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This presentation deals with 3D finite elements. Introduction was given and constitutive relations were written
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9/30/2013
1
rd_m
ech@
yaho
o.co
.inrd
_mec
h@ya
hoo.
co.in
IntroductionTetrahedron Element Hexahedral Element
rd_m
ech@
yaho
o.co
.in
3D problems –Sometimes there may be a demand for 3D simulations -Three independent variables – x, y & zFormulation – Virtual work , Total minimum PE, Weak formulation etc.Field variables & derived quantities function of x, y & z – steady state problems.Computationally expensive
9/30/2013
2
rd_m
ech@
yaho
o.co
.in
3D Solid meshed with tetrahedron elements
rd_m
ech@
yaho
o.co
.in
P P’
P’’ P’’’
3D solid meshed with hexahedral elements
rd_m
ech@
yaho
o.co
.in
( )( )
−
−
−−
−−
−+=
xy
zx
yz
z
y
x
xy
zx
yz
z
y
x
Symm
E
γγγεεε
ν
ν
νν
ννννν
νν
τττσσσ
221
0221
00221
000100010001
211
{ } [ ]{ }εσ D=
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