**The ANSYS program with the addition of the LS-DYNA program includes
the ability to address both implicit as well as explicit solutions.
Significantly, at Revision 5.4 the ANSYS program added the ability to perform
implicit-explicit or explicit-implicit sequential solution simulations. A major
step forward in the state-of-the-art in predicting results of many complex
processes in a highly efficient way. An example of an explicit-implicit
analysis would be sheetmetal forming and springback that follows. An example of
an implicit-explicit analysis would be drop testing of a preloaded or packaged
consumer product.**

**Let’s look at the differences between the two techniques in a
condensed summary form. Both processes involve a numerical time integration
scheme to solve for the unknown displacement solution, which is the basis for
calculating resulting strains and stresses. Implicit integration schemes (ANSYS
uses a Newmark Forward Differencing method) assume a constant average
acceleration over each time step, between t _{n} and t_{n+1}.
The value t_{n} is time at the beginning of each time step and the
value t_{n+1} is time at the end of each time step. The governing
equation is evaluated and the resulting accelerations and velocities at
t_{n+1} are calculated. Then the unknown displacements at
t_{n+1} are determined. Explicit integration schemes (LS-DYNA uses a
Central Differance method) assume a linear change in displacement over each
time step. The governing equation is evaluated and the resulting accelerations
and velocities at t_{n} are calculated. Then the unknown displacements
at t_{n+1} are determined.**

**There is one major difference between the two techniques in the
equations that are used to solve for displacements at t _{n+1}. The
implicit solution method requires matrix inversion of the structural stiffness
matrix, the explicit solution does not. However, unlike the implicit solution
scheme, which is unconditionally stable for large time steps, the explicit
scheme is stable only if the time step size is smaller than the critical time
step size for the structure being simulated. The undamped critical time step
size is 2/w_{n} (where w_{n} is
the largest natural circular frequency), which is usually a very small value.
This very small time step size requirement for stability thereby makes explicit
solutions useful only for very short transients. But, even though the number of
time steps in an explicit solution may be orders of magnitude greater than that
of an implicit solution, it is significantly more efficient than an implicit
solution since no matrix inversion is required. Neither an implicit nor
explicit solution is the clear winner in all cases.**

**ANSYS users can have the best of both
worlds in an integrated program that allows them to transfer geometry and
results to perform implicit-explicit or explicit-implicit sequential analysis.
Combined with the power of the ANSYS GUI (Graphical User Interface) to
postprocess their sequential analysis results, they have the tools to solve
some of the FEA world's most demanding simulations. Give us a call if
you’re interested in learning more about ANSYS/LS-DYNA.**