Discretization Techniques for Transient,Dynamic and Cyclic Problems in Geotechnical Engineering: Second Order Equation

摘要

The second order equations are the form more widely used both in solids and in soil dynamics. This Chapter is devoted to present the Discretization techniques which are used. The solution strategy consists on (i) perform a discretization in space from which a system of ordinary differential equations (ODE) is obtained, and (ii) discretize this system in time. An important aspect is that of imposing suitable boundary conditions. Here we will present a simple technique which can be used for elastic or viscoplastic materials assuming that the wave is planar in the neighbourhood of the boundary. Finally, we will present some applications to cyclic and dynamic problems.