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

Date 18-Mar-2014

Department of Land Air and Water

University of California Davis

## 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)