matlab.mathematica getting a warning while running the program

8/19/2019 Matlab.Mathematica Getting a Warning While Running the Program

1/28

Getting a warning while running theprogram.Matrix is close to singular or badlyscaled. Results may be inaccurate. RCOND =

1.!"!##e$%1&.. 's(ed by De)ipra(ash *padhyaya on #1 Mar #%1

+ am running the below gi)en program which gi)es the warning message.,ow to remo)e the warning.

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

A barrel vault has radius r=25 ft, subtended angle of 80 degrees,

length 50 f, and thickness 3in.Elastic modulus is 3 msi,Poissons ratio is0,and !eight of the shell is "0 lb #er s$uare ft. %!o curved edges are

su##orted b& rigid dia#hragm and the other t!o edges are free.

'olve using ( b& ( elements of a $uarter of the shell.

)ariable descri#tions

* k = element matri+ in the local a+es

* ke = element matri+ in the global a+es

* kb = element matri+ for bending stiffness

* ks = element matri+ for shear stiffness

* km = element matri+ for membrane stiffness

* f = element vector

* kk = s&stem matri+

* ff = s&stem vector

* dis# = s&stem nodal dis#lacement vector

* gcoord = coordinate values of each node

* nodes = nodal connectivit& of each element

* inde+ = a vector containing s&stem dofs associated !ith each element

http://in.mathworks.com/matlabcentral/profile/authors/3525591-deviprakash-upadhyayahttp://in.mathworks.com/matlabcentral/profile/authors/3525591-deviprakash-upadhyayahttp://in.mathworks.com/matlabcentral/profile/authors/3525591-deviprakash-upadhyaya


2/28

* #ointb = matri+ containing sam#ling #oints for bending term

* !eightb = matri+ containing !eighting coefficients for bending term

* #oints = matri+ containing sam#ling #oints for shear term

* !eights = matri+ containing !eighting coefficients for shear term

* bcdof = a vector containing dofs associated !ith boundar& conditions

* bcval = a vector containing boundar& condition values associated !ith

* the dofs in bcdof

* kinmtsb = matri+ for kinematic e$uation for bending

* matmtsb = matri+ for material #ro#ert& for bending

* kinmtss = matri+ for kinematic e$uation for shear

* matmtss = matri+ for material #ro#ert& for shear

* kinmtsm = matri+ for kinematic e$uation for membrane

* matmtsm = matri+ for material #ro#ert& for membrane

* tr3d = transformation matri+ from local to global a+es

-$$$$$$$$$$$$$$$$$$$$$$$$$$ - input data or control parameters -$$$$$$$$$$$$$$$$$$$$$$$$$$$

clear

nel=- * number of elements

nnel=( * number of nodes #er element

ndof=- * number of dofs #er node

nnode=25 * total number of nodes in s&stem

sdof=nnode/ndof * total s&stem dofs

edof=nnel/ndof * degrees of freedom #er element

emodule=3e- * elastic modulus


3/28

#oisson=0.0 * Poissons ratio

t=3 * #late thickness

ngl+b=2 ngl&b=2 * 2+2 auss1egendre $uadrature for bending

nglb=ngl+b/ngl&b * number of sam#ling #oints #er element for bending

ngl+s= ngl&s= * + auss1egendre $uadrature for shear

ngls=ngl+s/ngl&s * number of sam#ling #oints #er element for shear

-$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ - input data or nodal coordinate )alues -$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

gcoord=0.0 0.0 0.0 0.0 -.25 0.0 0.0 2.5 0.0 0.0 8.45 0.00.0 25.0 0.0

(.3( 0.0 10.38(.3( -.25 10.38(.3( 2.5 10.38(.3( 8.45 10.38(.3( 25.010.38

8.55 0.0 1.58.55 -.25 1.58.55 2.5 1.58.55 8.45 1.58.55 25.01.5

2.5 0.0 13.352.5 -.25 13.352.5 2.5 13.352.5 8.45 13.352.5 25.013.35

-. 0.0 15.85-. -.25 15.85-. 2.5 15.85-. 8.45 15.85-. 25.015.85

gcoord=2.0/gcoord

-$$$$$$$$$$$$$$$$$$$$$$$ - input data or nodal connecti)ity or each element -$$$$$$$$$$$$$$$$$$$$$$$

nodes=- 4 2 4 8 3 2 8 " ( 3 " 0 5 (

2 4 - 2 3 8 4 3 ( " 8 ( 5 0 "

- 4 2 4 8 3 2 8 " ( 3 " 20 5 (

2 22 4 - 22 23 8 4 23 2( " 8 2( 25 20 "

-$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ - input data or boundary conditions -$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

bcdof= 3 5 - 4 2 3 4 8 " 23 2( 25 2- 28 2" 30 ...


4/28

3 33 5- 58 -0 - -3 8- 88 "0 " "3 - 8 20 ...

2 22 23 (- (8 50 * constrained dofs

bcval=6eros7si6e7bcdof * !hose described values are 0

-$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ - initiali/ation o matrices and )ectors -$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

ff=6eros7sdof, * s&stem force vector

kk=6eros7sdof,sdof * s&stem matri+

dis#=6eros7sdof, * s&stem dis#lacement vector

inde+=6eros7edof, * inde+ vector

kinmtsb=6eros73,edof * kinematic matri+ for bending

matmtsb=6eros73,3 * constitutive matri+ for bending

kinmtsm=6eros73,edof * kinematic matri+ for membrane

matmtsm=6eros73,3 * constitutive matri+ for membrane

kinmtss=6eros72,edof * kinematic matri+ for shear

matmtss=6eros72,2 * constitutive matri+ for shear

tr3d=6eros7edof,edof * transformation matri+

-$$$$$$$$$$$$$$$$$$$$$$$$$$$$ - orce )ector -$$$$$$$$$$$$$$$$$$$$$$$$$$$$

ff73=1-3.- * transverse force at node

ff7"=1224.2 * transverse force at node 2

ff75=1224.2 * transverse force at node 3

ff72=1224.2 * transverse force at node (

ff724=1-3.- * transverse force at node 5

ff733=1224.2 * transverse force at node -


5/28

ff73"=12(5(.( * transverse force at node 4

ff7(5=12(5(.( * transverse force at node 8

ff75=12(5(.( * transverse force at node "


ff7-3=1224.2 * transverse force at node

ff7-"=12(5(.( * transverse force at node 2

ff745=12(5(.( * transverse force at node 3

ff78=12(5(.( * transverse force at node (


ff7"3=1224.2 * transverse force at node -

ff7""=12(5(.( * transverse force at node 4

ff705=12(5(.( * transverse force at node 8

ff7=12(5(.( * transverse force at node "


723=1-3.- * transverse force at node 2

ff72"=1224.2 * transverse force at node 22


ff7(=1224.2 * transverse force at node 2(

ff7(4=1-3.- * transverse force at node 25

-$$$$$$$$$$$$$$$$$$$$ - computation o element matrices and )ectors and their assembly -$$$$$$$$$$$$$$$$$$$$$

* for bending and membrane stiffness

#ointb,!eightb=fegl$d27ngl+b,ngl&b * sam#ling #oints 9 !eights


6/28

matmtsm=fematiso7,emodule,#oisson/t * membrane material #ro#ert&

matmtsb=fematiso7,emodule,#oisson/t:3;2 * bending material #ro#ert&

**

* for shear stiffness

*

#oints,!eights=fegl$d27ngl+s,ngl&s * sam#ling #oints 9 !eights

shearm=0.5/emodule;7.0


7/28

km=6eros7edof,edof * element membrane matri+

kb=6eros7edof,edof * element bending matri+

ks=6eros7edof,edof * element shear matri+

*111111111111111111111111111111111111111111111111111111

* numerical integration for bending term

*111111111111111111111111111111111111111111111111111111

for int+=ngl+b

+=#ointb7int+, * sam#ling #oint in +1a+is

!t+=!eightb7int+, * !eight in +1a+is

for int&=ngl&b

&=#ointb7int&,2 * sam#ling #oint in &1a+is

!t&=!eightb7int&,2 * !eight in &1a+is

sha#e,dhdr,dhds=feiso$(7+,& * com#ute sha#e functions and

* derivatives at sam#ling #oint

>acob2=fe>acob27nnel,dhdr,dhds,+#rime,rime * com#ute ?acobian

det>acob=det7>acob2 * determinant of ?acobian

inv>acob=inv7>acob2 * inverse of ?acobian matri+

dhd+,dhd&=federiv27nnel,dhdr,dhds,inv>acob * derivatives !.r.t.

* #h&sical coordinate

kinmtsb=fekinesb7nnel,dhd+,dhd& * bending kinematic matri+

kinmtsm=fekinesm7nnel,dhd+,dhd& * membrane kinematic matri+

*11111111111111111111111111111111111111111111

* com#ute bending element matri+


8/28

*11111111111111111111111111111111111111111111

kb=kbacob

km=kmacob

end

end * end of numerical integration loo# for bending term

*111111111111111111111111111111111111111111111111111111

* numerical integration for bending term

*111111111111111111111111111111111111111111111111111111

for int+=ngl+s

+=#oints7int+, * sam#ling #oint in +1a+is

!t+=!eights7int+, * !eight in +1a+is

for int&=ngl&s

&=#oints7int&,2 * sam#ling #oint in &1a+is

!t&=!eights7int&,2 * !eight in &1a+is

sha#e,dhdr,dhds=feiso$(7+,& * com#ute sha#e functions and

* derivatives at sam#ling #oint

>acob2=fe>acob27nnel,dhdr,dhds,+#rime,rime * com#ute ?acobian

det>acob=det7>acob2 * determinant of ?acobian

inv>acob=inv7>acob2 * inverse of ?acobian matri+

dhd+,dhd&=federiv27nnel,dhdr,dhds,inv>acob * derivatives !.r.t.

* #h&sical coordinate

kinmtss=fekiness7nnel,dhd+,dhd&,sha#e * shear kinematic matri+

*1111111111111111111111111111111111111111


9/28

* com#ute shear element matri+

*1111111111111111111111111111111111111111

ks=ksacob

end

end * end of numerical integration loo# for shear term

*11111111111111111111111111111111

* com#ute element matri+

*11111111111111111111111111111111

k=km


10/28

sum=sum

end

if 7sum @ e15

kk7i,i=

end

end

end

*11111111111111111111111111111

* a##l& boundar& conditions

*11111111111111111111111111111

kk,ff=fea#l&c27kk,ff,bcdof,bcval

*1111111111111111111111111111

* solve the matri+ e$uation

*1111111111111111111111111111

dis#=kkff

num=sdof

dis#lace=num dis# * #rint nodal dis#lacements

*11111111111111111111111111111111111111111111111111111111111111

* 'ubBroutines

*****************

function #oint2,!eight2=fegl$d27ngl+,ngl&

*1111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose


11/28

* determine the integration #oints and !eighting coefficients

* of auss1egendre $uadrature for t!o1dimensional integration

*

* '&no#sis

* #oint2,!eight2=fegl$d27ngl+,ngl&

*

* )ariable Cescri#tion

* ngl+ 1 number of integration #oints in the +1a+is

* ngl& 1 number of integration #oints in the &1a+is

* #oint2 1 vector containing integration #oints

* !eight2 1 vector containing !eighting coefficients

*1111111111111111111111111111111111111111111111111111111111111111111

* determine the largest one bet!een ngl+ and ngl&

if ngl+ D ngl&

ngl=ngl+

else

ngl=ngl&

end

* initiali6ation

#oint2=6eros7ngl,2

!eight2=6eros7ngl,2

* find corres#onding integration #oints and !eights

#oint+,!eight+=fegl$d7ngl+ * $uadrature rule for +1a+is


12/28

#oint&,!eight&=fegl$d7ngl& * $uadrature rule for &1a+is

* $uadrature for t!o1dimension

for int+=ngl+ * $uadrature in +1a+is

#oint27int+,=#oint+7int+

!eight27int+,=!eight+7int+

end

for int&=ngl& * $uadrature in &1a+is

#oint27int&,2=#oint&7int&

!eight27int&,2=!eight&7int&

end

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

function matmtr+=fematiso7io#t,elastic,#oisson

*111111111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* determine the constitutive e$uation for isotro#ic material

*

* '&no#sis

* matmtr+=fematiso7io#t,elastic,#oisson

*


* elastic 1 elastic modulus

* #oisson 1 Poissons ratio

* io#t= 1 #lane stress anal&sis


13/28

* io#t=2 1 #lane strain anal&sis

* io#t=3 1 a+is&mmetric anal&sis

* io#t=( 1 three dimensional anal&sis

*111111111111111111111111111111111111111111111111111111111111111111111111

if io#t== * #lane stress

matmtr+= elastic;71#oisson/#oisson/ ...

#oisson 0 ...

#oisson 0 ...

0 0 71#oisson;2

elseif io#t==2 * #lane strain

matmtr+= elastic;77


14/28

#oisson 71#oisson #oisson 0 0 0

#oisson #oisson 71#oisson 0 0 0

0 0 0 712/#oisson;2 0 0

0 0 0 0 712/#oisson;2 0

0 0 0 0 0 712/#oisson;2

end

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

function tr3d,+#rime,rime=fetransh7+coord,&coord,6coord,n

*11111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* om#ute direction cosines bet!een three1dimensional

* local and global coordinate a+es

*

* '&no#sis

* tr3d,+#rime,rime=fetransh7+coord,&coord,6coord,n

*


* +coord 1 nodal + coordinates 7(+

* &coord 1 nodal & coordinates 7(F

* 6coord 1 nodal 6 coordinates 7(F

* n 1 number of nodes #er element

* tr3d 1 3d transformation matri+ from local to global a+es

* +#rime 1 coordinate in terms of the local a+es 7(+


15/28

* rime 1 coordinate in terms of the global a+es 7(F

*

* Gote

* %he local +1a+is is defined in the direction from the first node

* to the second node. Godes , 2 and ( define the local +&1#lane.

* %he local 61a+is is defined normal to the local +&1#lane.

* %he local &1a+is is defined normal to the + and 6 a+es.

*11111111111111111111111111111111111111111111111111111111111111111111111111

*

* com#ute direction cosines

*

v2+=+coord721+coord7

v2&=&coord721&coord7

v26=6coord7216coord7

l2=s$rt7v2+:2


16/28

v(+=+coord7(1+coord7

v(&=&coord7(1&coord7

v(6=6coord7(16coord7

l(=s$rt7v(+:2


17/28

*

* transformation matri+

*

for i=2/n

i=7i1/3


18/28


19/28

* st node at 71,1, 2nd node at 7,1

* 3rd node at 7,, (th node at 71,

*111111111111111111111111111111111111111111111111111111111111111111111111

* sha#e functions

sha#e$(7=0.25/71rvalue/71svalue

sha#e$(72=0.25/7


20/28

* '&no#sis

* >acob2=fe>acob27nnel,dhdr,dhds,+coord,&coord

*


* >acob2 1 ?acobian for one1dimension

* nnel 1 number of nodes #er element

* dhdr 1 derivative of sha#e functions !.r.t. natural coordinate r

* dhds 1 derivative of sha#e functions !.r.t. natural coordinate s

* +coord 1 + a+is coordinate values of nodes

* &coord 1 & a+is coordinate values of nodes

*111111111111111111111111111111111111111111111111111111111111111111111111

>acob2=6eros72,2

for i=nnel

>acob27,=>acob27,acob27,2=>acob27,2acob272,=>acob272,acob272,2=>acob272,2acob

*111111111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* determine derivatives of 21C iso#arametric sha#e functions !ith


21/28

* res#ect to #h&sical coordinate s&stem

*

* '&no#sis

* dhd+,dhd&=federiv27nnel,dhdr,dhds,inv>acob

*


* dhd+ 1 derivative of sha#e function !.r.t. #h&sical coordinate +

* dhd& 1 derivative of sha#e function !.r.t. #h&sical coordinate &


* dhdr 1 derivative of sha#e functions !.r.t. natural coordinate r

* dhds 1 derivative of sha#e functions !.r.t. natural coordinate s

* inv>acob 1 inverse of 21C ?acobian matri+

*111111111111111111111111111111111111111111111111111111111111111111111111

for i=nnel

dhd+7i=inv>acob7,/dhdr7iacob7,2/dhds7i

dhd&7i=inv>acob72,/dhdr7iacob72,2/dhds7i

end

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

function kinmtsb=fekinesb7nnel,dhd+,dhd&

*11111111111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* determine the kinematic matri+ e+#ression relating bending curvatures

* to rotations and dis#lacements for shear deformable #late bending


22/28

*

* '&no#sis

* kinmtsb=fekinesb7nnel,dhd+,dhd&

*



* dhd+ 1 derivatives of sha#e functions !ith res#ect to +

* dhd& 1 derivatives of sha#e functions !ith res#ect to &

*11111111111111111111111111111111111111111111111111111111111111111111111111

for i=nnel

i=7i1/-


23/28

function kinmtsm=fekinesm7nnel,dhd+,dhd&

*111111111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* determine the kinematic e$uation bet!een strains and dis#lacements

* for t!o1dimensional solids

*

* '&no#sis

* kinmtsm=fekinesm7nnel,dhd+,dhd&

*





*111111111111111111111111111111111111111111111111111111111111111111111111

for i=nnel

i=7i1/-


24/28

kinmtsm73,i=dhd&7i

kinmtsm73,i2=dhd+7i

kinmtsm73,i-=0.0

end

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

function kinmtss=fekiness7nnel,dhd+,dhd&,sha#e

*111111111111111111111111111111111111111111111111111111111111111111111111

* Pur#ose

* determine the kinematic matri+ e+#ression relating shear strains

* to rotations and dis#lacements for shear deformable #late bending

*

* '&no#sis

* kinmtss=fekiness7nnel,dhd+,dhd&,sha#e

*





* sha#e 1 sha#e function

*111111111111111111111111111111111111111111111111111111111111111111111111

for i=nnel

i=7i1/-


25/28

i3=i2


26/28

* ndof 1 number of dofs #er node

*11111111111111111111111111111111111111111111111111111111111

edof = nnel/ndof

k=0

for i=nnel

start = 7nd7i1/ndof

for >=ndof

k=k


27/28

* inde+ 1 d.o.f. vector associated !ith an element

*11111111111111111111111111111111111111111111111111111111111

edof = length7inde+

for i=edof

ii=inde+7i

for >=edof

>>=inde+7>

kk7ii,>>=kk7ii,>>

end

end

________________________________________________________________________

function kk,ff=fea#l&c27kk,ff,bcdof,bcval

*1111111111111111111111111111111111111111111111111111111111

* Pur#ose

* A##l& constraints to matri+ e$uation kkI+J=IffJ

*

* '&no#sis

* kk,ff=fea#l&bc7kk,ff,bcdof,bcval

*


* kk 1 s&stem matri+ before a##l&ing constraints

* ff 1 s&stem vector before a##l&ing constraints

* bcdof 1 a vector containging constrained d.o.f


28/28

* bcval 1 a vector containing contained value

*

* Kor e+am#le, there are constraints at d.o.f=2 and 0

* and their constrained values are 0.0 and 2.5,

* res#ectivel&. %hen, bcdof7=2 and bcdof72=0 and

* bcval7=.0 and bcval72=2.5.

*11111111111111111111111111111111111111111111111111111111111

n=length7bcdof

sdof=si6e7kk

for i=n

c=bcdof7i

for >=sdof

kk7c,>=0

end

kk7c,c= ff7c=bcval7i endBBBBBBBB

matlab.mathematica getting a warning while running the program

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