Discussion1 FEA and theoretical difference: Bending of a long uniformly loaded rectangular plate

[Shu Jiang PEng SE]

A rectangular plate is simply supported along the two short edges, the plate length is 45” (width is randomly set as 6”) and thickness 3/8”, and the uniform distributed load is 10psi. The maximum membrane (tension) stress and bending stress of the plate from ANSYS is verified with theoretical solution. The maximum membrane stress is 10841psi and maximum bending stress is 12982psi (FEA), the theoretical solution is 11300pis of membrane stress and 14200pis of bending stress, (p.123, Strength of materials, part II, advanced theory and problems, second edition, by S. Timoshenko).

APDL file is attached.

What is the possible reason of the results differences?

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
/prep7
antype,static
nlgeom,on
mp,ex,1,2.9e7
mp,nuxy,1,0.0
et,1,shell181
l=45
b=6
sectype,1,shell
secdata,0.375,1


k,1,
k,2,l
k,3,l,,b
k,4,,,b
l,1,2
l,2,3
l,3,4
l,4,1

Al,1,2,3,4


lesize,1,,,9
lesize,2,,,1
mshkey,1
mshape,0,2d
amesh,1

nsel,s,loc,x,-0.1,0.1
d,all,ux,0
d,all,uy,0
!d,all,uz,0
nsel,a,loc,x,l-0.1,l+0.1
d,all,ux,0
d,all,uy,0

nsel,s,loc,x,-0.1,l+0.1
nsel,r,loc,y,-0.1,b+0.1
esln,s,1

sfe,all,2,pres,,-10

allsel,all


finish

/solu
solve
finish



/post1

ETABLE,N1,SMISC,1
ETABLE,N2,SMISC,2
ETABLE,N3,SMISC,3

ETABLE,sm1,SMISC,34
ETABLE,sm2,SMISC,35
ETABLE,sm3,SMISC,36

ETABLE,sb1,SMISC,37
ETABLE,sb2,SMISC,38
ETABLE,sb3,SMISC,39



plnsol,s,1
plnsol,s,x
plnsol,s,eqv
pletab,sm1
pletab,sb1

plnsol,u,y
prrsol,f,x

finish
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

 

[corus]

The FE method is an approximate numerical method. Try refining the mesh and see if you approach the theoretical solution.

 

[SPDL310]

You may not have your constraints set properly. My understanding is that a shell element will converge from above meaning that a more refined mesh will result in a lower result.