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This paper considers the size-dependent plane frictional contact problem of a homogeneous coated half-plane indented by a rigid punch based on the couple stress elasticity. Using the Fourier integral transform technique in addition to the boundary and compatibility conditions, the mixed-boundary value problem is converted into a singular integral equation of the second kind. The integral equation is further derived and normalized for the cylindrical and flat punch case profiles. Applying the Gauss–Jacobi integration formula, the resulting singular integral equation is reduced to a system of algebraic equations. The obtained results are first validated based on those published for the case of a frictionless contact problem of a half-plane indented by rigid cylindrical and flat punches and solved based on the couple stress theory. A detailed parametric study is then performed to investigate the effect of the characteristic material length, the friction coefficient, the layer height, the shear modulus, the indentation load and Poisson's ratio on the contact and in-plane stresses. [ABSTRACT FROM AUTHOR]

On the basis of the mathematical model of the continual description of functional-gradient metal systems, taking into account their structure, a computational computer scheme has been developed that makes it possible to assess the stress-strain state of local volumes of parts taking into account their spatial inhomogeneity. With the use of modern software components of computational mechanics - FEniCS finite element analysis package and its implementation in Python, the optimal structural characteristics of wheelsets of railway locomotive tires after plasma treatment have been established. It is shown that, depending on the value of the load, hardening of products must be carried out to a depth of 4.5 mm; with a further increase in thickness, the parameters of operational strength do not change. [ABSTRACT FROM AUTHOR]

This paper considers the frictionless contact plane problem of an infinitely graded layer supported by two rigid cylindrical punches and subjected to a concentrated normal force by means of a rigid cylindrical punch. The layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. Rather than assuming vanishing displacements or stresses at the bottom of the geometry, this study examines the effect of supports on the graded layer. Using standard Fourier transform and the related boundary conditions, the plane elasticity equations are converted analytically to a system of singular integral equations in which the unknowns are the contact stresses and areas. Gauss-Chebyshev integration formulas are then employed to discretize and solve numerically the derived integral equations. Numerical results for the contact stresses and areas are provided for various dimensionless quantities including material inhomogeneity, distance between the punches, external load and upper and lower punch radii. [ABSTRACT FROM AUTHOR]

The problem of the contact interaction of a rigid cylindrical ring punch and half-space with initial (residual) stresses is considered disregarding the friction forces in the case of unequal roots of the characteristic equation. The study is performed in common form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations within the framework of the linearized theory of elasticity for arbitrary elastic potential. The numerical results are presented in the form of graphs for Treloar's potential. [ABSTRACT FROM AUTHOR]

The problem of finding mechanical and electric fields in a piezo-elastic half-space with elastic inclusion is considered. The inclusion is loaded with forces of constant intensity. The tangential contact stresses along the contact surface are determined and the behavior of the contact stresses in the neighborhood of singular points is established. By using methods of the theory of analytic functions, the problem is reduced to a singular integro-differential equation in a finite interval. Using an integral transformation a Riemann problem is obtained, and the solution is presented in its explicit form. [ABSTRACT FROM AUTHOR]

S-lay is a widely used method for offshore pipe installation. In recent years, S-lay has gradually applied to the deepwater condition. Because of the increasing pipe weight in deep S-lay, there exist severe and complex contact problems between the overbend pipe and roller supports of the stinger. In deep S-lay design, it is difficult to solve this nonlinear mechanics problem, and there remain confusion and difficulties to predict the roller contact forces and the pipe strain level in S-lay design. The present paper develops a refined finite element model with the framework of ABAQUS, which considers the complex surface contact behaviors in the overbend section. The features of the contact state of different rollers within one roller box are discussed, and the resultant support forces from each roller box are calculated and compared with the commercial design code. The overbend strain level of five S-lay cases is investigated and the pipelaying safety is checked by DNV rules. The simulation results show that the proposed model can provide more accurate and reasonable predictions on roller forces and pipe strain distribution for deepwater S-lay design. [ABSTRACT FROM AUTHOR]

An analytical solution is presented to a doubly mixed boundary value problem of an elastic layer partially resting on a rigid smooth base. A circular rigid punch is applied to the upper surface of the medium where the contact is supposed to be smooth. The case of the layer with a cylindrical hole was considered by Toshiaki and all [5]. The studied problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer formula we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. The truncation method is used for getting the system coefficients. A closed form solution is given for the displacements, stresses and the stress singularity factors. The stresses and displacements are then obtained as Bessel function series. For the numerical application we give some conclusions on the effects of the radius of the punch with the rigid base and the layer thickness on the displacements, stresses, the load and the stress singularity factors are discussed. [ABSTRACT FROM AUTHOR]

We studied the time evolution problem driven by growth for a non-Euclidean ball which at its initial state is equipped with a non-compatible distortion field. The problem is set within the framework of non-linear elasticity with large growing distortions. No bulk accretive forces are considered, and growth is only driven by the stress state. We showed that, when stress-driven growth is considered, distortions can evolve along different trajectories which share a common attracting manifold; moreover, they eventually attain a steady and compatible form, to which there corresponds a stress-free state of the ball. [ABSTRACT FROM AUTHOR]

The problem of a Timoshenko beam of finite length loaded by concentrated forces and couples and perfectly bonded to a homogeneous elastic and isotropic half plane is considered in the present work. In particular, the effects induced by shear deformation of the beam on the contact stresses arising at the interface between the beam and the underlying half plane are investigated accurately. An asymptotic analysis of the stress field at the beam ends and in the neighborhood of the loaded section of the beam allows us to characterize the singular nature of the peeling and shear stresses. The problem is formulated by imposing the strain compatibility condition between the beam and the half plane, thus leading to a system of two singular integral equations with Cauchy kernel. The unknown interfacial stresses are expanded in series of Jacobi orthogonal polynomials displaying complex singularity. This approach allows us to handle the oscillatory singularity and to reduce the integral equations to a linear algebraic system of infinite equations for the unknown coefficients of the interfacial stresses, which is solved through a method of collocation. The interfacial peeling and shear stresses and, in turn, the displacement field along the contact region have been calculated under various loading conditions applied to the beam. The internal forces and bending moments along the beam have been calculated varying the shear and flexural stiffness of the beam. The complex stress intensity factors and the strength of the stress singularities have been assessed in detail. [ABSTRACT FROM AUTHOR]

Flexoelectric materials exhibit coupling between electric polarization and mechanical strain gradient. At the nano-scale and micro-scale, these materials offer a promising potential for the development of mechanical transducers and energy harvesters. This work proposes a new imperfect interface model simulating the behavior of a thin flexoelectric layer (adhesive) of vanishing thickness, embedded between two flexoelectric media (adherents). The adhesive is assumed to be mechanically compliant and electrically lowly-conducting. The interface model is obtained by using the asymptotic analysis. The contact laws, expressed in terms of the jumps and means values of the displacements, normal derivatives of the displacements, and electric potential across the interface, represent a formal generalization of the soft elastic and piezoelectric interface conditions. A simple application, considering a one-dimensional three-layer composite micro-bar subject to electro-mechanical loads, is developed in order to analytically/numerically assess the asymptotic model. Nonlocal phenomena and end-effects, related to a flexoelectric length-scale parameter, are highlighted. The example illustrates the usefulness of the proposed approach toward the design of thin nano- and microscale devices exploiting the flexoelectric effect. [ABSTRACT FROM AUTHOR]

The paper presents the stress-strain state simulation of the compound technical structure - vulcanizer diaphragm. A set of working plates in the form of a circular plate with the thickness discretely varied in the radial direction is modeled. An algorithm to solve the contact problem is developed. The obtained calculation results are compared with the experimental ones to demonstrate their practical use. [ABSTRACT FROM AUTHOR]

Highlights: [•] A half space of multi-ferroic composite is indented by a half-infinite punch. [•] Electro-magnetic properties of the indenter are taken into consideration. [•] Potential theory is extended to the contact problem in magneto-electro-elasticity. [•] Fundamental field variables are expressed in terms of elementary functions. [•] Stress singularity in the generalized stress is discussed. [Copyright &y& Elsevier]

Abstract: Surface tension plays an important role in micro/nanosized contact problems. Based on the solution of a point force acting on a half plane with surface tension, we consider the axisymmetric contact between a rigid sphere and an elastic half space. It is found that when the contact radius is comparable with the ratio of surface tension to elastic modulus, surface tension significantly affects the pressure distribution on the contact region. Compared to the classical Hertzian contact solution, the existence of surface tension decreases the displacements on the half plane and yields continuous slopes of normal stress and displacements across the contact fringe. In addition, the present model predicts the increase of hardness as the radius of indenter decreasing. This study is helpful to characterize and measure the mechanical properties of soft materials or biomaterials through micro-indentation. [Copyright &y& Elsevier]

In this study, the frictional contact problem for a layer bonded to a homogeneous substrate is considered according to the theory of elasticity. The layer is indented by a rigid cylindrical stamp which is subjected to concentrated normal and tangential forces. The friction between the layer and the stamp is taken into account. The problem is reduced to a singular integral equation of the second kind in which the contact pressure function and the contact area are the unknown by using integral transform technique and the boundary conditions of the problem. The singular integral equation is solved numerically using both the Jacobi polynomials and the Gauss-Jacobi integration formula, considering equilibrium and consistency conditions. Numerical results for the contact pressures, the contact areas, the normal stresses, and the shear stresses are given, for both the frictional and the frictionless contacts. [ABSTRACT FROM AUTHOR]

This paper considers a computation method in failure analysis of layered composites containing pin-loaded holes. The investigation is focused on developing a reliable computation procedure to analyze initial failure load for pin-loaded holes at layered composite structures. Finite element method (FEM) is used to determine stress distribution around the fastener hole, Combining Chang-Scott-Springer characteristic curve model and Tsai-Wu initial failure criterion are used to determine joint failure. Special attention in this work is paid to pin-load distributions and its effect on the load level of failure and its location. In previous work initial failure analysis was carried out using cosine distribution between pin/lug mechanically fastened joint. Here contact finite element pin/lug model is analysed. The influence of stacking sequences of layered composites containing pin-loaded holes is also investigated. Special attention is paid to failure load and mode analyses in composites with stacking sequence [0/(±45)3/903/5. The computation results are compared with available experimental results. Good correlations between computation and experimental results are obtained. [ABSTRACT FROM AUTHOR]

Abstract: In the contact problem of a rigid flat-ended punch on an elastic half-plane, the contact stress under punch is studied. The angle distribution for the stress components in the elastic medium under punch is achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor (abbreviated as PSSF) is defined. A fundamental solution for the multiple flat punch problems on the elastic half-plane is investigated where the punches are disconnected and the forces applied on the punches are arbitrary. The singular integral equation method is suggested to obtain the fundamental solution. Further, the contact problem for rigidly connected punches on an elastic half-plane is considered. The solution for this problem can be considered as a superposition of many particular fundamental solutions. The resultant forces on punches are the undetermined unknowns in the problem, which can be evaluated by the condition of relative descent between punches. Finally, the resultant forces on punches can be determined, and the PSSFs at the corner points can be evaluated. Numerical examples are given. [Copyright &y& Elsevier]

We present the analysis of the stress-and-strain state of a contact couple formed by two isotropic semi-infinite solids one of which has a small surface groove. Based on the classical fracture criteria, namely, on the criterion of maximal principal stresses and the criterion of maximal shear stresses, we determine the regions of the most possible formation of the zones of crack initiation and plastic zones. Brittle cracking can be induced both by tensile and compressive stresses arising on the interface. For some shapes of the groove considered as an example, our analysis reveals that the fracture process starts from the boundary of contacting solids. [ABSTRACT FROM AUTHOR]

Abstract: The axisymmetrical contact problem of elasticity connected with an indentation of a rigid spherical indenter in an elastic semi-space covered by an elastic layer is considered. Stress tensor components in interior points of the non-homogeneous half-space by numerical calculation of some integrals was obtained. Detailed analysis of the maximal tensile stress distributions and Huber-von Mises reduced stress distributions produced by contact pressure is presented. The dependence between these stresses and the ratio between the layer thickness and contact area width is explored. The obtained results for stresses are compared with results obtained for half-space loaded by the Hertz pressure. [Copyright &y& Elsevier]

This paper considers the problem of equilibrium of a nonlinearly elastic spherical shell filled with a heavy fluid and resting on a smooth, absolutely rigid, flat surface. The weight of the shell is assumed to be negligible in comparison with the weight of the fluid filling it. The contact region with the supporting plane is one of the unknowns in the problem. Equilibrium equations for a membrane shell are obtained in an accurate nonlinear formulation. Stresses and strains of a shell made of a Mooney-Rivlin material are numerically investigated. The results are compared with calculation results for the case of inflation of a spherical shell ignoring the weight of the fluid filling. The effect of the fluid weight on shell strains and stresses is estimated. [ABSTRACT FROM AUTHOR]

We present the method of functions of intercontact gaps extended to axially symmetric contact problems for two half spaces one of which contains a circular surface groove. This approach is based on the construction of integral representations for the displacements and stresses in each body of the contact couple via the functions defined in an unknown (but bounded) region of the contact interface. In the analyzed case of frictionless contact of the half spaces, the integral representations contain a single unknown function, namely, the height of the gap. As examples, the analytic solutions are obtained for some shapes of the initial groove. Thus, for some shapes of the groove, the normal contact stresses exhibit peaks at the point corresponding to the edge of the initial defect. The indicated feature of the distribution of stresses is discussed. [ABSTRACT FROM AUTHOR]

We study the interaction of a rigid die with a base of any shape and the surface of an elastic half space containing cracks in the presence of friction in the contact zone. The solution of the plane contact problem of the theory of elasticity is obtained by the method of singular integral equations. The detailed analysis of the problem is performed for the case where the base of the die is parabolic and a crack is rectilinear and appears on the surface of half space. We also investigate the effects of the friction coefficient, crack length, its orientation, and location on stress intensity factors KI and KII at the crack tip and the distribution of contact stresses under the die. [ABSTRACT FROM AUTHOR]

The contact problem between a split ring and a circular housing is mechanically examined. This contact is revisited in terms of receding contact, the zones along which the ring beds over the housing are investigated, and normalizing design parameters are evidenced. The split ring is modelled in terms of a straight, purely flexural beam as well as of a curved, shear-elastic beam; for both models, analytical solutions are obtained. Various easy accessible design diagrams, useful for estimating the maximum elastic stresses within the split ring and the axial insertion force, have been prepared with the aid of these two beam models and using finite elements. The mechanical response of the split ring when its angular width is appreciably lower than π is clarified. [ABSTRACT FROM AUTHOR]

Abstract: The plane-strain, elasto-plastic, contact problem described in the title is treated for a substrate that is perfectly plastic post yield, and so simulates compression molding of some metals at elevated temperatures. The analysis uses finite elements and is verified with test problems and convergence checks. The key finding is that, in what might reasonably be viewed as a fully-plastic state, the molding pressure normalized by the yield stress is equal to a constant plus a term that increases linearly with the depth of indentation. This is in contrast to Tabor’s classical result for hardness testing that has the normalized pressure solely equal to a constant when response is fully plastic. The additional linear stiffening term found with the finite element analysis of the present configuration is confirmed experimentally. An explanation of the source of this stiffening term even with a perfectly-plastic substrate is offered. Contact stresses are also tracked as indentation proceeds. These stresses initially have high stress concentrations near the edges of the strip punches. However, these peak stresses abate rapidly with plastic flow and approach a nearly uniform distribution within the fully-plastic state. Implications for compression molding are discussed. [Copyright &y& Elsevier]

The results of theoretical and experimental studies of contact interaction in frame-and-shell structures under local loading are analyzed. Contact problems for elements of frame-and-shell structures and structures with various foundations such as supports are solved. Critical states (local instability and ultimate plasticity) of frame-and-shell structures under local loading are examined. Numerous experimental results are presented [ABSTRACT FROM AUTHOR]

In the paper we investigate the effect of friction on the stress–strain state of a hyperelastic membrane in contact with a massive solid body. We consider the axisymmetric indentation of a thin circular rubber membrane by a cylindrical indenter for different contact conditions: dry contact, liquid lubrication, and gel lubrication. We present experimental results and a mathematical model of the indentation. We use the non-linear theory of elastic membranes and the Coulomb friction model in the simulation. We describe different contact conditions with different friction coefficients. We compare the experimental and theoretical dependences between indentation force and indenter displacement. • Mechanics of indentation process of circular membrane by cylindrical indenter is presented. • Experiments dry contact and contact with lubricates are presented. • Contact problem for different friction coefficient is numerical simulated. • Experimental and simulation results are compared. [ABSTRACT FROM AUTHOR]

• Analytical solution is presented for the problem of a beam resting on couple stress elastic half-plane. • The Green's functions for a point couple applied at the half-plane surface is given. • The distributions of contact pressure and couple stress tractions are calculated analytically. • Three different types of microstructural contact conditions are considered and discussed. • The size effects due to the characteristic length of the couple stress half-plane are clearly illustrated. The plane problem of a loaded Euler-Bernoulli beam of finite length in frictionless bilateral contact with a microstructured half-plane modelled by the couple stress theory of elasticity is considered here. The study is aimed to investigate the size effects induced on the beam internal forces and moments by the contact pressure and couple stress tractions transmitted across the contact region. Use is made of the Green's functions for point force and point couple applied at the surface of the couple stress elastic half-plane. The problem is formulated by imposing compatibility of strain between the beam and the half-plane along the contact region and three alternative types of microstructural contact conditions, namely vanishing of couple stress tractions, vanishing of microrotations and compatibility between rotations of the beam cross sections and microrotations of the half-plane surface. The first two types of boundary conditions are usually assumed in the technical literature on micropolar materials, without any sound motivation, although the third boundary condition seems the most correct one. The problem is thus reduced to one or two (singular) integral equations for the unknown distributions of contact pressure and couple stress tractions, which are expanded in series of Chebyshev orthogonal polynomials displaying square-root singularity at the beam ends. By using a collocation method, the integral equations are reduced to a linear algebraic system of equations for the unknown coefficients of the series. The contact pressure and couple stress along the contact region and the shear force and bending moment along the beam are then calculated under various loading conditions applied to the beam, varying the flexural stiffness of the beam and the characteristic length of the elastic half-plane. The size effects due to the characteristic length of the half-plane and the implications of the generalized contact conditions are illustrated and discussed. [ABSTRACT FROM AUTHOR]

A normalizing loading parameter useful in summarising the mechanical response of plane pin-in-plate-like contacts is extended to axisymmetric ball-in-socket-like contacts. An example addressing a compliant layered artificial hip joint is presented, and the usefulness of the normalizing loading parameter is evidenced. [ABSTRACT FROM AUTHOR]

Abstract: The axisymmetrical contact problem of pressure of a rigid sphere into a layered half-space with periodic structure is considered. The results obtained by using the classical elasticity and the homogenized model are compared. The range of problem parameters for which, the homogenized model stands for a good description of layered composites is presented. The contact parameters in which the homogenized model gives adequate large errors are also calculated. [Copyright &y& Elsevier]

Abstract: This paper presents a study on the postbuckling responses of shear deformable laminated plates resting on a tensionless foundation of the Pasternak-type and subjected to combined axial and thermal loads. Two different postbuckling cases are considered, namely (1) the compressive postbuckling of initially heated plates and (2) the thermal postbuckling of initially compressed plates. The postbuckling analysis of laminated plates is based on the higher order shear deformation plate theory with a von Kármán-type of kinematic non-linearity. It is assumed that the foundation reacts in compression only. The thermal effects are also included and the material properties are assumed to be temperature dependent. The initial geometric imperfection of the plates is taken into account. The analysis uses a two-step perturbation technique to determine the postbuckling response of the plates. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of the plates subjected to combined axial and thermal loads when the foundation stiffness is sufficiently large. The results also confirm that the postbuckling responses are significantly influenced by temperature dependency and initial membrane stress as well as initial thermal stress. [Copyright &y& Elsevier]

Transient vibrations and dynamic stability of an infinitely long, shallow thermoelastic circular cylindrical shell compressed along its generator by forces uniformly distributed along its guide are considered. The shell is embedded into an unbounded thermoelastic medium with a cylindrical cavity and is being in an external smooth contact with the surrounding medium, whose thermal features are described by Green-Naghdy theory. At the initial instant of time the shell's internal side is suddenly subjected to normal displacement velocities and/or to the instantaneous change in the shell temperature, resulting in generation and propagation of three types of cylindrical shock waves in the contacting thermoelastic isotropic medium. The solution behind the wave fronts up to the contact boundary is constructed using a ray series. Coefficients of the ray series are found from recurrent differential equations of the ray method within the accuracy of arbitrary functions dependent on angular and axial coordinates. Arbitrary functions, in turn, are determined from the conditions of continuity for displacements and stresses on the contact boundary of the shell and the medium and the condition of heat exchange between the shell and the surrounding medium, as well as from the initial conditions. The solution constructed allows one to investigate stability of the cylindrical shell with respect to nonstationary excitations. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the dynamic problem of contact interaction of two infinite strips arranged in parallel with an initial gap. Contact interaction of strips occurs due to impulse loading. Equations of the 2-dimensional generalized theory of plates and the theory of elasticity are used to describe the dynamic behavior of strips. The contact problem is solved using the collocation method with iterative refining of the contact area sizes at each time step. [Copyright &y& Elsevier]

Abstract: The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young’s modulus is represented by a polynomial in the thickness coordinate, but the Poisson’s ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel—the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of the beam with graded core increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load are reduced considerably due to grading of the core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites. [Copyright &y& Elsevier]

The elastic maximum equivalent stress in a pin-loaded, straight- or taper-shanked, round-ended lug subject to inclined loading is investigated using the finite element and the boundary element methods, and, partly, photoelasticity. The influence of the load direction, of the ratio between the bore diameter and lug width, and of the shank taper angle are particularly addressed. In addition, the effects of the axial length of the lug trunk and, partially, of the initial clearance between the lug bore and pin are numerically examined in the presence of a loading variously inclined to the lug axis. An interpolating expression for the maximum equivalent stress as a function of the ratio between the bore diameter and lug width, taper angle, and load inclination angle is proposed. [ABSTRACT FROM AUTHOR]

Having in mind con-rods for motorbike and car engines, and spurred by the disagreements evidenced in the pertinent literature, the maximum circumferential stresses within the small end are investigated analytically, photoelastically, and numerically. The analytical models are based upon a plane assumption, and they adopt both beam and theory of elasticity idealizations. The plane photoelastic study concentrates on small ends with outer to inner radii ratios ranging from 1.2 to 1.5. A plane numerical model aimed at thoroughly mimicking the pin ovalization is developed, and a design chart of the peak hoop stress within the small end is provided for a wide spectrum of small end and pin geometries, for zero initial clearance. Such diagrams allow a prompt preliminary dimensioning of the small end to be carried out, which may be refined by effecting a three-dimensional finite element study of the specific con-rod geometry. The consequences of an initial clearance between small end bore and gudgeon pin are examined for selected geometries, and three-dimensional aspects are explored for specific con-rod shapes. [ABSTRACT FROM AUTHOR]

Postbuckling responses of laminated thin plates supported by a tensionless foundation and subjected to in-plane compressive edge loads are investigated. The postbuckling analysis presented here is based on the classical laminated plate theory, and includes the plate-foundation interaction, for which the foundation reacts in compression only. The plate is assumed to be simply supported at four edges, while the two longitudinal unloaded edges may be either movable or immovable. The initial geometric imperfection of the plate is taken into account. The analysis uses a two step perturbation technique to determine the postbuckling response of the plate. An iterative scheme is developed to obtain numerical results without any prior assumption for the shape of the contact region. The numerical examples concern the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates with unilateral constraints, from which results for the same unconstrained plates are obtained as comparators. The numerical results show that the unilateral constraint has a significant effect on the postbuckling response of laminated thin plates. [Copyright &y& Elsevier]

The elastic deflection of gear teeth is analyzed to investigate the deformation overlap. The deformation overlap, which is a numerically calculated quantity through displacement analysis at the initial contact, is defined as the piled region of a contact tooth pair due to the elastic deformation. The deformation overlap is suggested for an effective indicator to represent the whole deformation of a meshing gear pair. The elastic contact theory and finite element method are used to compute the contact force and teeth deflection. The contact problem is defined as a QP problem, and the contact forces between teeth are calculated from the transmitted torque. Then the deformation overlap is calculated with the contact forces as boundary conditions. For a spur gear pair, the calculated deformation overlap is used for the basis of the tooth tip relief, analysis of deformation characteristics for a profile shifted gear pair, and the selection of profile shift coefficient considering teeth deflection. Deformation overlap is extended to a three-dimensional problem, and implemented to a helical gear pair. [Copyright &y& Elsevier]

A technique is developed to solve contact problems for annular punches interacting with a transversely isotropic layer. The contact problem for two heated annular punches interacting with a layer is solved. The formulas for the contact stresses under the punches are derived, and the effect of the shape of the punches on the magnitude and distribution of these stresses is analyzed. [ABSTRACT FROM AUTHOR]

A method is proposed to estimate the friction coefficient between a planar surface and an elastic finger-shaped sensor by only pressing a sensor against the surface of an object. The contact condition between a planar surface and a half-cylindrical finger is considered, using finite-element analysis. The deformation of the elastic finger, contact forces, and strain distribution inside the elastic finger are calculated for various friction coefficients between the finger and the surface. Results show that the shear strain differs when the friction coefficient differs. In addition, in this paper, an elastic finger-shaped sensor made of silicone rubber is designed and constructed. In an experiment using this newly designed sensor, the friction coefficient between the finger and the planar surface is estimated using the strain inside the finger. [ABSTRACT FROM AUTHOR]

The finite element method is used to model the thermomechanical behaviour of ductile cast iron using metallic moulds. Heat conduction is assumed for the heat transfer analysis and an elasto-viscoplastic model is employed to predict the development of thermal stresses and strains. Special finite elements with coincident nodes are used to model the heat transfer and the mechanical contact at the metal–mould interface. The local heat transfer coefficient between the casting and the mould may be dependent on the air-gap formation. The latent heat evolution effect is modelled by the use of the enthalpy method. An iterative procedure is required to take into account the material and the contact non-linearity. A real casting has been modelled and numerical results are compared with the experimental measurements. [Copyright &y& Elsevier]

It is well known that fretting fatigue is affected by various factors such as contact pressure, relative slip, contact length, specimen size, loading type and so on. In this study, the reason why these factors affect fretting fatigue was investigated on the basis of the stress distribution near the contact edge. The local stress distribution near the contact edge was experimentally measured using a small multi-element stress concentration gauge. It was shown that the magnitude of the stress concentration at the contact edge varied significantly depending on these factors. It was found that the S–N curve was expressed uniquely on the basis of the local stress amplitude at the contact edge. [ABSTRACT FROM AUTHOR]

This paper deals with the stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsion. The stress distributions in the adhesive layer of bonded shrink fitted joints are analyzed by the axisymmetric theory of elasticity when an external torsion is applied to the upper end of the shaft. The effects of the outer diameter and the stiffness of rings on the interface stress distributions are clarified by numerical calculations. Using the interface stress distributions, the joint strength is predicted. In addition, the joint strength was measured experimentally. It is seen that rupture of the adhesive layer is initiated from the upper edge of the interface when torsion is applied to the upper end of the shaft. The numerical results are in fairly good agreement with the experimental results. It was found that the joint strength of bonded shrink fitted joints is greater than that of shrink fitted joints. [ABSTRACT FROM AUTHOR]

Single-lap band adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a four-body contact problem using a two-dimensional theory of elasticity (plane strain state). In the analysis, the upper and lower adherends and the adhesive which are bonded in two regions are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends, the ratio of the adherend thicknesses, and the ratio of the band length to the half lap length on the stress distributions at the interfaces are examined. A method for estimating the joint strength is proposed using the interface stress and strain obtained by the analysis. An elasto-plastic finite element analysis (EP-FEA) was conducted for predicting the joint strength more exactly. Experiments to measure strains and the joint strength were also carried out. The results show that the strength of a single-lap band adhesive joint is almost the same as that of a single-lap adhesive joint in which the two adherends are completely bonded at the interfaces. Thus, the single-lap band adhesive joints are useful in the design of single-lap joints. [ABSTRACT FROM AUTHOR]

The determination of stresses induced in mechanical contacts arising in such components as gears, indenters and roller bearings is an important factor in the design procedure. In most cases the geometry of the contact problem is too complex to allow a full analytical solution. Some form of numerical method or semi-analytical method must then be employed. The influence function method has so far been useful but limited due to the nature of the influence functions employed. Piecewise constant elements have been used where piecewise linear elements would give a more sophisticated solution. In this paper the influence functions for a hexagonal-based pyramid of pressure (the shape needed for a piecewise linear function) are derived and some of their asymptotic properties considered. [ABSTRACT FROM AUTHOR]

We consider the contact problem for a particular class of compressible hyperelastic materials of harmonic type undergoing finite plane deformations. Using complex variable techniques, we derive subsidiary results concerning a half-plane problem corresponding to this class of materials. Using these results, we solve the contact problem for a harmonic material in the case of a uniform load acting on a finite area. Finally, we show how we can then deduce the corresponding results for the case of a point load. [ABSTRACT FROM AUTHOR]