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function [matmtrx]=fematiso(iopt,elastic,poisson)

%------------------------------------------------------------------------

% Purpose:

% determine the constitutive equation for isotropic material

%

% Snopsis:

% [matmtrx]=fematiso(iopt,elastic,poisson)%

% !aria"le #escription:

% elastic - elastic modulus

% poisson - Poisson$s ratio

% iopt= - plane stress analsis

% iopt=& - plane strain analsis

% iopt=' - axismmetric analsis

% iopt= - three dimensional analsis

%------------------------------------------------------------------------

if iopt== % plane stress

matmtrx= elastic(-poisson*poisson)* +++

[ poisson +++

poisson +++

(-poisson)&]

elseif iopt==& % plane strain

matmtrx= elastic((.poisson)*(-&*poisson))* +++

[(-poisson) poisson

poisson (-poisson)

(-&*poisson)&]

elseif iopt==' % axismmetr

matmtrx= elastic((.poisson)*(-&*poisson))* +++

[(-poisson) poisson poisson

poisson (-poisson) poisson

poisson poisson (-poisson)

(-&*poisson)&]

else % three-dimension

matmtrx= elastic((.poisson)*(-&*poisson))* +++

[(-poisson) poisson poisson

poisson (-poisson) poisson

poisson poisson (-poisson)

(-&*poisson)&

(-&*poisson)&

(-&*poisson)&]

end

function [point&,/ei0ht&]=fe0lqd&(n0lx,n0l)

%-------------------------------------------------------------------

% Purpose:

% determine the inte0ration points and /ei0htin0 coefficients

% of 1auss-2e0endre quadrature for t/o-dimensional inte0ration

%

% Snopsis:

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% [point&,/ei0ht&]=fe0lqd&(n0lx,n0l)

%

% !aria"le #escription:

% n0lx - num"er of inte0ration points in the x-axis

% n0l - num"er of inte0ration points in the -axis

% point& - vector containin0 inte0ration points

% /ei0ht& - vector containin0 /ei0htin0 coefficients

%-------------------------------------------------------------------

% determine the lar0est one "et/een n0lx and n0l

if n0lx 3 n0l

n0l=n0lx

else

n0l=n0l

end

% initiali4ation

point&=4eros(n0l,&)

/ei0ht&=4eros(n0l,&)

% find correspondin0 inte0ration points and /ei0hts

[pointx,/ei0htx]=fe0lqd(n0lx) % quadrature rule for x-axis

[point,/ei0ht]=fe0lqd(n0l) % quadrature rule for -axis

% quadrature for t/o-dimension

for intx=:n0lx % quadrature in x-axis

point&(intx,)=pointx(intx)

/ei0ht&(intx,)=/ei0htx(intx)

end

for int=:n0l % quadrature in -axis

point&(int,&)=point(int)

/ei0ht&(int,&)=/ei0ht(int)end

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function [5aco"&]=fe5aco"&(nnel,dhdr,dhds,xcoord,coord)

%------------------------------------------------------------------------

% Purpose:

% determine the 6aco"ian for t/o-dimensional mappin0

%

% Snopsis:

% [5aco"&]=fe5aco"&(nnel,dhdr,dhds,xcoord,coord)

%

% !aria"le #escription:

% 5aco"& - 6aco"ian for one-dimension% nnel - num"er of nodes per element

% dhdr - derivative of shape functions /+r+t+ natural coordinate r

% dhds - derivative of shape functions /+r+t+ natural coordinate s

% xcoord - x axis coordinate values of nodes

% coord - axis coordinate values of nodes

%------------------------------------------------------------------------

5aco"&=4eros(&,&)

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 for i=:nnel

5aco"&(,)=5aco"&(,).dhdr(i)*xcoord(i)

5aco"&(,&)=5aco"&(,&).dhdr(i)*coord(i)

5aco"&(&,)=5aco"&(&,).dhds(i)*xcoord(i)

5aco"&(&,&)=5aco"&(&,&).dhds(i)*coord(i)

end

function [dhdx,dhd]=federiv&(nnel,dhdr,dhds,inv5aco")

%------------------------------------------------------------------------

% Purpose:

% determine derivatives of &-# isoparametric shape functions /ith

% respect to phsical coordinate sstem

%

% Snopsis:

% [dhdx,dhd]=federiv&(nnel,dhdr,dhds,inv5aco")

%

% !aria"le #escription:

% dhdx - derivative of shape function /+r+t+ phsical coordinate x

% dhd - derivative of shape function /+r+t+ phsical coordinate

% nnel - num"er of nodes per element

% dhdr - derivative of shape functions /+r+t+ natural coordinate r

% dhds - derivative of shape functions /+r+t+ natural coordinate s% inv5aco" - inverse of &-# 6aco"ian matrix

%------------------------------------------------------------------------

 for i=:nnel

 dhdx(i)=inv5aco"(,)*dhdr(i).inv5aco"(,&)*dhds(i)

 dhd(i)=inv5aco"(&,)*dhdr(i).inv5aco"(&,&)*dhds(i)

 end

5

function [7inmtp"]=fe7inep"(nnel,dhdx,dhd)

%--------------------------------------------------------------------------

% Purpose:% determine the 7inematic matrix expression relatin0 "endin0 curvatures

% to rotations and displacements for shear deforma"le plate "endin0

%

% Snopsis:

% [7inmtp"]=fe7inep"(nnel,dhdx,dhd)

%

% !aria"le #escription:

% nnel - num"er of nodes per element

% dhdx - derivatives of shape functions /ith respect to x

% dhd - derivatives of shape functions /ith respect to

%--------------------------------------------------------------------------

 for i=:nnel

 i=(i-)*'.i&=i.

 i'=i&.

 7inmtp"(,i)=dhdx(i)

 7inmtp"(&,i&)=dhd(i)

 7inmtp"(',i)=dhd(i)

 7inmtp"(',i&)=dhdx(i)

 7inmtp"(',i')=

 end

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888

function [shapeq,dhdrq,dhdsq]=feisoq(rvalue,svalue)

%------------------------------------------------------------------------

% Purpose:

% compute isoparametric four-node quadilateral shape functions

% and their derivatves at the selected (inte0ration) point

% in terms of the natural coordinate

%

% Snopsis:

% [shapeq,dhdrq,dhdsq]=feisoq(rvalue,svalue)

%

% !aria"le #escription:

% shapeq - shape functions for four-node element

% dhdrq - derivatives of the shape functions /+r+t+ r

% dhdsq - derivatives of the shape functions /+r+t+ s

% rvalue - r coordinate value of the selected point

% svalue - s coordinate value of the selected point

%

% 9otes:

% st node at (-,-), &nd node at (,-)% 'rd node at (,), th node at (-,)

%------------------------------------------------------------------------

% shape functions

 shapeq()=+&*(-rvalue)*(-svalue)

 shapeq(&)=+&*(.rvalue)*(-svalue)

 shapeq(')=+&*(.rvalue)*(.svalue)

 shapeq()=+&*(-rvalue)*(.svalue)

% derivatives

 dhdrq()=-+&*(-svalue)

 dhdrq(&)=+&*(-svalue)

 dhdrq(')=+&*(.svalue)

 dhdrq()=-+&*(.svalue)

 dhdsq()=-+&*(-rvalue)

 dhdsq(&)=-+&*(.rvalue)

 dhdsq(')=+&*(.rvalue)

 dhdsq()=+&*(-rvalue)