shapeDerivPrism_Lin
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Computes the shape function derivatives and the determinant of the jacobian matrix for linear prism 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] = shapeDerivPrism_Lin(p, TRI, 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
TRI: [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 = (1-xi-eta)*(1-zta)/2;
N2 = xi*(1-zta)/2;
N3 = eta*(1-zta)/2;
N4 = (1-xi-eta)*(1+zta)/2;
N5 = xi*(1+zta)/2;
N6 = eta*(1+zta)/2;
Derivatives of shape functions
wrt. ksi:
dN1 = 1/2 - zta/2;
dN2 = 0;
dN3 = zta/2 - 1/2;
dN4 = zta/2 + 1/2;
dN5 = 0;
dN6 = - zta/2 - 1/2;
wrt. eta:
dN7 = 0;
dN8 = 1/2 - zta/2;
dN9 = zta/2 - 1/2;
dN10 = 0;
dN11 = zta/2 + 1/2;
dN12 = - zta/2 - 1/2;
wrt. zeta:
dN13 = -xi/2;
dN14 = -eta/2;
dN15 = eta/2 + xi/2 - 1/2;
dN16 = xi/2;
dN17 = eta/2;
dN18 = 1/2 - xi/2 - eta/2;