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Computational Framework (3)
• Description is Lagrangian: nodes and G.P.s remain always
associated to same material point (particle)
• Stress is “true”: expressed in fixed reference (but corotational
formulation may be useful for beams/plates/shells)
• All RHS terms are known (
f
ext , B
stresses must be obtained via material constitutive law
• Diagonalization of
where N
M
by lumping:
are the element shape functions
• We work on current configuration: no need to define a
M
reference configuration and no use of (total) deformation
) or computable:
e
= ∫
V
e
NρdV
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Direct Time Integration
• Time integration is achieved via a central
difference scheme, usually written as:
n stays for time t
n
1
1 stays for n +
n+ t = t n +∆t
∆t is the time increment
n+ 1 n ∆t
n n+
1
u = u + ( u + u
)
2
n+
1 n n ∆t
n
u = u +∆ t( u
+ u
)
2
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