Description on explicit and implicit analysis
When we applied a load it was applied in steps. And we
apply load in steps in implicit type of analysis .This phenomenon / approach is
called as incremental approach . Now Implicit and explicit solver both apply
this approach . Where they apply load in steps.
The only difference between this two solver is that
implicit ,uses an iterative approach along with the incremental method.
The implicit solver try’s to achieve the equilibrium
between the internal and external forces
at each steps ,within that particular model, only then it will
progressed to the next step.(force convergence graph)
But, for explicit solver it doesn’t try to achieve
equilibrium at each step. If there are unbalanced forces these unbalanced
forces are multiplied with step and we get wrong answer.
Here we have to specify a lowest time step
Also the research provides that data that the implicit
solver is not suitable / less accurate for simulation stress wave propagation
events,(drop event,car crash event).
Implicit solver only handle the static problem
accurately.
Explicit calculation
Consider a case
of simple bar in tension .suppose that the force in the bar is a non-linear
function of displacement .
F(u) = u3 +u2+4u -------------1
From1 it follows that the stifness of the bar is
K(u)=df/dx = 3u2+2u+4---------------2
∆F=K *∆u
|
Step1
u0 = 0.0 K(u0) =4 ∆F=1 ∆u1 =∆F/K(u0) = ¼
therefore,
u1=u0+∆u1 = 0+1/4 =0.25
Step2
K(u1)
=3*(1/4)2+2*1/2+4 =4.6875 ∆F=1 ∆u2 =∆F/K(u1) =0.2133
therefore,
u2=u1+∆u2 = 0.25+0.2133=0.4633
Step3
K(u2)
=3*(0.4633)2+2*0.4633+4 =5.5704 ∆F=1 ∆u3 =∆F/K(u2) =1/5.5704=0.1795
therefore,
u3=u2+∆u3 =0.4633+0.1795=0.6383
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Step i
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∆Fi
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∆ui
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ui
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(Fext)i
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(Fint)i
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Fint-Fext=R
|
|
1
|
1
|
0.25
|
0.25
|
1
|
1.0781
|
0.0781
|
|
2
|
1
|
0.2133
|
0.4633
|
2
|
2.1672
|
0.1672
|
|
3
|
1
|
0.1795
|
0.6383
|
3
|
3.2206
|
0.2206
|
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