# shapeDerivTriang_Lin

| main | Tutorials | Functions | website |

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

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]=shapeDerivTriang_Lin(p, MSH, n, proj)

## 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;

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)