• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.383-403
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• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.227-241
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• 2016

A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.

• Structural Engineering and Mechanics
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• v.37 no.3
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• pp.285-296
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• 2011

The plane crack-contact problem for an infinite elastic layer with two symmetric rectangular rigid stamps on its upper and lower surfaces is considered. The elastic layer having an internal crack parallel to its surfaces is subjected to two concentrated loads p on its upper and lower surfaces trough the rigid rectangular stamps and a pair of uniform compressive stress $p_0$ along the crack surface. It is assumed that the contact between the elastic layer and the rigid stamps is frictionless and the effect of the gravity force is neglected. The problem is reduced to a system of singular integral equations in which the derivative of the crack surface displacement and the contact pressures are unknown functions. The system of singular integral equations is solved numerically by making use of an appropriate Gauss-Chebyshev integration formula. Numerical results for stress-intensity factor, critical load factor, $\mathcal{Q}_c$, causing initial closure of the crack tip, the crack surface displacements and the contact stress distribution are presented and shown graphically for various dimensionless quantities.

• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.241-255
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• 2013

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.

• Structural Engineering and Mechanics
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• v.18 no.4
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• pp.441-459
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• 2004

This paper explores the potential use of neural networks (NNs) in the field of contact mechanics. A neural network model is developed for predicting, with sufficient approximation, the contact lengths between the elastic layer and two elastic circular punches. A backpropagation neural network of three layers is employed. First contact problem is solved according to the theory of elasticity with integral transformation technique, and then the results are used to train the neural network. The effectiveness of different neural network configurations is investigated. Effect of parameters such as load factor, elastic punch radii and flexibilities that influence the contact lengths is also explored. The results of the theoretical solution and the outputs generated from the neural network are compared. Results indicate that NN predicted the contact length with high accuracy. It is also demonstrated that NN is an excellent method that can reduce time consumed.

• Structural Engineering and Mechanics
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• v.77 no.1
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• pp.137-149
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• 2021

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.

• Structural Engineering and Mechanics
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• v.58 no.3
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• pp.423-442
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• 2016

This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel's transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1638-1649
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• 2003

A study is made on the characterization of damage tolerance by spherical indentation in hardly coated layer structure with modest elastic modulus mismatch. A hard silicon nitride is prepared for the coating material and silicon nitride with 5wt% of boron nitride composites for underlayer. Hot pressing to eliminate the effect of interface delamination during the fracture makes strong interfacial bonding. The elastic modulus mismatch between the layers is not only large enough to suppress the surface crack initiation from the coating layer but sufficiently small to prevent the initiation of radial crack from the interface. The strength degradation of the layer structure after sphere contact indentation does not significantly occur, while the degradation of silicon nitride-boron nitride composite is critical at a high load and high number of contacts.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.85-105
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• 2011

The influence of surface elasticity and surface residual stress on the elastic field of an isotropic nanoscale elastic layer of finite thickness bonded to a rigid material base is considered by employing the Gurtin-Murdoch continuum theory of elastic material surfaces. The fundamental solutions corresponding to buried vertical and horizontal line loads are obtained by using Fourier integral transform techniques. Selected numerical results are presented for the cases of a finite elastic layer and a semi-infinite elastic medium to portray the influence of surface elasticity and residual surface stress on the bulk stress field. It is found that the bulk stress field depends significantly on both surface elastic constants and residual surface stress. The consideration of out-of-plane terms of the surface stress yields significantly different solutions compared to previous studies. The solutions presented in this study can be used to examine a variety of practical problems involving nanoscale/soft material systems and to develop boundary integral equations methods for such systems.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.811-818
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• 1998

A cylindrical elastic layer in finite deformation s con-sidered. The characteristics of the linear longitudinal wave and the nonlinear shear wave are investigated; the dependence of the later on the parameter of large deformation is given.