I have used FEA for a couple of years now, but using it and using it correctly are two different things, safety factor is not the solution to everything. I have the feeling I won't be using it right unless I have a clear answer to that question:I am aware elements must be close to their ideal shape (based on the Jacobian only?) in order to get accurate results.. But why? Since I understand it comes from a coordinate transform, unless two vectors of the element become colinear shouldn't the results be accurate no matter its shape?A step-by-step answer based on an illustrated example (arbitrary stress distribution) would be ideal, especially given that it is a relatively common question (but never well answered from what I have seen).
Why do the shape of finite elements matter?
finite element;simulation
A good introduction to how issues of element shape influence quality and ease of solution, with pictures, is Jon Shewchuk's What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measureshttp://www.cs.berkeley.edu/~jrs/papers/elemj.pdf