| A two-dimensional finite element procedure for oblique impact analyses with friction is developed, employing Coulomb's friction law. Proportional material damping is implemented into the finite element procedure to model real engineering materials more accurately, as well as to attenuate the spurious high-frequency oscillations in finite element solutions. The classical discrete impact and release conditions are modified to include additional material damping terms. A two-step, iterative approach is developed to consider the impact conditions of sliding contact nodes when damping exists. A finite element program CIFE has been established for contact-impact analyses. Several static and dynamic numerical examples have been solved to illustrate the accuracy and reliability of the finite element procedure.;Dispersion properties of one-dimensional, constant strain, finite element discretizations are investigated by using the complex variable method. A general form of dispersion relation has been derived in which both the spatial and temporal discretizations are taken into account. The possible sources of spurious wave components in impact analysis are discussed. The frequency response functions of finite element meshes are shown to be very useful to reveal the physical essence of the wave front dispersion and spurious oscillations caused by finite element spatial discretizations. In order to expose the effect of the spatial discretization alone, the modal superposition method is employed to integrate the discretized equations of motion. It is found that the non-dimensional stress distribution depends only on the percentage of modes which are included in the modal superposition method and the number of elements through which the stress wave has propagated. It is also found that the amplitude of the spurious oscillations cannot be reduced by using a finer mesh. |
