# shapeDerivPrism_Lin

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

Version : 1.0

Author : George Kourakos

email: giorgk@gmail.com

Date 18-Mar-2014

Department of Land Air and Water

University of California Davis

## Usage

[B Jdet] = shapeDerivPrism_Lin(p, TRI, 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

TRI: [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.

## Output

B: Shape function derivatives

Jdet: The determinant of the Jacobian Matrix

## Shape functions

N1 = (1-xi-eta)*(1-zta)/2;

N2 = xi*(1-zta)/2;

N3 = eta*(1-zta)/2;

N4 = (1-xi-eta)*(1+zta)/2;

N5 = xi*(1+zta)/2;

N6 = eta*(1+zta)/2;

## Derivatives of shape functions

wrt. ksi:

dN1 = 1/2 - zta/2;

dN2 = 0;

dN3 = zta/2 - 1/2;

dN4 = zta/2 + 1/2;

dN5 = 0;

dN6 = - zta/2 - 1/2;

wrt. eta:

dN7 = 0;

dN8 = 1/2 - zta/2;

dN9 = zta/2 - 1/2;

dN10 = 0;

dN11 = zta/2 + 1/2;

dN12 = - zta/2 - 1/2;

wrt. zeta:

dN13 = -xi/2;

dN14 = -eta/2;

dN15 = eta/2 + xi/2 - 1/2;

dN16 = xi/2;

dN17 = eta/2;

dN18 = 1/2 - xi/2 - eta/2;