Hello!,

I will try to explain you the differences between implicit & explicit formulations in Finite Element Analysis: the main criterion governing the selection of the implicit (NX NASTRAN Advanced Nonlinear Solution 601) or explicit (SOL701) formulations

is the time scale of the solution:

• The

implicit method can use much larger time steps since it is unconditionally stable. However, it involves the assembly and solution of a system of equations, and it is iterative. Therefore, the computational time per load step is relatively high.

• The

explicit method uses much smaller time steps since it is conditionally stable, meaning that the time step for the solution has to be less than a certain critical time step, which depends on the smallest element size and the material properties. However, it involves no matrix solution and is non-iterative. Therefore, the computational time per load step is relatively low.

• For

slow-speed dynamic problems, the solution time spans a period of time considerably longer than the time it takes the wave to propagate through an element. The solution in this case is dominated by the lower frequencies of the structure. This class of problems covers most structural dynamics problems, certain metal forming problems, crush analysis, earthquake response and biomedical problems. When the explicit method is used for such problems the resulting number of time steps will be excessive, unless mass-scaling is applied, or the loads are artificially applied over a shorter time frame. No such modifications are needed in the implicit method. Hence, the implicit method is the optimal choice.

• For

high-speed dynamic problems, the solution time is comparable to the time required for the wave to propagate through the structure. This class of problems covers most wave propagation problems, explosives problems, and high-speed impact problems. For these problems, the number of steps required with the explicit method is not excessive. If the implicit method uses a similar time step it will be much slower and if it uses a much larger time step it will introduce other solution errors since it will not be capturing the pertinent features of the solution (but it will remain stable). Hence, the explicit method is the optimal choice.

• A large number of dynamics problems cannot be fully classified as either slow-speed or high-speed dynamic. This includes many crash problems, drop tests and metal forming problems. For these problems both solution methods are comparable. However, whenever possible (when the time step is relatively large and there are no convergence difficulties) we recommend the use of the

implicit solution method.

• Since the explicit time step size depends on the length of the smallest element, one excessively small element will reduce the stable time step for the whole model. Mass-scaling can be applied to these small elements to increase their stable time step. The implicit method is not sensitive to such small elements.

• Since the explicit time step size depends on the material properties, a nearly incompressible material will also significantly reduce the stable time step. The compressibility of the material can be increased in explicit analysis to achieve a more acceptable solution time. The implicit method is not as sensitive to highly incompressible materials (provided that a mixed formulation is used).

Well, the above are more or less the main differences between implicit/explicit formulations, I have more but are code-specific element types supported, etc.., then not of interest general, unless you are user of NX NASTRAN.

Best regards,

Blas.

~~~~~~~~~~~~~~~~~~~~~~

Blas Molero Hidalgo

Ingeniero Industrial

Director

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