A simply supported glass/polyvinyl butyral (PVB)/glass beam is modelled by plane finite elements. The distribution of strain and stress through the beam thickness and along its axis is obtained as a result of linear finite element analysis. It shows that the bending stress in the glass layers is determinant for the load-bearing capability of laminated glasses, but the shear in the PVB-interlayer plays an important role for glass-layer interaction. A mathematical model of triplex glass beam is derived, consisting of a bending curvature differential equation and a differential equation of PVB-interlayer shear interaction. The derived equations are solved analytically with boundary conditions of simply supported beam under uniform transverse load. A parametric study of the derived mathematical model is carried out. The model is utilized for lightweight structure optimization of layer thicknesses. The results of the optimization show that laminated glasses could be superior to monolithic glasses.

SUMMARYThis work presents a computational material model of exible woven fabric for ÿnite element impact analysis and simulation. The model is implemented in the non-linear dynamic explicit ÿnite element code LSDYNA. The material model derivation utilizes the micro-mechanical approach and the homogenization technique usually used in composite material models. The model accounts for reorientation of the yarns and the fabric architecture. The behaviour of the exible fabric material is achieved by discounting the shear moduli of the material in free state, which allows the simulation of the trellis mechanism before packing the yarns. The material model is implemented into the LSDYNA code as a user deÿned material subroutine. The developed model and its implementation is validated using an experimental ballistic test on Kevlar J woven fabric. The presented validation shows good agreement between the simulation utilizing the present material model and the experiment.

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SUMMARYA computational micro-mechanical material model of loosely woven fabric for non-linear finite element impact simulations is presented in this work. The model is a mechanism incorporating the crimping of the fibres as well as the trellizing. The equilibrium of the mechanism allows the straightening of the fibres depending on the fibre tension. The contact force at the fibre crossover point determines the rotational friction dissipating a part of the impact energy. The stress-strain relationship is viscoelastic based on a three-element model. The failure of the fibres is strain rate dependent. The model is implemented as user defined subroutine in the transient finite element code LS-DYNA. The ballistic impact simulations with the model are in good agreement with the experimental results.

The temperature and frequency dependences of the permittivity , the dielectric loss factor and the resistance R of the ceramic Ti in the interval 100-800C were studied. A ferroelectric phase transition at temperature C was observed. Hysteresis loops typical for ceramic ferroelectrics were observed. Relaxation maxima of the dielectric loss factor in the temperature interval 150-300C at various frequencies are formed. A value of 0.785 eV for the relaxation polarization activation energy was deduced. A strong low-frequency dielectric dispersion was observed. A relaxation maximum for the dielectric loss factor in the interval 10-50 kHz is formed. The activation energy of the conductivity depends on the frequency.