Terminology issues in the Finite Element Analysis
The Finite Element Analysis (FEA), or Finite Element Method as
mathematicians call it, is one of many numerical techniques of solving partial
differential equations that describe, among others, the structural and thermal
problems presented in this book. FEA has seen rapid development during the
last few decades and it has displaced other numerical techniques into niche
applications assuming a dominant position in the market of engineering
analysis tools. Still, FEA is a relatively new engineering tool that has evolved
from being an exclusive tool for highly trained analysts, to the present day
where it has become an everyday tool of design engineers. Deeply rooted in
mathematics and developed, often independently by competitive commercial
firms, FEA shows discrepancies in development of terminology, which has
not yet been unified across the industry.
Users of different FEA programs may use different terminology for the
similar problems or use the same term describing different things. Constraints,
restraints, supports and fixtures may all mean the same for some people while
others will understand them differently. Many FEA users will argue that loads
and boundary conditions are different entities; while other will say that loads
are just one type of boundary condition because they are applied to the
boundary of a model (loads external to the model are in fact boundary
conditions, volume loads are not). Make sure you understand what is meant
by each term you use and do not be afraid to ask what exactly does it mean
that element "locks" or what is "A nonconforming hexahedral element" when
you hear such a term. Many of those terms come from legacy sources and
have long lost their relevance in modern programs such as SolidWorks
Simulation.
While volumes could and in fact should be written about FEA terminology,
here we will only review terminology issues that apply to names of analysis
types used by SolidWorks Simulation. As you know, the following studies
are available: Static, Frequency, Buckling, Thermal, Drop test, Fatigue,
Nonlinear, Linear Dynamic and Pressure Vessel Design. Don't take each
name literally as a short description of the analysis capabilities of each study.
Instead treat them just as labels, here is why:
Static
This can be linear static analysis or nonlinear static analysis however
nonlinear analysis is limited to large displacements and/or contact. In
nonlinear analysis conducted under a Static study, the user has no control
over the load time history which must be linear ("ramping-up" the load at a
uniform pace). Nonlinear material is not available.
Frequency
A common name for this type of analysis is modal analysis as you find in
every textbook on vibration analysis. Modal analysis finds natural frequencies
and the associated shapes of vibration. A combination of frequency and shape
is called a mode of vibration. Modal analysis does not find displacements,
strains and stresses.
Buckling
This is linear buckling analysis which finds buckling load factors and the
associated buckling shapes. The name "Eigenvalue based buckling analysis"
is sometimes used. Linear buckling analysis does not say how far a structure
will buckle or if it will survive buckling. To solve these questions, you must
use a nonlinear buckling analysis which is available in Simulation under
Nonlinear analysis.
Thermal
Thermal analysis can be executed as Steady State thermal analysis or
Transient Thermal analysis and is utilized to find temperatures, temperature
gradients and heat flux. Notice that thermal stresses are not calculated in
thermal analysis; they are calculated in Static or Nonlinear analysis using the
temperature results from Thermal analysis.
Drop Test
This is a specialized type of analysis intended for analysis of collision
between two bodies. This is dynamic analysis based on the direct integration
method, which is stable but very time consuming.
Fatigue
Fatigue analysis used results of Static analysis to calculate fatigue life under
cyclic loads.
Nonlinear
Nonlinear analysis will do everything that Static analysis can do and much
more but at a higher computational cost. All types of nonlinear behaviors can
be analyzed including nonlinear buckling and nonlinear materials. Simulation
features an extensive library of nonlinear materials available in a Nonlinear
study. Beware of common misconception that the only reason why Nonlinear
analysis may be required is nonlinear materials. In this book we have
presented many examples where other types of nonlinear behavior were
present. Additionally, Nonlinear analysis can be executed as static or
dynamic. And so it is more general than Linear Dynamic analysis.
Linear Dynamic
This should be really called Linear Vibration analysis. Remember that FEA is
a tool of structural analysis and as such, deals with elastic bodies. Any motion
of elastic bodies can only take a form of vibration about the position of
equilibrium. Linear Dynamic (Vibration) analysis is based on the Modal
Superposition method and this makes it very numerically efficient, but less
general than Nonlinear Dynamic (Vibration) analysis. Linear Dynamic
analysis has four sub-categories in Simulation: Modal Time History,
Harmonic, Random Vibration Analysis and Response Spectrum
Analysis.
Modal Time History
Vibration analysis textbooks call this Time Response analysis (the term
Dynamic Time is also used). This analysis is intended for problems
where load is an explicit function of time.
Harmonic
Vibration analysis textbooks often call this Frequency response (the
terms Steady State Harmonic analysis and Dynamic Frequency analysis
are also used). This analysis is intended for problems where load is a
function of frequency which in turn is a function of time. It is assumed
that frequency changes very slowly (if at all), hence the alternative name:
Steady State Harmonic analysis.
Random Vibration Analysis
Here, loads are given as a Power Spectral Density (PSD) of
displacements, velocities or accelerations. Results such as RMS and PSD
displacements, velocities and accelerations are calculated only in
probabilistic terms.
Response Spectrum Analysis
This analysis is intended for excitation loads of longer duration that are
non-stationary and therefore, cannot be presented as PSD. Instead, the
excitation is presented as a Response Spectrum which is useful to
analyze events such as earthquakes.
Pressure Vessel Design
This analysis offers a convenient way of superposing results of different Static
studies as required in the analysis of pressure vessels for compliance with
safety codes. Notice that a Pressure Vessel Design study can be used to
analyze superposed results of anything, not just pressure vessels.