Impacts in forced dynamic systems lead to non-smooth vibrations, showing a scenario of bifurcations. Mechanical and numerical modelling is known for rigid body systems with distinct points of contact. In contrast, continuous systems can have a line of possible contact. As an example a vibrating beam with a delaminated layer will be considered. The objective is to establish a finite element formulation for stationary nonlinear oscillation arising from the evolution of impacts along the contact line between the delaminated layer and the remaining beam. The objectives are focussed on the choice of the unknown values of a set of parameters that mainly describe energy dissipation. A calibration of these parameters can be achieved by experimental results and by investigation of a minimal mechanical model.
Abstract. Forced oscillations of delaminated composite laminates lead to non-smooth dynamic systems due to continuously developing impact-like contacts along the delamination. The primary aim of this study is to investigate a realistic model situation for delamination problems based on experiments and numerical simulation. First, the properties of lateral impacts on beam-type structures are studied, in particular in regard to the amount of energy dissipation during contact. Taking these results into account the Finite Element method based on beam elements is employed to simulate the stationary state of typical oscillations observed on the delaminated structure paying special attention to the dynamically developing and strongly dissipative contact. To deal with that kind of contact arising between delaminated layers, an effective technique combining a law of impact with the classical penalty method is presented. Confronting numerical results with the experimental reference provides an insight into the accuracy and robustness of the simulation technique.
SUMMARY:We present results o f off-lattice Monte Carlo simulations of weakly charged chains where the charged beads interact with a screened Coulomb potential of Debye-Huckel type. The behaviour of the mean square end-to-end distance and mean-square radius of gyration versus chain length is discussed for various solution conditions characterized by the parameter < = 2AD/b, with A , being the Debye screening length and b the contour distance between neighbouring charged beads. We also evaluate the probability-density distribution for the end-to-end distance R. From the angular correlation function (cosy we estimate the persistence length as well as the chain length dependence of (R') and (Ra). With increasing [it is found to come close to that which is directly obtained from (R ' ( N ) ) and (Ra ( N ) ) . Furthermore, the nonexponential decay of correlations indicates our charged chains to be not wormlike.
The integration of continuous fiber-reinforced structures into short or long fiber-reinforced plastics allows a significant increase in stiffness and strength. In order to make the best possible use of the high stiffness and strength of continuous fiber-reinforcements, they must be placed in the direction of load in the most stressed areas. A frequently used tool for identifying the most heavily loaded areas is topology optimization. Commercial topology optimization programs usually do not take into account the material properties associated with continuous fiber-reinforced hybrid structures. The anisotropy of the reinforcing material and the stiffness of the base material surrounding the reinforcement are not considered during topology optimization, but only in subsequent steps. Therefore in this publication, existing optimization methods for hybrid and anisotropic materials are combined to a new approach, which takes into account both the anisotropy of the continuous fiber-reinforcement and the stiffness of the base material. The results of the example calculations not only show an increased stiffness at the same material input but also a simplification of the resulting reinforcement structures, which allows more economical manufacturing.
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