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Uxyzxyzxxz Vxyzxyzxxz Wxyzxyzxz: A General Three Dimensional Shape Function of NTH Order Complete Polynomial Is Given by

The document describes a general 3D shape function for modeling an nth order polynomial. The shape function is defined as a summation of terms with coefficients and monomials of x, y, and z up to nth order. The number of terms m in the polynomial is calculated as (n+1)(n+2)(n+3)/6, where n is the order of the polynomial.

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72 views2 pages

Uxyzxyzxxz Vxyzxyzxxz Wxyzxyzxz: A General Three Dimensional Shape Function of NTH Order Complete Polynomial Is Given by

The document describes a general 3D shape function for modeling an nth order polynomial. The shape function is defined as a summation of terms with coefficients and monomials of x, y, and z up to nth order. The number of terms m in the polynomial is calculated as (n+1)(n+2)(n+3)/6, where n is the order of the polynomial.

Uploaded by

11520035
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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_'____#____$___$%_#_$________ ___

A general three dimensional shape function of nth order complete polynomial is given by
uxyzxyzxxz
vxyzxyzxxz
wxyzxyzxz
m
n
mmmmmm
n
mmmmm
n
, , ...
, , ...
, , ...

__
__
__

12345
21
12345
2
2
1
212223243
1
(5.9)
or x y z
uxyz
vxyz
wxyz
G
G
G
G
,,
,,
,,
,,

_ _
_ _
_ _
_ _
____

_
_
_
_
_
_

_
_

_
___
1
1
1
00
00
00
(5.10)
Where G1 = [1 x y z x2 xy y2 yz z2 zx zn zn-1x zxn-1]

__
and T
m 1 2 3 ... 3
It may be observed that a complete nth order polynomial in three dimensional case is having number of
terms m given by the expression
m
nnn

1 2 3
6

_ __ __ _

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