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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


web :

Date 18-Mar-2014

Department of Land Air and Water

University of California Davis



[B Jdet] = shapeDerivLine_quad(p, MSH, xi)


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.


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;

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