In this work, a comparative analysis of existing methods for determining the compliance of mechanical joints such as ‘composite-composite’ and ‘composite-metal’ is performed. Polymer composite materials are widely used in modern aircraft industry. As a result, it is necessary to take into account the characteristics of joints of composite aggregates with composite and metallic ones. Considering the compliance of connections in the global finite element models of structural units of aircraft allows increasing the accuracy of calculations. The use of empirical formulae can significantly reduce time and labour costs in calculating the compliance of bolted connections for use in global finite element models. In this paper we review and analyse the existing empirical dependencies. Calculation of rigidity and compliance of single-shear ‘composite-composite’ and ‘composite-metal’ joints by finite element method for small, medium and large membrane thicknesses is carried out, and the results are compared with the calculations using empirical formulae. As a result of the analysis for medium and small thicknesses it is proposed to determine the value of bolted joint flexibility by the empirical formula Boeing 1, and for large thicknesses of connecting membranes it is proposed to use empirical formula Huth.

In performing design strength analysis of connection areas of composite — metal and composite — composite types of structural load-bearing wing and empennage elements of the aircraft implemented using mechanical fasteners, it is necessary to considerthe factors determining the local strength of these areas: the conditions of mechanical contact of the body, bolt head and cap with connected elements, the connected elements contact with each other and the effects of friction. These factors can be taken into account only by applying the global-local modeling approach for constructing 3D prediction models of composite — metal and composite — composite joint zones of aircraft caisson structural members. To solve this problem, a method is proposed defining the means and tools of modeling, algorithms for constructing a prediction model and performing calculations, as well as procedures for analyzing the results of calculations.

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Calculation of the modal and damping characteristics necessary to eliminate resonant oscillation of products made of polymeric materials requires reliable data on the elastic characteristics of the material. The problem is that the mechanical properties of polymer composite materials depend on a large number of factors. The aim of the work is to determine the damping coefficients for a layered composite material and the subsequent validation of the mathematical model. The Rayleigh damping model was chosen to calculate the damping coefficients. The choice is due to the fact that the resulting stiffness and mass matrix is determined by the natural oscillation modes of the problem without attenuation, which makes it possible to split the modes into separate dynamic subtasks. A sample made according to the ASTM standard was chosen as the object of study. To increase an error of the calculation, the mathematical model of the sample was modeled in detail by the finite element method using the technique of layer-by-layer modeling. The method for determining the damping coefficients is carried out in three stages. At the first stage, with the help of modal analysis, the natural oscillation modes are determined, corresponding to the nature of the oscillation studied in the experiment. At the second stage, an implicit dynamic analysis with default damping parameters in order to calculate the damping ratio is performed. At the last stage, a steady-state dynamic analysis taking into account the characteristics obtained in the previous stages. Next, an iterative process begins, including implicit and steady-state dynamic analyses, performed alternately. At each step, the previously calculated Rayleigh proportionality coefficients are introduced into the model. As a result of the identification of the mathematical model, the damping coefficients α and β are calculated. The damping experiment was chosen as a validation problem. The damping ratio ζ was chosen as the criterion of convergence with the experimental data.

In all real materials, energy is dissipated during deformation. You can think of it as a kind of internal friction. The load curve for the full period does not fit into a straight line. Usually, to describe the damping in the material, a model is used in terms of the hysteresis loss coefficient, since the energy losses per period depend weakly on frequency and amplitude. At the same time, the mathematical description in the loss factor model is based on complex values, that is, it implies only the case of harmonic vibration. Therefore, this damping model can only be used for frequency-domain studies. Rayleigh damping is a simple approach to forming the damping matrix as a linear combination of the mass matrix and the stiffness matrix. This damping model is unrelated to any physical loss mechanisms. In this paper, we consider a model of a mathematical pendulum for the experimental and computational determination of the damping properties of a polymer composite material. For the experimental part, a stand was designed and created that simulates the excitation of a plate made of a polymer material. The computational repetition of the experiment was performed by the finite element method and using the analytical Runge-Kutta method of the 4th and 5th order.