The influence of the contact between specimen and machine jaw in Brazilian disc testing method is investigated by the reflection photoelasticity technique. To this end, six brackets with various angles from 5° to 30° are employed. A polycarbonate plate cut by a water-jet cutting machine is employed as the reflection specimen. To figure out which contact is the best alternative for the flat one, stress distributions in contact with various angles under various applied forces are correlated. Results show only in contacts with 5° angle the distributions of stresses remain completely similar to the usual Brazilian disc. In the second step, polycarbonate specimens with various notch lengths from one-eighth of the disc diameter to half are tested. The distribution of stresses around notches resulting from photoelasticity fringes is similar to flat contacts only for contacts with 5° slope. It is also notable that using inclined brackets the concentration of the stress at contacts dramatically declines to around half of the flat contacts.

A FINITE ELEMENT MODEL IS DEVELOPED for discretization and analysis of the functionally graded piezoelectric material (FGPM) beam based on the Timoshenko beam theory and assuming linear constitutive relation for the corresponding piezoelectric material behavior. Results obtained using the developed finite element code are compared with the available experimental and numerical results for smart structures with and without graded properties. Static shape control of the beam is conducted using the Buildup Voltage Distribution (BVD) algorithm by implementing this method in the finite element routine. Numerical simulations have been performed to study the performance of the shape control algorithm by optimizing the distribution of the applied voltages. Furthermore, the effect of the number of iterations on the result accuracy as well as the variation of the control voltage distribution with the number of discretized regions and the volume fractions of the constituent material is studied. A fast numerical convergence with good accuracy is observed for the shape control of FGPM beams using the developed method. The proposed technique is a good candidate for the modeling, analysis, and control of smart structures with graded properties.

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.

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.

This article introduces a weight function method for fracture analysis of a circumferentially cracked functionally graded hollow cylinder subjected to thermal loads. The non-Fourier hyperbolic heat conduction model is used to determine the transient temperature distribution in the functionally graded cylinder. Solutions for transient temperature and stress distributions in the uncracked cylinder are derived by converting the governing differential equations into Fredholm integral equations in the Laplace domain. A numerical Laplace inversion technique is used to calculate the wave-like temperature and stress solutions in the time domain. These solutions are utilized to determine stresses acting on the faces of the circumferential crack in the local perturbation problem. A weight function technique is developed to compute the corresponding mode I thermal stress intensity factors. Comparisons to the results generated by finite difference and finite element methods demonstrate the high level of accuracy attained by the application of the developed procedures. Further parametric analyses are presented to illustrate the influences of dimensionless time, crack depth to thickness ratio, power law index, and thermal relaxation time upon the stress intensity factors.

A new domain-boundary element method is developed for elastodynamic analysis of functionally graded Timoshenko beams. Three governing partial differential equations of motion are derived by considering through-the-thickness variations of the physical properties. Weighted-residual forms are imposed utilizing the static fundamental solutions. These forms are then reduced to three integral equations containing domain integrals with time derivatives of unknown functions. Through domain discretization and shape function approximation, integral equations are converted to a system of ordinary differential equations in time. Forced dynamic response is revealed by solving the system of equations via Houbolt method. Comparison of dynamic responses generated for homogeneous beams to those calculated through an analytical solution and finite difference method verify the developed procedures. Further parametric analyses are performed for functionally graded Timoshenko beams under step, harmonic, and impulsive loadings. The numerical results presented illustrate the influence of material inhomogeneity on time histories of deflection and stress. Domain-boundary element method is demonstrated to be an effective technique for elastodynamic analysis of functionally graded structures.

Effects of temperature on fracture characteristics of type 304 stainless steel at cryogenic to elevated temperatures are investigated. Three point bending fracture tests according to ASTM E1820 guidelines are conducted on single edge notched bending specimens made of cold drawn flat bars in a temperature range of −195 °C to 500 °C. The test setup includes a thermal chamber, a temperature display and control unit capable of maintaining desired thermal conditions and a remote displacement recording device. Crack lengths are estimated by using load-load line displacement curves with proper calibration equations. The temperature dependency of tensile properties of the test material is also considered. Resistance curves (J-Δa) are then determined for ten values of test temperature. Finally, fracture parameters of test specimens such as critical J values and tearing modulus are extracted. Results reveal that harsh thermal conditions have significant effects on ductile fracture performance of type 304 stainless steel.

Effects of temperature dependent material properties on mixed mode fracture parameters of functionally graded materials subjected to thermal loading are investigated. A domain form of the J(k)-integral method including temperature-dependent material properties and its numerical implementation using finite element analysis is presented. Temperature and displacement fields are calculated using finite element analysis and are used to compute mixed mode stress intensity factors using the J(k)-integral. Numerical results indicate that temperature-dependency of material properties has considerable effect on the mixed-mode stress intensity factors of cracked functionally graded structures.

This article introduces a weight function method for fracture analysis of a circumferentially cracked functionally graded hollow cylinder subjected to transient thermomechanical loading. Analytical solutions for transient temperature and stress distributions in the uncracked cylinder are derived by applying finite Hankel transformation. These solutions are utilized to determine stress acting on the faces of the circumferential crack in the local perturbation problem. Thermomechanical material properties are assumed to be power functions of the radial coordinate in the derivations. Coefficients of the weight function are found using reference stress intensity factors computed through the finite element method. Domain form of the J-integral is used in the finite element calculations. Comparisons of the numerical results calculated by the proposed weight function method to those generated by finite element analysis demonstrate the high level of accuracy attained by the application of the developed procedures. Further parametric analyses are presented to illustrate the influences of dimensionless time, crack depth to thickness ratio, power law index, and convection coefficient upon transient mode I thermomechanical stress intensity factors.

In this paper, transient thermomechanical stress intensity factors for functionally graded cylinders with complete internal circumferential cracks are obtained using the weight function method. The finite difference method is used to calculate the time dependent temperature distribution and thermal stresses along the cylinder thickness. Furthermore, finite element analysis is performed to determine the weight function coefficients and to investigate the accuracy of the predicted stress intensity factors from the weight functions. Variation of the stress intensity factors with time and effects of the material gradation on the results are investigated, as well. It is shown that the proposed technique can be used to accurately predict transient thermomechanical stress intensity factors for functionally graded cylinders with arbitrary material gradation.

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

In this paper, the weight function method is used to derive mathematical expressions in terms of the Gauss hypergeometric function for the mode-I thermal stress intensity factor of functionally graded cylinders with internal circumferential cracks. To determine the weight function coefficients, a unique function is fitted to reference stress intensity factors obtained from finite element analysis. Effects of the internal convection cooling coefficient and the material power law index are investigated, as well. It is shown that the thermal stress intensity factors predicted by the developed mathematical expression are in good agreement with those directly obtained from finite element analysis. Results of this study may be used in material selection, design optimization, safety assessment against fracture, and fatigue life evaluation of functionally graded cylinders. (C) 2015 Elsevier Ltd. All rights reserved.

We introduce solution methods capable of treating static bending and free vibration problems involving thermally loaded functionally graded annular and circular micro-plates. Formulation is based on modified couple stress theory; and related governing partial differential equations and boundary conditions are derived by means of Hamilton’s principle. Displacement field is expressed in a unified way so as to produce numerical results in accordance with Kirchhoff, Mindlin, and third-order shear deformation theories. All material properties, including the length scale parameter, are assumed to be functions of the thickness coordinate. The static and dynamic problems are solved by means of differential quadrature method. Proposed procedures are verified through comparisons made to the findings available in the technical literature on thermally stressed axisymmetric plates. Detailed numerical results are presented in order to demonstrate the influences of thermal loading magnitude, and material and geometric parameters upon static deformation profiles, stresses, and natural vibration frequencies.

Vibration characteristics of functionally graded electro-rheological (FGER) sandwich beams are investigated. While a vast majority of studies have been reported about functionally graded material (FGM) or electrorheological fluids (ERF) composite beams, few, if any, works are conducted about FGER models. In order to validate the present finite element formulation of the FGER beam model, the results of the developed finite element (FE) model are compared with the results of an experimental test on a fabricated ERF composite beam. The effects of FGM volume fraction index, electric field, and thickness of the viscoelastic core are studied on the natural frequencies and modal loss factors of the FGER beam.

This article introduces new methods for static and free vibration analyses of functionally graded annular and circular micro-plates, which can take into account spatial variation of the length scale parameter. The underlying higher order continuum theory behind the proposed approaches is the modified couple stress theory. A unified way of expressing the displacement field is adopted so as to produce numerical results for three different plate theories, which are Kirchhoff plate theory (KPT), Mindlin plate theory (MPT), and third-order shear deformation theory (TSDT). Governing partial differential equations and corresponding boundary conditions are obtained following the variational approach and the Hamilton's principle. Derived systems of differential equations are solved numerically by utilizing the differential quadrature method (DQM). Comparisons to the results available in the literature demonstrate the high level of accuracy of the numerical results generated through the developed methods. Extensive analyses are presented in order to illustrate the influences of various geometric and material parameters upon static deformation profiles, stresses, and natural vibration frequencies. In particular, the length scale parameter ratio -which defines the length scale parameter variation profile-is shown to possess a profound impact on both static and dynamic behaviors of functionally graded annular and circular micro-plates.

Polymethyl methacrylate (PMMA) tension specimens with double edge cracks are considered in this study. Surface displacements of the samples are obtained using digital image correlation technique using different values of subset size and subset distance. Results of displacement components from various regions in front of the crack are utilized in a least squares fitting procedure to obtain the first stress intensity factor. This is accomplished using series representation of displacement components of a cracked structure in plane loading conditions. Effects of two adjustable parameters of digital image correlation analysis, including subset size and subset spacing, on the obtained values of stress intensity factor are investigated, while the number of terms truncated from the series representation and the radius of data extraction zone are varied. Results indicate that small subsets may not properly converge to accurate results, irrespective of the value of subset spacing. Moderate subset sizes will usually yield acceptable results while large subset sizes and subset spacing may not include sufficient data to reproduce the desirable value of stress intensity factor. It is also shown that at least three or more terms in conjunction with a sufficiently large radius of data extraction region should be considered in least squares fitting to acquire a reasonable estimate of stress intensity factor in cracked specimens.

This paper tackles amplitude-dependent dynamic characteristics of functionally graded electrorheological (FGER) sandwich beams. Nonlinear characteristics of the electrorheological fluid (ERF) layer is introduced and modeled by an exponential function. In addition, considering geometrical nonlinearity and assuming continuous variation for functionally graded material (FGM) properties through the layers thickness, the nonlinear governing equations for free vibration of the FGER beam are derived by means of the finite element method (FEM). The developed governing equations are solved using a combined modal-recursive approach and verified by related studies in the literature. Further numerical investigations are conducted for the validated FGER beam model, where the trends of dynamic characteristics of the beam vs. vibration amplitude are studied. Nonlinear fundamental frequency and modal loss factor ratio are extracted in different boundary conditions, applied electric fields, FGM volume fraction indices and thickness ratios.

The complex shear modulus of an electrorheological (ER) adaptive sandwich beam is optimally estimated to model the system for vibration control. In the composition of a three layered beam, the ER fluid layer is embedded between two constraining layers. Using finite element (FE) method, the governing equations of the composite viscoelastic beam are derived. The developed model is compared with the results found in the literature. In addition, for a fabricated ER sandwich beam, the ASTM E756 standard is employed to estimate the complex shear modulus of the viscoelastic layer in different electric fields. An optimization procedure is conducted based on particle swarm optimization (PSO). In this process, the rough estimation of complex shear modulus extracted by ASTM E756 is modified to correlate the results of the FE model and the experimental tests. The updated FE model is mapped into an appropriate form that can be used for control objectives. Finally, a semi-active sliding mode control is utilized to attenuate the vibration of the adaptive sandwich beam by tuning its electric field dependent characteristics.

Dynamic behavior of adaptive sandwich beams is studied, where middle layer is electro-rheological fluid (ERF) and constraining layers are functionally graded materials (FGM). Despite various research regarding FGM or ERF composite beams, few studies are carried out on functionally graded electro-rheological (FGER) beams. To do this, finite element (FE) formulation of FGER beams is developed, and the FE model is validated by comparative studies in the literature. Due to the fact that complex shear modulus of the viscoelastic core has significant role in dynamic behavior of the beam, a dependable procedure is proposed to estimate this characteristic to ensure the reliability of the FE model for predicting the dynamic behavior of FGER beams. In this process that combines experimental and computational analysis, firstly, the complex shear modulus is roughly estimated using the ASTM E756 method. Secondly, the results are updated by means of particle swarm optimization (PSO). The optimized FE model is then utilized to investigate the effects of FGM volume fraction index, electric field and different boundary conditions on the dynamic response of adaptive sandwich beams.