Analytical and computational methods are used to perform stress analyses for an advanced material architecture comprising symmetric thin films bonded to a graded half-plane. The thin films are assumed to be under perfect bonding with the substrate. Related partial differential equations are derived in terms of an inhomogeneity parameter based on the theory of elasticity. To address this problem, Fourier sine and Fourier cosine transformations are employed to derive singular integral equation. Parametric analysis reveals that, compared to works on single-film model in literature, the presence of an adjacent symmetric thin film significantly affects interfacial shear stress, normal stress in the thin films, and lateral stress in the graded half-plane as a novelty of the study. Additionally, the study conducts a detailed investigation into the effects of the symmetric thin-film spacing, the graded substrate inhomogeneity parameter, and the substrate-to-film stiffness ratio under two distinct loading scenarios. Also, the finite element method is employed as a computational approach by using the general-purpose software ANSYS. Comparisons among different stress components demonstrate that the proposed analytical and numerical methods exhibit a high degree of accuracy and reliability.

To increase the fracture toughness, the two-dimensional laminated textiles can be stitched with fibers throughout their thickness. But the stitch properties effect the mechanical behavior of the composite plates. Because of this reason, in this study, translaminar toughness of carbon fiber composites stitched with different densities and angles is investigated for the first time, experimentally and numerically. In the experimental study, fracture tests are performed according to ASTM E1922 standard and critical load; crack tip opening displacements and fracture toughness values are determined. In the numerical study, the critical stress intensity factor is determined using the M-integral method and the displacement correlation method. Modeling and fracture toughness analyses are performed in ANSYS finite element package. In order to find the crack propagation directions numerically, the model prepared in ANSYS is transferred to the LS-DYNA program and progressive failure analysis is performed. Stitching the layered composites perpendicular to the plane has increased the fracture toughness by 23.5–80.6

In this study, the translaminar fracture toughness of carbon fiber laminated composites with different layer sequences was investigated experimentally and numerically for different crack directions. In the numerical study, first of all, the critical stress intensity factor was determined by using the M-integral method. Three-dimensional model and M-integral analysis were achieved in the ANSYS finite element package program. The non-local stress fracture criterion was used to in order to find failure curves of the materials. Then, in order to find the crack propagation directions numerically, the solid model was transferred to the LS-DYNA program and progressive failure analysis was performed. Fracture toughness decreased by 9.92 % with the change of crack angle from 15 degrees to 90 degrees. As the fiber angle changed from 0 degrees to 45 degrees, it decreased by 9.17 %. The biggest error between the experimental and numerical study results was found at alpha = 45 degrees, with a rate of 12.3 %.

In this study, the impact resistance of reinforced composite panels with unsupported, and U profile supported by I profile was numerically examined. For this purpose, firstly, unsupported glass fiber/epoxy composite panels were designed, and then I-profile composite supports were added to these panels. The impact strength, and damage behavior of supported, and unsupported specimens under low-velocity impact were compared numerically. In the analysis, the MAT22 material card, also known as the Chang-Chang damage model for composite material, was used in the LS-DYNA program. As a result of the analysis, maximum damage load of the unsupported specimen is determined to be approximately 294 N. It was determined that by adding an I profile to the structure, the maximum damage load increased to 543 N. It was seen that the added I profile supports increased the maximum contact force of the composite structure by approximately 85%. Fiber breakage damages were observed in both supported, and unsupported specimens. However, with the use of I profile support, the damaged area was further reduced. It has been determined that under low-velocity impact, supported specimens exhibit more rigid material behavior than unsupported specimens.

A multilayer approach is developed to solve the moving Hertzian contact problem involving a circular punch and a functionally graded multiferroic coating. The mathematical model constructed consists of arbitrary numbers of multiferroic layers and elastic interlayers, and a half -plane substrate. The formulation is based on wave equations of plane elastodynamics and Maxwell's equations. The problem is reduced to a singular integral equation by applying Galilean and Fourier transformations. The integral equation is solved numerically through an expansion -collocation technique. A convergence analysis is performed to determine the number of homogeneous multiferroic layers required to simulate the behavior of functionally graded coatings. Presented parametric analyses illustrate the influences of coating type, punch speed, kinetic friction coefficient, and coating thickness upon contact stresses, electric displacement, magnetic induction, and the required contact force. Magnetoelectricity of the system is shown to be significantly coupled with mechanical parameters such as the kinetic friction coefficient and coating thickness.

In this work, the thermal contact problem of a rigid flat punch sliding over functionally graded material (FGM) coating with a surface crack is investigated. The surface of a homogeneous isotropic substrate is ideally coated by FGM. The coefficient of friction on the contact surface is assumed to be constant, and dry Coulomb friction law is applied. The major purpose of this study is to compute the stress intensity factors at the tip of a surface crack under thermomechanical loading. In this perspective, the thermoelastic contact and the surface crack problems are modeled using finite element method. An iterative solution procedure based on finite elements is developed to solve the contact/crack problem until generated frictional heat reach the steady‐state condition. Obtained results are compared to those available in the open literature, and a good agreement is observed. Presented results involve stress intensity factors computed under various thermoelastic sliding conditions.

THIS ARTICLE INTRODUCES SOLUTION PROCEDURES for moving contacts involving functionally graded multiferroic coatings. A moving rigid punch of a flat or a triangular profile is assumed to be in contact with a multi-layer medium comprising magneto-electro-elastic coating layers, elastic interlayers, and an elastic substrate, that is modelled as a half-plane. The formulation is based on wave equations of plane elastodynamics and Maxwell's equations. Applying Fourier and Galilean transformations, a singular integral equation of the second kind is derived for each of the flat and triangular punch problems. An expansion-collocation technique utilizing Jacobi polynomials is developed to numerically solve the integral equations. Proposed procedures are verified through comparisons to the results available in the literature. Parametric analyses carried out considering functionally graded magneto-electro-elastic coatings demonstrate the effects of the property variation profile, punch speed, and coating thickness on contact stresses, electric displacement, and magnetic induction. The methods presented could be of use in analysis and design studies of multiferroic layered systems subjected to moving contacts.

This article presents analytical solution procedures for moving Hertzian contact problems involving multi-layer and functionally graded coatings. A frictional circular punch is assumed to slide down the surface of the coating with a specified velocity. Formulation is based on wave equations of plane elasticity, and reduced to a singular integral equation by Galilean and Fourier transformations. Developed procedures are verified through comparisons to the findings available in the literature. Numerical results illustrate influences of factors such as dimensionless punch speed, coefficient of kinetic friction, property variation profile, and contact length-to-thickness ratio upon the contact stresses, and the required contact force.

This paper presents a multi-layer model for moving contact problems of functionally graded coatings whose physical properties have general spatial variations. The coating is assumed to be composed of an arbitrary number of layers and perfectly bonded to an elastic substrate. Wave equations for the layers and the substrate are derived in accordance with the plane theory of elastodynamics. The equations are solved by the application of Galilean and Fourier transformations. Flat and triangular punch profiles are considered, and the formulation is reduced to a singular integral equation of the second kind in both cases. The integral equations are solved by means of Jacobi expansion and collocation techniques. Proposed procedures are verified through comparisons to the results available for a special case in the literature. Parametric analyses are carried out for functionally graded coatings possessing ceramic-rich, metal-rich, and linear profiles. The results presented demonstrate the influences of factors such as punch speed, coefficient of friction, material property variation profile, and contact-length-to-thickness ratio on contact stresses, punch stress intensity factors, and required contact force. It is shown that the multi-layer model is required to account for general property distributions in a functionally graded coating subject to moving contact.

A computational technique based on domain-boundary element method (D-BEM) is developed for elastodynamic analysis of functionally graded thick-walled cylinders and annular coatings subjected to pressure shock type of loadings. The formulation is built on the wave equation, which is derived in accordance with plane elastody-namics. Weighted residual statement for the wave equation is expressed by using the static fundamental solution as the weight function. Applying integration by parts and incorporating the boundary conditions, the problem is reduced to an integral equation. Problem domain is discretized by quadratic cells to transform the integral equation into a system of ordinary differential equations in time. Equation system is solved numerically applying Houbolt's method. Developed procedure is verified through comparisons to the analytical results available in the literature. Parametric analyses are carried out considering short-time ramp and exponential variation types of pressure shocks. Presented numerical results illustrate the influence of material property gradation on time histories and spatial distributions of displacement and stress components in FGM thick-walled cylinders and annular coatings.

A DOMAIN-BOUNDARY ELEMENT METHOD, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. In-corporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is ob-tained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro-and macro-scale beams. Numerical results illustrate elasto-dynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.

Axi-symmetric dynamic response of functionally graded circular and annular Mindlin plates with through-the-thickness variations of physical properties is investigated by a new domain-boundary element formulation. Three governing partial differential equations of motion of the inhomogeneous plate are converted to integral equations by utilizing the static fundamental solutions of the displacement components. These integral equations are then spatially discretized by dividing the entire domain into a number of cells and incorporating suitable shape functions to approximate the variation of unknown parameters across the cells. The resulting set of ordinary differential equations in time are then solved by the Houbolt method. To verify the accuracy of the developed procedure, dynamic responses generated for a homogeneous plate are compared to those calculated through an analytical solution. Different loading conditions such as step, harmonic, and impulsive loadings are considered for generation of numerical results of dynamic responses of functionally graded circular and annular plates. Convergence characteristics and effects of material inhomogeneity, and geometric parameters are extensively investigated. It has been shown that the presented method is a fast and accurate and technique in elastodynamic analysis of functionally graded plates.

This article presents analytical methods for analysis of an inclined surface crack in an orthotropic medium subjected to contact loading. Governing partial differential equations are derived in accordance with plane theory of orthotropic elasticity. Contact and crack problems are formulated separately utilizing Fourier transformation techniques. The contact problem consists of a rigid flat punch pressing upon an orthotropic half-plane, and is reduced to a singular integral equation of the second kind. The surface crack is assumed to be tilted at an arbitrary angle with respect to the normal of the half-plane surface. Three different crack configurations are considered, which are completely closed, partially-closed, and fully-open cracks. Frictional contact between the crack faces is implemented in the cases of completely closed, and partially-closed cracks. A single singular integral equation is derived for the completely closed crack, whereas each of the problems of partially- and fully-open cracks requires derivation of a set of two singular integral equations. The contact problem and each of the crack problems are solved numerically by means of the expansion-collocation technique. A flowchart is developed and implemented to detect the type of crack closure configuration under a given contact loading. The parametric analyses carried out illustrate the influences of factors such as crack inclination angle, crack face and contact surface friction coefficients, material orthotropy, and relative punch location on crack face contact stresses, degree of crack closure, and mode I and II stress intensity factors.

A domain-boundary element method for forced vibration analysis of fiber-reinforced laminated composite beams is introduced. Utilizing static fundamental solutions as weight functions in weighted residual statements, governing partial differential equations of motion are reduced to a system of four coupled integral equations. Domain discretization leads to a system of ordinary differential equations in time, which is solved by the Houbolt method. Developed procedures are verified through comparisons to analytical solution for isotropic beams. Parametric results illustrate elastodynamic responses of composite beams subjected to various loading types. It is shown that angle-ply laminates undergo higher displacements compared to cross-ply laminates.

Frictional contact mechanics analysis for a rigid moving punch of an arbitrary profile and a functionally graded coating/homogeneous substrate system is carried out. The rigid punch slides over the coating at a constant subsonic speed. Smooth variation of the shear modulus of the graded coating is defined by an exponential function and the variation of the Poisson's ratio is assumed negligible. Coulomb's friction law is adopted. Hence, tangential force is proportional to the normal applied force through the coefficient of friction. An analytical method is developed utilizing the singular integral equation approach. Governing partial differential equations are derived in accordance with the theory of elastodynamics. The mixed boundary value problem is reduced to a singular integral equation of the second kind, which is solved numerically by an expansion-collocation technique. Presented results illustrate the effects of punch speed, coefficient of friction, material inhomogeneity and coating thickness on contact stress distributions and stress intensity factors. Comparisons indicate that the difference between elastodynamic and elastostatic solutions tends to be quite larger especially at higher punch speeds. It is shown that use of the elastodynamic theory provides more realistic results in contact problems involving a moving punch. (C) 2020 Elsevier Inc. All rights reserved.

This paper presents an analytical method developed to investigate the dynamic frictional contact mechanics between a functionally graded coating and a rigid moving cylindrical punch. Governing partial differential equations of elastodynamics are solved analytically by applying Galilean and Fourier transformations. Interface continuity and boundary conditions are written and contact problem is then reduced to a singular integral equation of the second kind. The singular integral equation is solved numerically by means of an expansion-collocation method. Developed solution procedures are verified through the comparisons made to the results available in the literature. Presented parametric analyses illustrate the effects of punch speed, coefficient of friction, material inhomogeneity and geometric parameters upon the contact stresses. It is shown that, especially at higher punch speeds, the difference between contact stresses obtained through elastodynamic and elastostatic solutions is rather significant. A formulation based on the elastodynamic theory, as presented in the current study, is required to compute more realistic contact stresses. (C) 2018 Elsevier Ltd. All rights reserved.

The dynamic contact mechanics of isotropic elastic coating bonded to homogeneous substrate was examined. The coating is indented by a sliding rigid punch of a cylindrical profile. The rigid punch moves over the coating at a steady subsonic speed. To determine contact stresses, an analytical method based on the singular integral equation technique is put forward. Governing partial differential equations are derived considering general theory of elastodynamics. The influences of dimensionless punch speed, mass density ratio, shear modulus, coefficient of friction, relative coating thickness and Poisson’s ratio on contact stresses and contact related parameters were found. Comparison of the contact stresses computed by elastodynamic and elastostatic theories clearly shows that the relative difference between these two results is quite remarkable. Hence, in sliding contact problems incorporating punches with relatively high speed, elastodynamic theory is required to find more realizable stress results.

Modified couple stress based model is presented to investigate statics, dynamics and stability of functionally graded micro-plates subjected to mechanical and thermal loadings. The features of FGM micro-plate including length scale parameter of modified couple stress theory assumed to be graded across the thickness by varying volume fractions of constituents. The governing equations of motion and boundary conditions are derived by means of Hamilton’s principle. Displacement field is expressed in a unified way capable of producing results on the base of Kirchhoff, Mindlin, and third order shear deformation theories. The system of equations is solved numerically by implementing differential quadrature method. Verification studies are carried out by comparing the results of special cases to those available in the literature. Further numerical results regarding static thermal bending, natural frequencies and critical buckling loads of micro-plates undergoing uniform temperature change are provided. Presented numerical results clearly illustrate size effect at micro-scale, impact of length scale parameter variations and influence of initial thermal displacements and stresses upon mechanical behavior of functionally graded rectangular micro-plates.

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.