Space-Time Finite Elements and a Moving Load

Non-classical problems are usually poorly treated by classical and commonly known solution methods. Time dependent problems, especially vibrations, described by partial differential equations are classically treated with the finite element method in space and the family of Newmark methods in time. Such time integration methods were described in Chapter 5. We discussed in the introduction to Chapter 6 the disadvantages of such an approach and the necessity for a more general treatment of phenomena in space and time. The space-time finite element method extends the finite element approximation of the differential equation over the time domain. The main advantage in our moving mass problems concerns its facility in treating the partial derivatives obtained from the chain rule applied to the acceleration of the inertial particle in a moving coordinate system, equations (3.119) or (3.121).