9/30/2013

1

rd_m

ech@

yaho

o.co

.inrd

_mec

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hoo.

co.in

IntroductionTetrahedron Element Hexahedral Element

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.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@

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.in

P P’

P’’ P’’’

3D solid meshed with hexahedral elements

rd_m

ech@

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( )( )

−

−

−−

−−

−+=

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=