Search Results (152)

The dynamic contact problem describing collision of an elastic bar with a rigid obstacle, prescribed by an initial velocity, is considered in a variational formulation. The non-smooth, piecewise-linear solution is constructed analytically using partition of a 2D rectangular domain along characteristics. Challenged by the discontinuous velocity after collision, full discretization of the problem is applied that is based on a space-time finite element method. For an iterative solution of the discrete variational inequality, a primal–dual active set algorithm is used. Computer simulation of the collision problem is presented on uniform triangle grids. The active sets defined in the 2D space-time domain converge in a few iterations after re-initialization. The benchmark solution at grid points is indistinguishable from the analytical solution. The discrete energy has no dissipation, it is free of spurious oscillations, and it converges super-linearly under mesh refinement. Full article

The design of the buckling configuration for a rolling soft robot has a significant effect on its rolling performance, but a thorough analysis remains lacking for many soft robot buckling configurations because of the difficulty of analyzing the buckling problem. This work comprehensively analyzes the static buckling morphology of two nested elastic rings under gravity based on a theoretical model using the minimum potential energy principle. Two nested rings present a tank-track-like buckling morphology under gravity, which depends on the length ratio, the bending stiffness ratio, and the gravity ratio of the inner ring to the outer ring. Increases in these three ratios lead to a lower tank-track-like buckling structure with an increased ground contact length and a reduced gravity moment on the slope. The tank-track-like buckling structures predicted using the theory agree well with Finite Element Method (FEM) simulations and experimental results. This work provides design guidance on achieving the maximum slope stability and the required robot configuration by tuning the geometrical and material parameters of rolling soft robots. Full article

The closed-form solution of the problem regarding elastic contact between a transversely, uniformly loaded circular membrane and a spring-reset rigid flat circular plate has potential application value in sensor developments or bending-free shell designs, but it still needs to be further improved. In this paper, on the basis of existing studies, the plate/membrane elastic contact problem is reformulated by improving the system of differential equations governing the elastic behavior of a large deflection of a circular membrane. Specifically, the radial geometric equation used in the existing studies is improved by giving up the assumption of a small rotation angle for the membrane, and an improved closed-form solution to the plate/membrane elastic contact problem is presented. The convergence and validity of the improved closed-form solution are analyzed, and the difference between the closed-form solutions before and after improvement is graphically shown. In addition, the effect of changing some important geometric and physical parameters on the improved closed-form solution is investigated. Full article

Aiming at the engineering problems of the severe wear and limited service life of mandrels during the hole extrusion strengthening of critical aerospace components, this study proposes a surface modification strategy for mandrels based on the anti-friction mechanism of micro-textures. Based on the Lame stress equation and the Mises yield criterion, a plastic strengthening stress distribution model of the hole wall was developed. Integrating Bowden’s adhesive friction theory, a parameterized numerical model was constructed to investigate the influence of micro-texture morphology on interfacial friction and wear behavior. An elastic–plastic contact model for micro-textured mandrels during hole extrusion strengthening was established using ANSYS. The effects of key parameters such as the micro-texture depth and area ratio on the contact pressure field, friction stress distribution, and strengthening performance were quantitatively analyzed. The results show that a circular micro-texture with a depth of 50 μm and an area ratio of 20% can reduce the fluctuation and peak value of the contact pressure by 41.0% and 29.7%, respectively, and decrease the average friction stress by 8.1%. The interfacial wear resistance and the uniformity of the residual compressive stress distribution on the hole wall are significantly enhanced, providing tribological insight and surface optimization guidance for improving the anti-wear performance and extending the service life of mandrels. Full article

In this paper, a parallel plate variable capacitor-based wind pressure sensor is proposed, which uses a wind-driven peripherally fixed circular membrane as its pressure-sensitive element and a spring-reset parallel plate variable capacitor as its sensing element. The circular membrane is first driven by the wind, and then it pushes the spring-reset movable electrode plate of the parallel plate variable capacitor to move, resulting in a change in the capacitance of the capacitor. The wind pressure, i.e., the direct action force per unit area exerted by the wind on the circular membrane, is thus detected by measuring the capacitance change of the capacitor. The elastic contact problem between the circular membrane and the spring-reset movable electrode plate is analytically solved, and its closed-form solution is presented, where the usually adopted small rotation angle assumption of the membrane is given up. The analytical relationship between the input pressure and output capacitance of the capacitive wind pressure sensor proposed here is derived. The validity of the closed-form solution is proved, and how to use the closed-form solution and input/output analytical relationship for the numerical design and calibration of the capacitive wind pressure sensor proposed here is illustrated. Finally, the qualitative and quantitative effects of changing design parameters on the capacitance–pressure analytical relationship of the wind pressure measurement system are investigated comprehensively. Full article

This work aims to propose an iterative method for approximating solutions of two-dimensional weakly singular Fredholm integral Equation (2D-WSFIE) by incorporating the product integration technique, an appropriate cubature formula, and the Picard algorithm. This iterative approach is utilized to approximate the solution of the 2D-WSFIE that arises in some contact problems in linear elasticity. Under some sufficient conditions, the existence and uniqueness of the solution are established, an error bound for the approximate solution is estimated, and the order of convergence of the proposed algorithm is discussed. The effectiveness of the proposed method is illustrated through its application to some contact problems involving weakly singular kernels. Full article

The locking mechanism is crucial for the reliable connection and disconnection of electrical connectors. Aiming at the lack of theoretical support for the reliability evaluation in long-term storage, a comprehensive multi-theory modeling method is proposed to solve unlocking failure and related performance-evaluation problems. An analysis reveals that metal-crystal dislocation glide, causing pull-rod deformation and spring stress relaxation, is the main cause of unlocking failure. Based on Hertz’s contact theory, a locking-state mechanical model is established. Integrating the crystal dislocation-slip theory, an accelerated degradation trajectory model considering design parameters is developed to characterize the friction between the pull rod and steel ball and the spring’s elastic-force degradation. Finally, the model is verified using the unlocking-force accelerated test data. It offers a theoretical basis for the reliability evaluation and design of locking mechanisms in long-term storage environments. Full article

At the microscale, the three-dimensional morphological features of contact surfaces have a significant impact on the performance of electrical contacts. This paper aims to reconstruct the microscopic contact state of contact groups and to deeply study the effect of contact morphological features on electrical contact performance. To fully obtain multimodal data such as the three-dimensional micro-morphological features and chemical composition distribution of contact surfaces, this paper proposes a contact surface feature-matching method based on entropy rate superpixel seed point adaptive morphological reconstruction. This method can adaptively retain meaningful seed points while filtering out invalid seed points, effectively solving the problem of over-segmentation in traditional superpixel segmentation method. Experimental results show that the proposed method achieves a segmentation accuracy of 92% and reduces over-segmentation by 30% compared to traditional methods. Subsequently, on the basis of the moving and static contact group difference plane model and the W-M model, this paper constructs a three-dimensional surface fractal contact model with an irregular base. This model has the ability to layer simulate multi-parameter elastic and plastic and to extract fractal parameter point cloud height, which can more accurately reflect the actual contact state of the contact group. The model demonstrates a 15% improvement in contact area prediction accuracy and a 20% reduction in contact resistance estimation error compared to existing models. Finally, this paper compares and verifies the theoretical feasibility of the model, providing a new theoretical contact model for the study of the impact of three-dimensional micro-morphology on the electrical contact reliability. Full article

In this paper, we investigate the thermal friction sliding contact of a functionally graded piezoelectric material (FGPM)-coated half-plane subjected to a rigid conductive cylindrical punch. This study considers the effect of the thermal convection term in heat conduction. The thermo-electro-elastic material parameters of the coating vary exponentially along its thickness direction. Utilizing thermoelastic theory and Fourier integral transforms, the problem is formulated into Cauchy singular integral equations of the first and second kinds with surface stress, contact width, and electric displacement as the unknown variables. The numerical solutions for the contact stress, electric displacement, and temperature field of the graded coating surface are obtained using the least-squares method and iterative techniques. It can be observed that the thermo-electro-elastic contact behavior of the coating surface undergoes significant changes as the graded index varies from −0.5 to 0.5, the friction coefficient ranges from 0.1 to 0.5, and the sliding velocity changes from 0.01 m/s to 0.05 m/s. The results indicate that adjusting the graded index of the coating, the sliding speed of the punch, and the friction coefficient can improve the thermo-electro-elastic contact damage of the material’s surface. Full article

One of the challenging problems in the research and development of vibration sensors relates to the formation of Ohmic contacts for the removal of an electrical signal. In some cases, it is proposed to use arrays of carbon nanotubes (CNTs), which can serve as highly elastic electrode materials for vibration sensors. The purpose of this work is to study the effect of a current-collecting layer of CNTs grown over silicon on the properties of a lead zirconate titanate (PZT) film, which is frequently employed in mechanical vibration sensors or energy harvesters. For the experiments, a vibration sensor mock-up was created with the PZT-CNT-Ni-V-SiO₂-Si and PZT-CNT-Ni-V-Si structures where an array of vertically oriented CNTs was grown over an oxidized or high-alloyed silicon substrates by plasma chemical deposition from a gas phase. Then, a thin film of PZT was applied to the CNT layer with a high-frequency reactive plasma spraying. For comparison, the PZT film was applied to silicon without a CNT layer (PZT-Si structure). The calculated average value of the piezoelectric module is 112 pm/V for the Ni-PZT-PT-Ni-Si-SiO₂ sample, and 35 pm/V for PZT-Ni-SiO₂-Si. It can be seen that the contact realized with the help of CNT ensures more than three times the best efficiency in terms of the piezoelectric module. The value of the piezoelectric module of the vibration sensor with the PZT-CNT-Ni-V-Si structure was 186 pm/V, and the value of the residual polarization was 23.2 µC/cm², which is more than eight and three times, respectively, higher than the values of these properties for the vibration sensor with the PZT-Si structure. It is shown that the vibration sensor can operate in the frequency range of 0.1–10 kHz. Full article

This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact occurs between two elastic bodies. The elastic plate may contain a thin rigid delaminated inclusion. Neumann-type boundary conditions are considered at the external boundary of the plate. The existence of a solution to the considered problems is proven. A sufficient and necessary condition imposed onto the external forces for the solvability of the problems is found. Passages to the limit with respect to the rigidity parameter of the elastic beam are justified. For all problems, we analyze variational statements as well as differential ones. Full article

Accurate analyses of contact problems for rough surfaces are important but complicated. Some assumptions, namely that all asperities can be approximated by a hemisphere with the same radius and assuming a Gaussian distribution of the asperity heights, are convenient but may lead to less accurate results. The purpose of this work is to investigate these assumptions and analyze the conditions under which they are valid. The finite element method is used to construct spherical asperity contact models with different radii and materials. The validity of the assumptions is assessed by comparatively analyzing the results of four models in terms of contact loads, contact radii, and average contact pressures under different yield strengths. The results show that these assumptions are fully applicable under elastic deformation. For plastic cases, the lower yield strength of the two contacting bodies is the dominant factor affecting the contact results. Assuming the same lower yield strength, the ratio of the yield strengths of two spheres has an influence on contact characteristics in the range from 1.2 to 3, but a negligible influence when the ratio is greater than 3. With an equivalent yield strength and yield ratio, the plastic contact of asperities can be analyzed in detail, which be conducive to clarifying the application scope of the above assumption. The work reported in this study provides some theoretical basis for an accurate contact model of rough surfaces. Full article

Predictive assessments of the performance characteristics of metal-polymer (MP) plain bearings at the design stage are necessary and important for engineering practice. They include assessments of bearing capacity, linear wear of the bushing, and bearing life. However, no method for their calculation has been developed. The authors created a generalized analytical method for the mathematical modeling of MP sliding bearings as a classical science-based method to study the contact mechanics of conformal cylindrical bodies with consideration of polymer bushing wear. The contact problem of the theory of elasticity takes into account the significant difference in the elasticity characteristics of polymeric materials from those of steel: their Young’s modulus is 60–250 times smaller, and Poisson’s ratio is 1.27–1.37 times larger. The method was used to study MP bearings with bushings made from several common groups of tribopolymers: polyamides (PAs), polytetrafluoroethylenes (PTFEs), polyethylene terephthalates (PETs), and polyetheretherketones (PEEKs). The maximum contact pressures and durability of the dry friction bearings were calculated while taking into account the load; radial clearance; bushing thickness; the tribopolymers’ elasticity characteristics and wear resistance; the sliding friction coefficient; and the type of tribopolymer material. The Young’s modulus of a polymer material had a significant impact on the level of maximum contact pressures. Polymer fillers, depending on their type and the type of polymer, had very different effects on pressure changes (increase, no change, or decrease). An increase in pressure caused an increase in contact pressures. The durability of a mechanical bearing depended not only on the contact pressure but also on the polymer’s wear resistance, Young’s modulus, and friction coefficient. This study determined the quantitative and qualitative effects of these factors on the maximum contact pressures and bearing durability. The presented analytical method provides an effective and reasonable assessment of the specified service characteristics of sliding bearings with consideration of the multifactorial influence of the above factors. Full article

We consider an elliptic variational–hemivariational inequality $\mathcal{P}$ in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution $u\in K$. We associate inequality $\mathcal{P}$ to a sequence of elliptic variational–hemivariational inequalities $\left\{{\mathcal{P}}_n\right\}$, governed by a set of constraints $\tilde{K}\supset K$, a sequence of parameters $\left\{{\lambda }_n\right\}\subset {\mathbb{R}}_{+}$, and a function $\psi$. We prove that if, for each $n\in \mathbb{N}$, the element $u_n\in \tilde{K}$ represents a solution to Problem ${\mathcal{P}}_n$, then the sequence $\left\{u_n\right\}$ converges to u as ${\lambda }_n\to 0$. Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set $\tilde{K}$ and the function $\psi$. The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation. Full article

Frost-resistant rubbers retain their highly elastic properties over a wide temperature range. They are used in various friction units (e.g., seals), but their high friction coefficient and low wear resistance lead to the need for frequent replacement. In this paper, we propose applying thin (several hundred microns) UHMWPE coatings to formed rubber rings. The application technology depends on the required coating thickness. Friction tests of the coatings and pure UHMWPE were performed using the ball-on-disk (unidirectional sliding) scheme for various loads and velocities. In the experiments, the friction coefficients and temperatures near the contact area were determined. Friction tracks were studied using microscopy methods. The sliding contact of the ball and the two-layer material was modeled to obtain the dependences of the deformation component of friction on the sliding velocity for coatings of different thicknesses. UHMWPE is sensitive to frictional heating, so the thermal problem of determining the temperature in the contact area was also solved. It is shown that the minimum friction coefficient occurs for coatings with a thickness of 600 μm. At the same time, in the case of the 300 μm coating, the surface of the friction track is practically no different from the initial one. Thus, the studied combination of polymers provides antifrictional properties and wear resistance to the surface layer while maintaining the damping properties of rubber. Full article