shapeDerivHex_Lin
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Computes the shape function derivatives and the determinant of the jacobian matrix for hexahedral linear elements. This function is used internally from shapeDerivatives.
Version : 1.0
Author : George Kourakos
email: giorgk@gmail.com
web : http://groundwater.ucdavis.edu/msim
Date 18-Mar-2014
Department of Land Air and Water
University of California Davis
Contents
Usage
[B Jdet]=shapeDerivHex_Lin(p, MSH, n)
Input
p: [Np x 3] Coodrinates of nodes [x1 y1 z1; x2 y2 z2;...xn yn zn], where Np is the number of nodes
MSH: [Nel x Np_el] id of elements. Each row correspond to an element. Nel is the number of elements and Np_el is the number of nodes to define the element
n: the integration point where the derivatives will be evaluated.
Output
B: Shape function derivatives
Jdet: The determinant of the Jacobian Matrix
%% Shape functions N1 = 0.125*(1-ksi)*(1-eta)*(1-zta);
N2=0.125*(1+ksi)*(1-eta)*(1-zta);
N3 = 0.125*(1+ksi)*(1+eta)*(1-zta);
N4 = 0.125*(1-ksi)*(1+eta)*(1-zta);
N5 = 0.125*(1-ksi)*(1-eta)*(1+zta);
N6 = 0.125*(1+ksi)*(1-eta)*(1+zta);
N7 = 0.125*(1+ksi)*(1+eta)*(1+zta);
N8 = 0.125*(1-ksi)*(1+eta)*(1+zta);
Derivatives of shape functions
wrt. ksi:
dN1 = -((eta - 1)*(zta - 1))/8;
dN2 = ((eta - 1)*(zta - 1))/8;
dN3 = -((eta + 1)*(zta - 1))/8;
dN4 = ((eta + 1)*(zta - 1))/8;
dN5 = ((eta - 1)*(zta + 1))/8;
dN6 = -((eta - 1)*(zta + 1))/8;
dN7 = ((eta + 1)*(zta + 1))/8;
dN8 = -((eta + 1)*(zta + 1))/8;
wrt. eta:
dN9 = -((ksi - 1)*(zta - 1))/8;
dN10 = ((ksi + 1)*(zta - 1))/8;
dN11 = -((ksi + 1)*(zta - 1))/8;
dN12 = ((ksi - 1)*(zta - 1))/8;
dN13 = ((ksi - 1)*(zta + 1))/8;
dN14 = -((ksi + 1)*(zta + 1))/8;
dN15 = ((ksi + 1)*(zta + 1))/8;
dN16 = -((ksi - 1)*(zta + 1))/8;
wrt. zeta:
dN17 = -((eta - 1)*(ksi - 1))/8;
dN18 = ((eta - 1)*(ksi + 1))/8;
dN19 = -((eta + 1)*(ksi + 1))/8;
dN20 = ((eta + 1)*(ksi - 1))/8;
dN21 = ((eta - 1)*(ksi - 1))/8;
dN22 = -((eta - 1)*(ksi + 1))/8;
dN23 = ((eta + 1)*(ksi + 1))/8;
dN24 = -((eta + 1)*(ksi - 1))/8;