Semi-Analytical Solution for Elastic Impact of Two Beams

Original scientific paper This paper presents semi-analytical solution for the problem of elastic impact of two beams. The solution is based on the finite element discretization of the structure and equation of motion solution using diagonalization method for solving a system of differential equations. This procedure avoids temporal discretization typical for numerical methods, and in this way eliminates influence of the time-step size on the solution and numerical stability problems that can occur if time step isn’t defined properly. Computer code is developed for calculation, and application of the procedure is illustrated with the case of collision of communication bridge between two floating objects and safety structure called arrestor. The results are compared to those obtained by numerical procedure using the same discretization of the structure and applying energy conservation principle. Very good agreement of the results obtained by three methods is achieved.