Computes the shape function derivatives and the determinant of the jacobian matrix for quadrilateral linear 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] = shapeDerivQuad_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=0.25*(1-ksi)*(1-eta)

N2=0.25*(1+ksi)*(1-eta)

N3=0.25*(1+ksi)*(1+eta)

N4=0.25*(1-ksi)*(1+eta)

## Derivatives of shape functions

dN1=eta/4 - 1/4; dN2=1/4 - eta/4; dN3=eta/4 + 1/4; dN4=- eta/4 - 1/4; (wrt. ksi)

dN5=ksi/4 - 1/4; dN6=- ksi/4 - 1/4; dN7=ksi/4 + 1/4; dN8=1/4 - ksi/4; (wrt. eta)