development of a mathematical representation of a physical/biological/chemical/ economic/etc. system Putting our understanding of a system/problem into math Numerical methods are one means by which

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' CVEN302-502' - ishmael-mosley


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
cven302 502
CVEN302-502

Computer Applications in

Engineering and Construction

slide2

Modeling is the development of a mathematical

representation of a physical/biological/chemical/

economic/etc. system

Putting our understanding of a system/problem

into math

Numerical methods are one means by which

mathematical models are solved

slide3

Example:

Falling Parachutist

F=ma

=Fdown +Fup

=mg-cv (gravity minus air resistance)

Where does mg come from?

Observations.

Where does -cv come from?

More observations!

slide4

Now we have fundamental physical laws,

so we combine those with observations to model

system.

A lot of what you will do is “canned” but need

to know how to make use of observations.

How have computers changed problem solving in engineering?

Allow us to focus more on the correct description of the problem at hand, rather than worry about how to solve it.

slide5

Example: Finite elements and structural analysis

Complex truss

Simple truss - force balance

Instead of limiting our analysis to simple cases, numerics allows us to work on realistic cases.

slide6

What are the fundamental laws we use in modeling?

Conservation of mass - i.e. traffic flow estimation

Conservation of momentum -i.e. force balance in structures

Conservation of energy - i.e. redox chemistry in water treatment plant

slide7

Issues to be considered in modeling and numeric methods

1.Nonlinear vs. Linear

2.Large vs. Small systems

3.Nonideal vs. Ideal

4.Sensitivity analysis

5.Design

slide8

Back to our example: the falling parachutist

F=ma=mg-cv

dv

m

=

mg

-

cv

dt

dv

mg

-

cv

=

dt

m

Analytic solution (from calculus)

gm

(

)

(

)

(

)

-

/

c

m

t

v

t

=

1

-

e

c

slide9

Numerical solution

discretize original equation

(

)

(

)

dv

D

v

v

t

-

v

t

i

+

1

i

@

=

dt

D

t

t

-

t

i

+

1

i

(

)

(

)

v

t

-

v

t

c

(

)

i

+

1

i

=

g

-

v

t

i

t

-

t

m

i

+

1

i

c

é

ù

(

(

)

(

(

)

)

)

v

t

=

v

t

+

g

-

v

t

t

-

t

ê

ú

i

+

1

i

i

i

=

1

i

m

ë

û

slide10

Finally, combining analytical and numerical techniques

Catenary cable (power lines)

From force balances, displacement can be modeled by a differential equation

2

2

d

y

w

dy

æ

ö

=

1

+

ç

÷

2

dx

T

dx

è

ø

a

slide11

Forces acting on catenary

12

Tb

10

8

6

W=ws

Ta

4

2

0

-6

-4

-2

0

2

4

6

8

10

12

slide12

Can solve by integration

æ

ö

T

T

w

ç

÷

a

a

y

=

x

+

y

-

cosh

ç

÷

0

w

T

w

è

ø

a

Where

1

(

)

x

x

-

cosh

x

=

e

+

e

2

This equation is not analytically solvable for w or Ta

slide13

Say we are given w, y0 and the value of y at an x. Can solve for Ta using numerical methods

æ

ö

T

T

w

ç

÷

a

a

y

=

x

+

y

-

cosh

ç

÷

0

w

T

w

è

ø

a

Becomes

Try different values of Ta until lhs is 0

slide14

We will use Matlab as the computer language of choice for this course

  • Anything you can do in Fortran or C you can do in Matlab
  • Easier debugging system
  • Built-in graphics
  • Many, many functions already exist
  • Excellent help capabilities

Matlab Truss example – nice animation

14

slide15

In short, you will use numeric methods throughout your career

- even if you don’t write programs

- even if you go into management

If we didn’t have numerical methods, we might as well be...

ad