When to use Abaqus explicit for solving quasi static
problems?
What are the advantages to solve?
Solving quasi static
problems using explicit will be economical when the problem involves complex
nonlinear effects involving complex non-linear contact analysis, example manufacturing
problems like rolling which is performed at slow speeds. The explicit method
uses central difference method to integrate the equations in time. The explicit
method uses central difference method to integrate the equations in time. The
explicit procedure requires no iterations and no tangent stiffness matrix. The
explicit integration rule is quite simple but by itself does not provide the
computational efficiency associated with explicit dynamic procedure. The key to
computation efficiency of the explicit procedure is to use of diagonal element
mass matrices. The lumped mass matrix is used because it inverse is simple to
compute and vector multiplication of mass inverse by internal force require
only n operations, where n is number of degree of freedom.
2) How to decide time step and number of increments in quasi
static problem in explicit?
The number of increments required is given by the equation
N=
Where dt
Assuming element distortion le and lamis’ constant, density
are not changed then
To get the optimum number of increments which is directly
related to the speed of the solution, there are two ways to speed of the
solution. One method is artificially reduce the time period of the event t. If
t is decrease too much then the event becomes impulse, where inertia forces
will be larger and will change the predicted response. Also one problem is
material behaviour is rate dependent. Another way to reduce the number of
increments is artificially increasing the material density. Mass scaling is
attractive to rate dependent static problems efficiently.
3) How to decide the mass scaling factor in quasi static
problem?
The mass scaling is
an efficient way to solve rate dependent quasi static problems. But we cannot
take the solution too fast to allow inertia forces to dominate and thus change
the solution. The solution need to be solved using trial and error method. The
solution accuracy can be compared with Abaqus standard. The appropriate mass
scaling factor can be selected which will yield the same accurate solution, at
the same time it will reduce the solution time. Refer to example problem 1.3.6
for more details on arriving the mass scale factor. The Abaqus explicit will
set the mass scaling factor automatically based on the rolling segments and
mesh properties.
