Chapter15 (1).pdf

(961 KB) Pobierz
Chapter 15 Explicit Dynamics
1
Chapter 15
Explicit Dynamics
15.1 Basics of Explicit Dynamics
15.2 Step-by-Step: High-Speed Impact
15.3 Step-by-Step: Drop Test
15.4 Review
970288167.008.png
Chapter 15 Explicit Dynamics
Section 15.1 Basics of Explicit Dynamics 2
Section 15.1
Basics of Explicit Dynamics
Key Concepts
•
Implicit Integration Methods
•
Explicit Integration Methods
•
Solution Accuracy
•
Integration Time Steps
•
Automatic Mass Scaling
•
Static Damping
970288167.009.png
Chapter 15 Explicit Dynamics
Section 15.1 Basics of Explicit Dynamics 3
Implicit Integration Methods
⎡ ⎣ ⎤ ⎦ D
⎡ ⎣ ⎤ ⎦ D
M
C
⎡ ⎣ ⎤ ⎦ D
K
F
+
+
=
{}
{}
{}
{}
•
<Transient Structural> solves the above equation using the following algorithm:
D n + 1 = D n +Δ t γ D n + 1 + (1 −γ ) D n
⎡
⎣
⎤
⎦
D n + 1 = D n +Δ t D n + 1
2 β D n + 1 + (1 − 2 β ) D n
Δ t 2
⎡
⎣
⎤
⎦
2
•
The parameters γ and β are chosen to control characteristics of the algorithm such as
accuracy, numerical stability, etc.
•
It is called an implicit method because the response at the current time step depends on
not only the historical information but also the current information; iterations are
needed in a single time step.
970288167.010.png
Chapter 15 Explicit Dynamics
Section 15.1 Basics of Explicit Dynamics 4
Explicit Integration Methods
⎡ ⎣ ⎤ ⎦ D
⎡ ⎣ ⎤ ⎦ D
M
C
⎡ ⎣ ⎤ ⎦ D
K
F
+
+
=
{}
{}
{}
{}
•
<Explicit Dynamics> solves the above equation using the following algorithm:
D n + 2
= D n − 2
+ D n Δ t
D n + 1 = D n + D n + 2
Δ t
•
It is called explicit methods because the response at the current time can be calculated
explicitly; no iterations within a time step is needed.
970288167.011.png
Chapter 15 Explicit Dynamics
Section 15.1 Basics of Explicit Dynamics 5
Solution Accuracy
•
<Explicit Dynamics> uses the principle of conservation of energy to monitor the solution
accuracy.
(Reference Energy) + (Work Done) Reference → Current = (Current Energy)
•
It calculates overall energy at each cycle. If the energy error reaches a threshold, the
solution is regarded as unstable and stops. The default threshold is 10%.
•
The Energy Error is defined by
Energy Error = (Current Energy)-(Reference Energy) - (Work Done) Reference → Current
max Current Energy , Reference Energy , Kinetic Energy
(
)
970288167.001.png 970288167.002.png 970288167.003.png 970288167.004.png 970288167.005.png 970288167.006.png 970288167.007.png
 

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin