ACCURATE EXPLICIT FINITE ELEMENT METHOD FOR WAVE PROPAGATION AND DYNAMIC CONTACT PROBLEMS

An accurate explicit integration algorithm in the predictor-corrector form for finite element computations of wave propagation and contact problems in solids is presented. The nominated algorithm, with the component-wise partition of equations of motion to longitudinal and shear parts, is designed to more precisely integrate wave propagation in accordance with their different propagation wave speeds and their stability limits. The suggested three-time step integrator is fully explicit with a diagonal mass matrix requirement, second-order accurate, conditionally stable and exhibits minimal sensitivity behaviour on the time step size satisfying the stability limit. The submitted time algorithm is able to be easily implemented into standard finite element codes for general non-linear dynamics problems - wave propagation, dynamic plasticity with small and large deformations, dynamic crack propagation with cohesive fracture models and impact/contact problems. In a numerical test of wave propagation in a disc, we compare results obtained by the proposed scheme with existing conventional time integrators.