Please provide more details about your problem. My opinios are below for your problem.
Mesh size is a factor that influence stiffness of the system. An elastic system has infinite degree of freedom, and you can make the system more stiffer by discretization. As for your problem, decreasing the mesh size for the same problem means more element and more DOF. Normally, decreasing the mesh size makes the system less stiffer. Have you checked other parameters ?
Thank you very much Murat Ozdemir, I checked other parameters. The load-deflection curve of the beam in FE didn`t reach the entered load ( failure load of experimental test)
Another question related, is there option in ABAQUS that stops running at failure load ?
Firstly, I am not familiar with ABAQUS. As for your problem please see below;
Ultimate capacity may not reach the experimental load carrying capacity because of several reasons. For instance, it is quite difficult to satisfy exactly same BCs for FE simulations and expeirments. Another possible reason is initial imperfections, such as initial deflections, welding residual stress etc. If you can model both BCs and initial conditions exactly same as experiment conditions, you could obtain similar results with experiments.
What type of analysis are you trying to do static/dynamic?
Usually when you make finer mesh due to decrease in proximity of nearest nodes and also increase in number of DoF of system, the highest frequency of model goes high (obviously as your range of covered natural frequencies increase). This will make model stiffer and in case of dynamic analysis will cause stable time step to get smaller.
I have not further comment regarding your first question, however, with respect to your second question, ABAQUS does not have a negative tangent so it cannot predict failure unless you use one of the available failure models such as XFEM, VCCT. For instance, in XFEM simulations, cracks begin to initiate when your applied load reaches the failure load.
in general F.E.A effect by the mesh size up to limit.. that's appear within the results of any case study.. you can check my articles .. many are used FEA.. specially my PhD thesis , .. where this factor studied there..
Hussam Ali Mohammed, "Experimental and Nonlinear Analysis of Non-Prismatic Double Tee Prestressed Concrete Beams", PhD Thesis, Baghdad University, 2005.