Skip to Main Content
Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
192 Applied calculus of variations for engineers
We also require that these functions at a certain node point reduce to zero
at the other two nodes. This is called the Kronecker property and presented as
N
i
=
1atnodei,
0atnode= i.
Furthermore, a shape function is zero along the edge opposite to the particular
node at which the shape function is non-zero.
The solution for the nodes of a particular triangular element e can be ex-
pressed in matrix form as
u
e
=
u
1
u
2
u
3
=
1 x
1
y
1
1 x
2
y
2
1 x
3
y
3
a
b
c
.
This system of equations is solved for the unknown coefficients that produce
the shape functions
a
b
c
=
1 x
1
y
1
1 x
2
y
2
1 x
3
y
3
1
u
1
u
2
u
3
=
N
1,1
N
1,2
N
1,3
N
2,1
N
2,2
N
2,3
N
3,1
N
3,2
N
3,3
u
1
u
2
u
3
.
By substituting into the matrix form of the bilinear interpolation
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Calculus of Variations for Engineers, Third edition, 3rd Edition

Applied Calculus of Variations for Engineers, Third edition, 3rd Edition

Louis Komzsik
Algebraic and Stochastic Coding Theory

Algebraic and Stochastic Coding Theory

Dave K. Kythe, Prem K. Kythe

Publisher Resources

ISBN: 9781482253597