Matrix or Vector | Shape Functions | Integration Points |
---|---|---|
Stiffness Matrix | None (lumped) | None |
Damping Matrix | None (lumped, harmonic analysis only) | None |
Load Vector | None (lumped) | None |
CIRCU124 contains 10 linear electric circuit element options. These may be classified into two groups:
Independent Circuit Element options, defined by 2 or 3 nodes:
Resistor (KEYOPT(1) = 0)
Inductor (KEYOPT(1) = 1)
Capacitor (KEYOPT(1) = 2)
Current Source (KEYOPT(1) = 3)
Voltage Source (KEYOPT(1) = 4)
Dependent Circuit Element options, defined by 3, 4, 5, or 6 nodes:
Mutual inductor (KEYOPT(1) = 8)
Voltage-controlled current source (KEYOPT(1) = 9)
Voltage-controlled voltage source (KEYOPT(1) = 10)
Current-controlled voltage source (KEYOPT(1) = 11)
Current-controlled current source (KEYOPT(1) = 12)
All circuit options in CIRCU124 are based on Kirchhoff's Current Law. These options use stiffness matrices based on a simple lumped circuit model.
For transient analysis, an inductor with nodes I and J can be presented by:
(13–171) |
where:
L = inductance |
VI = voltage at node I |
VJ = voltage at node J |
Δt = time increment |
θ = time integration parameter |
n = time step n |
A capacitor with nodes I and J is represented by:
(13–172) |
where:
C = capacitance |
Similarly, a mutual inductor with nodes I, J, K and L has the following matrix:
(13–173) |
where:
L1 = input side inductance |
L2 = output side inductance |
M = mutual inductance |
For harmonic analysis, the above three circuit element options have only a damping matrix. For an inductor:
(13–174) |
for a capacitor:
(13–175) |
and for a mutual inductor:
(13–176) |