# shapeDerivLine_Lin

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Computes the shape function derivatives and the determinant for of 1D linear isoparametric 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_Lin(p, MSH, n)

## 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. For linear line elements this is empty because the derivative is constant.

## Output

* B*: Shape function derivatives

* Jdet*: The determinant of the Jacobian Matrix

## Shape functions

N1 = 0.5 * (1 - xi)

N2 = 0.5 * (1 + xi)

## Derivatives of shape functions

dN1 = -1/2;

dN2 = 1/2;