discontinouity, finite difference method, beam bending, concentrated force
The finite difference metod (FDM) is widely used numerical method for numerical computation of different physical problems. The method is very useful for time-dependent problems. The sequence of finite difference method solutions with increasing the number of discrete points converge to analytical solutions. It converges rapidly for smooth problems. The simple structural engineering problem with concentrated force has discontinouity in third derivative. The problem is how to model that kind of loading for finite difference method. New approach is explained. The concentrated force is not taken as loading. It is taken as the difference of third derivative (difference between value very close left from value very close right) at loading point. The procedure for numerical evaluation is described. The presented numerical example shows that the sequence of numerical results converges with quadratic order of convergence to anaytical solution.
Cite this paper
Mladen Mestrovic. (2017) Discontinouity Modelling for Finite Difference Method. International Journal of Theoretical and Applied Mechanics, 2, 21-24