SummaryThis paper investigates the behaviour of a receding contact when a cylindrical indenter presses an unbonded layer resting on a substrate. The problem is analysed by using FEM within the scope of the linear theory of elasticity and under the assumption of plane strain. This paper presents new and original results in the analysis of influence of load intensity and indenter geometry on the contact parameters. In addition, in the investigation into material properties a reference analysis was carried out for the case of material similarity between all three bodies, and material properties were subsequently varied for each body. This class of problems shows nonlinear behaviour, with both contact pressure distributions and contact half-widths found to depend nonlinearly on the applied load. The experimental analysis was carried out by employing the digital image correlation method and the ARAMIS 4M system was used. The obtained measurement results show good agreement with the numerical results.
Numerical analysis is carried out for a frictionless receding contact problem of a perfect-fit pin and bushing in a uniaxially loaded plate. The problem is analysed using the finite element method under the assumption of plane strain and linear elasticity. The problem is investigated for the influence of external load and for different geometries. The obtained contact pressures show uncharacteristic behaviour, where higher peak values occur on contact surfaces with larger contact angles. This seemingly contradicts not only the physics of receding contact problems, but also the physical laws of contact problems in general. It is shown that the reason for this unusual behaviour is, in fact, in the physical reduction of the contact area as the radius of curvature decreases. This class of problems shows to be linearly dependent on the intensity of load as regards the contact stresses, and load has no influence on the contact angles.
This paper presents a comparison between two analytic methods for the determination of natural frequencies and mode shapes of Euler-Bernoulli beams. The subject under scrutiny is the problem of a beam supported by an arbitrary number of translational springs of varying stiffness, which is solved first by the method of Laplace transform and then by the Green’s function method. The two methods are compared on the level of algebraic equivalence of the resulting formulas and these are compared to the results obtained by FEM analysis for the case when the beam is supported with a single spring. It can be shown that both methods result in equivalent algebraic expressions, whose results are to be regarded as accurate for any given set of boundary conditions. This is also verified by means of FEM analysis, whose solutions converged to almost identical values. Hence, the two methods are found to be equally accurate for the calculation of natural frequencies and natural modes. This paper also brings a new formulation for the mode shape equation, obtained by the Laplace transform method, which to the best of the authors’ knowledge has not been reported in existing literature. Additional comments about the advantages and disadvantages of the two employed analytical methods are given from the standpoint of mathematical structure and practicality of implementation, which is also supplemented by a comment on the comparative advantages and disadvantages of FEM analysis.
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