# shapeDerivLine_quad

| main | Tutorials | Functions | website |

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

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] = shapeDerivLine_quad(p, MSH, xi)

## 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

* xi*: the integration point where the derivatives will be evaluated.

## Output

* 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;