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Computes the shape function derivatives and the determinant of the jacobian matrix for linear triangle elements. This function is used internally from shapeDerivatives.

Version : 1.0

Author : George Kourakos


web :

Date 18-Mar-2014

Department of Land Air and Water

University of California Davis



[B Jdet]=shapeDerivTriang_Lin(p, MSH, n, proj)


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


B: Shape function derivatives

Jdet: The determinant of the Jacobian Matrix

Shape functions

N1 = ksi;

N2 = eta;

N3 = 1 - ksi - eta;

Derivatives of shape functions

dN1 = 1; dN2 = 0; dN3 = -1; (wrt. ksi)

dN4 = 0; dN5 = 1; dN6 = -1; (wrt. eta)

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