4.5. LESSONS LEARNED 67
particular problem, it requires substantially more computational eﬀort and cost than the corre-
sponding two-dimensional plane stress approximation.
4.5 LESSONS LEARNED
ese two case studies point out several realities in application of the ﬁnite element method.
1. When one proceeds to higher dimensions, while Poisson eﬀects, i. e., lateral dimensional
changes and out-of-plane warping, are captured, the precise manner in which classical
boundary conditions such as simple supports or clamped supports are applied can have
signiﬁcant inﬂuence on the numerical results.
2. Improper boundary conditions can lead one to purposefully choose poorer element formu-
lations and coarser meshes in attempts to validate a solution.
3. While one- and two-dimensional idealizations help reduce computational eﬀort, they must
be understood and substantiated.
ese lessons illustrate several of the common errors encountered in using the ﬁnite element
method [Chalice Engineering, LLC, 2009]. ese include:
1. using wrong elements for an analysis,
2. incorrectly prescribing boundary conditions,
3. incorrectly applying theory for solution validation,
4. assuming ﬁnite element analysis is conservative, and
5. using ﬁnite element analysis for the sake of it.
ere are arguably only two types of errors made in numerical simulation: either in faulty
assumptions regarding the relevant physics governing the engineering system or discretization
error in the numerical solution algorithm employed. Good analysts must understand and take
responsibility for both. Modeling is, therefore, necessarily an iterative enterprise involving re-
assessing the validity of one’s physical assumptions as one hones in on an acceptable solution.
Because our numerical simulations are only approximations, this book has emphasized that users
should be skeptical of their solutions prior to validating them. Further interesting reading re-
garding modeling approximation and anomalies can be found in Deaton [2010, 2013], Dvorak
, Fleenor , Grieve , and Kurowski [2001, 2002a,b,c].