shapeDerivLine_quad
| main | Tutorials | Functions | website |
Computes the shape function derivatives and the determinant of the jacobian matrix for 1D quadratic line 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] = shapeDerivLine_quad(p, MSH, xi)
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
xi: the integration point where the derivatives will be evaluated.
Output
B: Shape function derivatives
Jdet: The determinant of the Jacobian Matrix
Shape functions
N1 = 0.5 * ksi * (ksi - 1)
N2 = 0.5 * ksi * (ksi + 1)
N3 = 1 - ksi^2
Derivatives of shape functions
dN1 = ksi - 1/2;
dN2 = ksi + 1/2;
dN3 = -2*ksi;