how do you know if a problem is linear

huangyhg

how do you know if a problem is "linear"?
how does one go about determining if a structural problem is linear or non-linear?  people talk about "large deflection", non-linear materials, etc. but there have to guidelines somewhere!  what if one assumes a non-linear problem is linear and uses a linear fea code?  will there by any indication that you've gone down the wrong path or will the code give you misleading answers?
tunalover
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hey, you know tuna has mercury in it, right?  just giving you a hard time, lol.
it depends on the type of problem.  consider a few examples.  
if you have cables with catenary action, pretensions, etc., you obviously have a nonlinear problem, right?
if you have a 3 story bldg with concrete shearwalls, you have a linear problem unless a specification forces you to do a nonlinear analysis.  then you'll have a nonlinear analysis that gives you the same result as a linear one, lol.
if you have a steel frame, you probably have a nonlinear problem just because the aisc spec forces you to do a nonlinear analysis.  your answer will be slightly nonlinear.
the bottom line is that you have to understand the program you're using and its limitations.  some use things like consistent geometric stiffness matrices.  some don't.  some iterate by updating these matrices.  some iterate by changing geometry.  it is very possible to mis-use a program, especially when dealing with very nonlinear things like cable nets.
sorry for indirectly answering.
i don't think your question has a standard "good" answer.
2.71828
you have to know something about the material prior to beginning the analysis.  it's very hard to place one simple constraint on many different types of materials.
you can have material, geometric, and contact nonlinearities.  what you need to do is understand the assumptions involved in the equations you use.  you may assume small deflections for instance, which essentially means that the deformation doesn't affect loading and sin(a)=tan(a)=a.  as qshake mentioned, if you use equations derived assuming small deflections and you get large ones, then you need to redo your analysis.  you'll need to research this to figure out what constitutes large and small.  you may have a material that yields or buckles at a certain point.  beyond that, strength or resistance is no longer directly proportional to deformation, so by definition the problem is no longer linear.
there are many other examples and cases of nonlinear behavior.  the best thing to do would be to find some texts that will explain things more in depth.
it's linear as long as it's scaleable... if you do twice as much to it and twice as much happens, then it's linear.
dik
dik, i have to disagree, if i understand you correctly.
by "do twice as much," i assume that you mean "apply twice as much load."  if it deflects twice as far, then all that means is that the model's prediction was linear.  for example, i can put a cable net into a linear program and run it subject to 1 kip.  i can change it to 2 kips and will get twice as much deflection, which is obviously wrong.
sorry... maybe the analogy was fuzzy... but a system is linear if it is directly scaleable nx something produces nx effect.
dik