What are you talking about ?  That is exactly what you want to do.  This is the basic understanding of calculus and limits.  There is no problem with having constant strain across a very small element.  Hit the books again.

The displacement function must be capable of representing constant strain states within the element. the reason for this requirement can be understood if we imagine the condition when the body or structure is divided into smaller and smaller elements. as these elements approach infinitesimal size, the  strains in each element also approach constant values. Hence the assumed displacement field must include terms for representing constant strain states.For one, two and three dimensional elasticity problems, the linear terms present satisfy this requirement. However, in the case of beam, plate and shell elements, this condition will be referred to as 'constant curvature' instead of 'constanst strains'.
Ref. CS Krisnamoorty

I don't understand the statement that you get constant strain states irrespective of the element order. Clearly this state will never be reached as a singularity of say order 0.5 (crack) is approached, no matter how small the elements. You may be able to find elements with strains 'nearly' constant, but that is only limited by the number of sig-figs, it would seem.

Hi all,
I agree with Prost, that this state will never be reached as a singularity of say order 0.5 (crack) is approached, no matter how small the elements. Another consideration is that the numerical error grows with the number of elements, so the accuracy will very, very poor in such a situation, unless one use a computer with very long binary representation, say more then 200 bits , think that the next PC generation will have only 64 bit representaion. May be we should realize, that the word "Finite" has several meanings, any suggestion?

cheers

Any type of numerical solution will have these limitations..so if you are looking for a numerical solution devoid of such problems you are out of luck. As far as singularity type problems such as cracks much research is going on in this field...take a look at some work by Dolbow et al at Duke on meshless methods...be aware though that your worries won't subside for these types of methods either...they only attempt to model such problems with greater efficiency since remeshing becomes expensive when attempting to model crack propagation.

All FEA models are just that "models" they are mathematical "Idealizations" of continuous systems. Therefore, all results from any FEA code are not "closed formed solutions". The results are numerical approximations... good approximations, but approximations.

David R. Dearth, P.E.
Applied Analysis & Technology
E-mail "AppliedAT@aol.com"

Thanks a lot for those rsponses
raj

Raj
Structural Engr.