The growing power of modern workstations enables engineers to simulate more and more complex mechanical models by computers. In particular, nonlinear problems from structural dynamics are computationally intensive. Hence, there is ongoing demand in the development of new and improvement of existing algorithms. The present thesis deals with the simulation of the dynamics of flexible bodies subject to material and geometrical nonlinearities, as well as discontinuous phenomena arising from collisions. The equation of motion is discretized following the principle of variational integration, by what conservation laws of the continuous problem are valid in the discrete model. Existing approaches are presented. By combination of different procedures a mollified implicit-explicit algorithm is developed. It allows larger critical time steps and is particular suited for problems with non-dominant nonlinearities. The presentation of variational integrators includes the temporal discretization of holonomic and unilateral constraints. The spatial discretization is performed by a modified finite element method.
The accuracy of isoparametric elements is increased by enforcing stress continuity locally. This happens by the assumption of a continuously interpolated deformation gradient. The stability of the formulation is discussed in detail. For the temporal discretization an asynchronous strategy is employed. The equation of motion is integrated explicitly, whereby some critical time step length must not be exceeded.
Asynchronous methods apply individual time steps to each spatial domain.
Substructures with softer material behaviour or larger finite elements can, therefore, be integrated by a larger time step. The thesis develops strategies to estimate the local time step size for the new element formulation and to efficiently treat nodal restraint conditions. It studies, how temporally-adaptive step sizes influence stability and accuracy.Furthermore, this work presents procedures for spatial discretization and detection of collision problems. In particular, the concept of distance fields is enhanced in this respect. The contact conditions from impenetrability and friction are enforced by discontinuous velocity changes in a spatially asynchronous and temporally adaptive manner.