Hermite main-interpolation functions for two-dimensional surface (update:24-07-07)
Keine Lizenz
DESCRIPTION:
Under the bending or twisting effect a thin-plate element's conforming shape functions be derivative basis displacement functions on Pascal Triangle. This solution technique is non-conforming [1] high-order-degree plate element's shape functions and plate's bending and twisting motion.
for example [1];
(9node-27Dof plate element)
Rank 27 (non-conforming)
w=[ 1 ...
x y ...
x^2 x*y y^2 ...
x^3 x^2*y x*y^2 y^3 ...
x^4+x^3*y x^2*y^2 x*y^3+y^4 ... Pascal tree
x^5 x^4*y x^3*y^2 x^2*y^3 x*y^4 y^5 ...
x^5*y+x^4*y^2 x^3*y^3 x^2*y^4+x*y^5 ...
x^5*y^2+x^4*y^3 x^3*y^4+x^2*y^5 ...
x^5*y^3 x^4*y^4 x^3*y^5]
SYNTAX:
[Nshape,Shapefunctions]=Hermiten(totalx,totaly,nodevalue)
Syntax.inputs
totalx : two-dimensional interpolation area's "x" axis length
totaly : two-dimensional interpolation area's "y" axis length
nodevalue: hermite basis functions nodevalues (interpolation node-degree)
Syntax.outputs
Nshape : n. order-degree Hermite basis interpolation functions
Shapefunctions :two-dimensional area plate shape functions for bending
motion
EXAMPLE:
Example.inputs
[A,B,C]=hermiten(1,1,3,1) <---|
A =
1-92*x^2+528*x^3-1088*x^4+768*x^5
x-12*x^2+52*x^3-96*x^4+64*x^5
64*x^2-256*x^3+256*x^4
-16*x^2+128*x^3-320*x^4+256*x^5
28*x^2-272*x^3+832*x^4-768*x^5
-2*x^2+20*x^3-64*x^4+64*x^5
B =
Node(1) ---->Node(n)
w [ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
Qxx [ (-46*x+198*x^2-272*x^3+120*x^4)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
Qyy [ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(-46*y+198*y^2-272*y^3+120*y^4), ..
C =
Node(1)------->Node(n)
w [ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
Qxx [ (-46*x+198*x^2-272*x^3+120*x^4)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
Qyy [ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(-46*y+198*y^2-272*y^3+120*y^4), ..
Qxy [ (-46*x+198*x^2-272*x^3+120*x^4)*(-46*y+198*y^2-272*y^3+120*y^4), ..
Example.inputs
[A,B,C]=hermiten(1,1,3,0) <---| or
[A,B,C]=hermiten(1,1,3) <---|
Example.outputs
A =
1-23*x^2/a^2+66*x^3/a^3-68*x^4/a^4+24*x^5/a^5
x-6*x^2/a+13*x^3/a^2-12*x^4/a^3+4*x^5/a^4
16*x^2/a^2-32*x^3/a^3+16*x^4/a^4
-8*x^2/a+32*x^3/a^2-40*x^4/a^3+16*x^5/a^4
7*x^2/a^2-34*x^3/a^3+52*x^4/a^4-24*x^5/a^5
-x^2/a+5*x^3/a^2-8*x^4/a^3+4*x^5/a^4
B =
Node(1)----->Node(n)
[ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
[ (-46*x+198*x^2-272*x^3+120*x^4)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
[ (1-23*x^2+66*x^3-68*x^4+24*x^5)*(-46*y+198*y^2-272*y^3+120*y^4), ..
C = Node(1)----->Node(n)
[(1-23*x^2+66*x^3-68*x^4+24*x^5)*(1-23*y^2+66*y^3-68*y^4+24*y^5), .. [(-46*x+198*x^2-272*x^3+120*x^4)*(1-23*y^2+66*y^3-68*y^4+24*y^5), ..
[(1-23*x^2+66*x^3-68*x^4+24*x^5)*(-46*y+198*y^2-272*y^3+120*y^4), .. [ (-46*x/a^2+198*x^2/a^3-272*x^3/a^4+120*x^4/a^5)*(-46*y+198*y^2- ..
Zitieren als
Ali OZGUL (2024). Hermite main-interpolation functions for two-dimensional surface (update:24-07-07) (https://www.mathworks.com/matlabcentral/fileexchange/15676-hermite-main-interpolation-functions-for-two-dimensional-surface-update-24-07-07), MATLAB Central File Exchange. Abgerufen .
Kompatibilität der MATLAB-Version
Plattform-Kompatibilität
Windows macOS LinuxKategorien
Tags
Quellenangaben
Inspiriert von: HermitePoly.m, Hermite Quadrature
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Live Editor erkunden
Erstellen Sie Skripte mit Code, Ausgabe und formatiertem Text in einem einzigen ausführbaren Dokument.
html/
Version | Veröffentlicht | Versionshinweise | |
---|---|---|---|
1.0.0.0 |