shapeDerivQuad_Lin
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Computes the shape function derivatives and the determinant of the jacobian matrix for quadrilateral 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] = shapeDerivQuad_Lin(p, MSH, n, proj)
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.
proj : if proj is true then the elements will be projected on the 2D plane before computing the determinant usign mapElemto2D
Output
B: Shape function derivatives
Jdet: The determinant of the Jacobian Matrix
Shape functions
N1=0.25*(1-ksi)*(1-eta)
N2=0.25*(1+ksi)*(1-eta)
N3=0.25*(1+ksi)*(1+eta)
N4=0.25*(1-ksi)*(1+eta)
Derivatives of shape functions
dN1=eta/4 - 1/4; dN2=1/4 - eta/4; dN3=eta/4 + 1/4; dN4=- eta/4 - 1/4; (wrt. ksi)
dN5=ksi/4 - 1/4; dN6=- ksi/4 - 1/4; dN7=ksi/4 + 1/4; dN8=1/4 - ksi/4; (wrt. eta)