Week - 2 - Explicit and Implicit Analysis

There has not been any relevant input/discussion in the Skill-Lync course executed so far to
answer these questions. As the questions are irrelevant in the context of the videos, I am
attempting to write my answers on the basis of my general understanding of the subject.
Moreover, the lingual skill of the person written the details are too poor to write anything
meaningful.
1. Implicit and Explicit explanation:
Explicit Method:
Explicit Finite Element Method is used to calculate the state of a given system at a different
time from the current time using direct iterative calculations. The solution doesn’t have to
converge at each time increment, but for the solution to be accurate time increments
must be super small. The solution is performed with direct iterative calculations.
Mathematical Definition of Explicit Method:
u(n+1) = u(n) +Δt. F(u(n))
F(u) = du/dt
M d2u/dt2 + Ku = F(t)
At t=0, we know the value of u and v and use them to compute M and K and then use them
to compute the acceleration, from which velocity and displacement can be calculated at Δt.
a = M-1(F(t) – Ku)
v(Δt) = v(0) + a Δt
u(Δt) = u(0) + v(0) Δt + ½ a Δt2
Where, a = Nodal Acceleration, v = Nodal Velocity, u = Nodal Displacement, k = Stiffness, t
= Time, F = Load/Force, M = Mass
For the explicit analysis simulation to be stable, the Time-Step Should be Smaller than the
Time taken for an Elastic Web to Travel from one side to the other side of the smallest
element:
i.e. Δt < L√𝜌(1 − 2𝜗)/2𝜇(1 − 𝜗)
L is the smallest length of smallest element
roh is the density of the material
v is the web velocity
mu is the shear modulus of the material
Implicit Method:
In contrast, an Implicit Analysis finds a solution by solving equations of state of the system
based on both the current and later states of the given system. In Implicit analysis the
solution at each time increment have to converge and the time increment can be set
pretty long. In Implicit analysis the solution needs to be computed.
In implicit method, M and K are computed not at t=0, but at Δt and then progressed as
above. However, it requires more calculations and cost of computing is large.
Implicit analysis is not subjected to the condition of the Time-Step to be smaller than the
Time taken for an Elastic Web to Travel from one side to the other side of the smallest
element. Accordingly, it is unconditionally stable.
2. Aim, Explanation and Conclusion
Aim: Aim of any CAE analysis of a structural system is to ascertain its suitability to sustain
under the applied loading and constraints over a period of time desired.
Explanation: To enable the desired modelling for CAE analysis of the structure, the problem
must be explained with Geometrical Diagram, Constraints, Loading, Materials, Section
Properties of the individual parts, etc.
Conclusion: With Post-Processing of the analysis results, the CAE executive should make a
conclusion with logics that the Structural System is Safe enough or if it is likely to fail when it
is put in operation.
3. Report Presentation:
FEA analysis of any structure is performed with the purpose of assuring the designer that the
design is safe in intended operation and if there is any scope of optimisation of the design.
Accordingly, on completion of the analysis, the results need to presented in a fashion that
conveys the
- Objective of the analysis,
- Geometry of the structure and Components
- Materials of the components
- SPCs and Boundary conditions applied
- Loadings applied
Post-Processing / Analysis results
- Contour plots: Stress, Strain, etc.
- Resultant reaction forces/moments, other nodal/elemental outputs
- Graphical output plots
Analytical observations and interpretations of the analysis executives, inferences if any.
Concluding statement with respect to the objectives of the analysis.
4. Clear Explanation of the Plots:
Plots provides graphical representation of some vital analysis results like Nodal
Displacements, Velocities, Accelerations at specific point of interests, Elemental Stress,
Strain, etc. For the purpose of plotting results Ls-Dyna Post-Processing provides the options
of ASCII result plot, XY-Plot, History Plot. One can use these utilities to see the results as
well as store/save them for subsequent references or to use in presentation documents.