Download User's Manual

310
Nodal masses
Mass matrix
type
Nodal masses will be taken into account like in a vibration analysis.
Dynamic analysis uses Diagonal matrix type.
Nonlinearity
Follow nonlinear behaviour of materials and finite elements
If nonlinear elements are defined (e.g. a tension-only truss) here you can activate or
deactivate the nonlinear behaviour.
Follow geometric nonlinearity of beams, trusses, ribs and shells
If this option is activated loads will be applied to the displaced structure in each step.
Convergence
criteria
If Perform with equilibrium iterations is checked convergence criteria has to be set and will be
taken into account like in a nonlinear static analysis. Otherwise the actual E(U), E(P) and
E(W) values (their final values appear in the Info window) are compared to the reference
values set here.
Solution method
Linear or nonlinear equilibrium equations are solved by the Newmark-beta method. If t is
the time increment, in t+t we get:

K  U t  t  C  U t  t  M  U
t  t  P(t) ,
where C is the damping matrix, M is the mass matrix, K is the stiffness matrix.
 t2
  2  U

U t  t  U t   t  U t 
(1  2  ) U
t
t  t
2
   U

U t  t  U t  t (1   ) U
t
t  t .




AxisVM uses  = 1/4,  = 1/2.
The differential equation of the motion is solved by the method of constant mean
acceleration. This step by step integration is unconditionally stable and its accuracy is
satisfying.
AxisVM assumes that no dynamic effect is applied in t=0. Time-limited loads appear in t>0.
C is calculated from the Rayleigh damping constants:
C  a M  bK
Where a and b should be calculated from the damped frequency range (between i and j)
and the damping ratio according to the following figure:
a
b 
2i j
 i  j
2
 i  j