shapeDerivTriang_quad
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Computes the shape function derivatives and the determinant of the jacobian matrix for quadratic triangle 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 = ksi*(2*ksi-1); N2 = eta*(2*eta-1); N3 = (1-ksi-eta)*(2*(1-ksi-eta)-1);
N4 = 4*ksi*eta; N5 = 4*eta*(1-ksi-eta); N6 = 4*(1-ksi-eta)*ksi;
Derivatives of shape functions
dN1 = 4*ksi - 1; dN2 = 0; dN3 = 4*eta + 4*ksi - 3; dN4 = 4*eta; dN5 = -4*eta; dN6 = 4 - 8*ksi - 4*eta; (wrt. ksi)
dN7 = 0; dN8 = 4*eta - 1; dN9 = 4*eta + 4*ksi - 3; dN10 = 4*ksi; dN11 = 4 - 4*ksi - 8*eta; dN12 = -4*ksi; (wrt. eta)