In this paper, bending analysis of a circular sandwich plate under distributed load with simply supported and clamped boundary conditions is investigated. First, the governing equations of the circular sandwich plate are obtained and they are solved using the Bessel functions. Then in order to validate the correctness of analytical results, numerical finite element method is used and its results are presented in the forms of contours and graphs. The results indicate that under distributed load, maximum deflection happens at 0.3 of outside radius, away from centre, and minimum deflection occurs at the outer edge of the circular sandwich plate. The results from analytical and numerical methods are compared and it shows that analytical method provides an acceptable accuracy.
Elastomer materials are often used for components such as tire treads or hydraulic sealings, when deformable and damping behavior of components are desired and high dynamic loads appear. Such elastomers show time- and frequency-dependent characteristics, called viscoelasticity. The modelling of viscoelastic material is mainly implemented in simulations by rheological models, which often consists of elastic and damping elements. A viscoelastic model can be parametrized to experimental data to describe a specific elastomer with high accuracy. The most common model is the Prony-series. This model uses several Maxwell-branches (connection of one elastic and one damping element in series). Every branch is only able to fit the experimental behavior at one single excitation frequency. This fact makes it necessary to use a lot of parameters for adapting the frequency- and temperature-dependent characteristics over decades of the excitation frequency. To overcome this need for a huge amount of parameters we formulate a fractional viscoelastic model approach that gets along with a much smaller set of parameters, using finite elements. In order to reduce the numerical effort, a similarly formulated model is set up on force-displacement level additionally. In this way, the complexity of the simulation can be reduced with mapping of the material behavior.
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