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Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous generalizations including 3-dimensional ones, and supplied by numerical examples obtained from...
Sources of dynamic damping may be various. Mostly, the damping is implemented into calculations in a form of introduction of damping forces, as a product of the velocity vector and the damping matrix in an equation of motion. In practice, the damping matrix is usually assumed to be a linear combination of the mass matrix and the stiffness matrix (so called Rayleigh’s damping). This kind of damping primarily assumes the external environment viscosity as the source of damping, even though the part...
The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately,...
The article deals with the analysis of the dynamic behavior of a~concrete structural element during fast dynamic processes. The constitutive material model must be chosen appropriately so that it takes material viscosity into account when describing the behavior of material. In this analysis, it is necessary to use fairly complex viscous material models which can affect, for example, vibration damping and the dependence of strength or even of the entire stress-strain curve on the strain rate. These...
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