Showing papers in "Acta Mechanica in 2014"
TL;DR: In this paper, a coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) analysis on the impacting behavior of a granular flow falling from an inclined slope into a water reservoir is presented.
Abstract: Massive debris flows or rock avalanches falling into a water reservoir may cause devastating hazards such as overtopping or dam breakage. This paper presents a coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) analysis on the impacting behaviour of a granular flow falling from an inclined slope into a water reservoir. The coupling between CFD and DEM considers such important fluid–particle interaction forces as the buoyancy force, the drag force and the virtual mass force. It is found that the presence of water in the reservoir can generally help to reduce direct impact of granular flow on the check dam behind the reservoir, minimizes the intense collisions and bouncing among particles and helps form a more homogeneous final deposited heap as compared to the dry case. While the interparticle/particle–wall frictions and collisions dominate the energy dissipation in the dry granular flow, the majority of kinetic energy of the granular system in the wet case is first transferred to the water body, which leaves the granular flow itself to become a contact-shearing dominant one and causes impulse wave travelling between the check dam and the slope surface for a rather sustained period before settling down. A power law distribution is found for the velocity profile of the granular flow travelling on both the slope and the reservoir ground surfaces, and it may change temporarily to a linear distribution at the transition point of the slope toe where the Savage number depicts a peak. The consideration of rolling friction among particles may homogeneously reduce the travelling velocity of the granular flow and alleviate the overall impact on the check dam. The impact on the check dam depends on both the initial debris releasing height and the reservoir water level. Medium water levels in the reservoir have been found to be generally safer when the initial debris height is relatively high.
126 citations
TL;DR: The suitability of the 4-parameter Weibull equation to describe size effects on the crushing strength reported in the literature is discussed in this article, where the impact of size effects obtained from the experiments is analyzed and discussed in terms of the factor of safety of rockfill slope stability.
Abstract: Testing the mechanical response of coarse granular materials requires very large and expensive laboratory equipments. During the 1960s, pioneering experimental programs were carried out on several rockfill dam materials, and those results are still a reference for engineers and researchers. However, only few experimental works have been reported to this day, and due to the scarcity of empirical data, the role of the size effect caused by grain crushing is not well known. To improve understanding of this rarely studied issue and the influence of individual particle strength, this paper analyzes the size effect on rock aggregate crushing strength and its connection with the shear envelope of rockfills. The suitability of the 4-parameter Weibull equation to describe size effects on the crushing strength reported in the literature is discussed. Furthermore, a Weibull statistical analysis was carried out for a wide number of experimental results on rock aggregates, where it has been observed that strength decreases with particle size. In parallel, the results of large triaxial tests on homothetic scaled rockfill samples of 250 and 1,000 mm in diameter reveal that the coarser the material, the higher the amount of grain breakage and the lower the shear strength. The impact of size effects obtained from the experiments is analyzed and discussed in terms of the factor of safety of rockfill slope stability. Furthermore, the results are compared with the only existing theoretical method that links the rock aggregate with the strength of the granular assembly. Good agreement between the empirical results and this theoretical method has been confirmed.
121 citations
TL;DR: A comprehensive review of the currently most widely employed mechanical methods for coating adhesion assessment and analysis is presented in this paper, with emphasis on the principles, merits, limitations, typical applications, and recent improvements of each method.
Abstract: Coatings have been applied widely in aerospace, biomedical, electronic, and many other industries. The performance of a coating is dictated by the adhesion between the coating and the underlying substrate. Thus, the evaluation of coating adhesion is critical for the assessment of the quality of a coating and its fitness for service. However, this evaluation is not straightforward, and various mechanical and non-mechanical evaluation methods have been developed. This paper presents a comprehensive review of the currently most widely employed mechanical methods. The interface fracture mechanics that provides the fundamental knowledge for conducting adhesion assessment and analysis is briefly introduced. Detailed discussions are presented on various sandwich specimen-based and bimaterial specimen-based testing methods, with emphasis on the principles, merits, limitations, typical applications, and recent improvements of each method.
106 citations
TL;DR: In this article, a nonlinear relationship between the strain and the stress in the range of strain was shown, which led to a dilemma concerning the modeling of the response, as the classical nonlinear Cauchy elastic model would collapse to the linearized elastic model in this range.
Abstract: The classical linearized approximation to describe the elastic response of solids is the most widely used model in solid mechanics. This approximate model is arrived at by assuming that the norm of the displacement gradient is sufficiently small so that one can neglect the square of the norm in terms of the norm. Recent experimental results on Titanium and Gum metal alloys, among other alloys, indicate with unmistakable clarity a nonlinear relationship between the strain and the stress in the range of strain wherein one would have to use the classical linearized theory of elasticity, namely wherein the square of the norm of the strain can be ignored with regard to the value of the strain, leading to a dilemma concerning the modeling of the response, as the classical nonlinear Cauchy elastic model would collapse to the linearized elastic model in this range. A novel and important generalization of the theory of elastic materials has been suggested by Rajagopal in Appl Math 48: 279–319, 2003 and Zeit Angew Math Phys 58: 309–317, 2007 that allows for an approximation wherein the linearized strain can be a nonlinear function of the stress. In this paper, we show how this new theory can be used to describe the new experiments on Titanium and Gum metal alloys and also clarify several issues concerning the domain of application of the classical linearized theory.
86 citations
TL;DR: In this article, an integral equivalence procedure is used to derive micropolar, second-gradient and classical models of masonry, and the differences in the material responses of the various continua are identified referring to their internal work formulas.
Abstract: The description of the mechanical behaviour of brick/block masonry through equivalent continua is presented here as a paradigmatic example of the problem of gross modelling of discontinuous and heterogeneous materials as continua with microstructure. The approaches reported in the literature differ for the way identification of the continuum is carried out or the nature of the continuum itself. In this paper, continuous models equivalent to rigid particle systems with free or constrained rotations are derived within the general framework of the principle of virtual work. In particular, an integral equivalence procedure is used to derive micropolar, second gradient and classical models. The non-classical models have in the field equations non-standard kinematic and static descriptors accounting for the presence of the material internal structure. The differences in the material responses of the various continua are identified referring to their internal work formulas. For the reference material, it is shown that, unlike the Cauchy continuum, both micropolar and second gradient models are effective in the presence of load and geometrical singularities, which involve significant scale effects on the material response. On the other hand, the second gradient model, as well as the classical model, disregards the role of relative rotation between the local rigid rotation (macrorotation) and the microrotation, which is related to the presence of non-symmetric strains. This circumstance, significant in strongly anisotropic systems, allow us to point out the advantages of the micropolar modelling especially for orthotropic masonry assemblies made of elements of any size. These statements are discussed by means of selected numerical examples of masonry panels differing in size, shape and arrangement, under shear loading conditions.
84 citations
TL;DR: In this paper, the free vibration of functionally graded material (FGM) nanobeams is investigated by considering surface effects including surface elasticity, surface stress, and surface density as well as the piezoelectric field using nonlocal elasticity theory.
Abstract: Free vibration of functionally graded material (FGM) nanobeams is investigated by considering surface effects including surface elasticity, surface stress, and surface density as well as the piezoelectric field using nonlocal elasticity theory. The balance conditions between the nanobeam bulk and its surfaces are satisfied assuming a cubic variation for the normal stress, \({\sigma_{zz}}\) , through the piezoelectric FG nanobeam thickness. Accordingly, the surface density is introduced into the governing equation of the free vibration of nanobeams. The results are obtained for various gradient indices, voltage values of the piezoelectric field, nanobeam lengths, and mode numbers. It is shown that making changes to voltage values and modifying mechanical properties of piezoelectric FGM nanobeams are two main approaches to achieve desired natural frequencies.
79 citations
TL;DR: In this paper, a new hybrid reliability analysis technique based on the convex modeling theory is developed for structures with multi-source uncertainties, which may contain randomness, fuzziness, and non-probabilistic boundedness.
Abstract: A new hybrid reliability analysis technique based on the convex modeling theory is developed for structures with multi-source uncertainties, which may contain randomness, fuzziness, and non-probabilistic boundedness. By solving the convex modeling reliability problem and further analyzing the correlation within uncertainties, the structural hybrid reliability is obtained. Considering various cases of uncertainties of the structure, four hybrid models including the convex with random, convex with fuzzy random, convex with interval, and convex with other three are built, respectively. The present hybrid models are compared with the conventional probabilistic and the non-probabilistic models by two typical numerical examples. The results demonstrate the accuracy and effectiveness of the proposed hybrid reliability analysis method.
77 citations
TL;DR: Armstrong et al. as mentioned in this paper applied dislocation and continuum mechanics models of the H-P relationship to predict order-of-magnitude increases in strength properties of nanopolycrystalline materials, including description of the strain rate sensitivity dependence on average grain diameter.
Abstract: Hall and Petch had established in the early 1950s a linear inverse square root of grain diameter dependence for yielding and cleavage of polycrystalline iron and steel materials, with ordinate intercept stress, σ
0, and slope value, k. Petch and colleagues extended the relationship in 1962 to the full stress–strain behavior of a diverse number of metals and alloys. Connection with other mechanical properties such as the hardness, fatigue and strain rate sensitivity properties was demonstrated in 1970. In 1983, Weng incorporated the dependence into a micromechanical analysis of material strength by building onto earlier Taylor-initiated work on multiply-coupled grain deformations. More recently, Armstrong, Weng and colleagues have applied dislocation and continuum mechanics models of the H–P relationship to predict order-of-magnitude increases in strength properties of nanopolycrystalline materials, especially including description of the strain rate sensitivity dependence on average grain diameter. These topics are assessed from a dislocation mechanics viewpoint in the present report that provides H–P connection with the Taylor dislocation density-based theory of strength properties, in σ
0 ɛ
, and with the Griffith brittle fracture theory by way of pointing to the H–P slope value, k
ɛ
, being a microstructural stress intensity analogous to the fracture mechanics parameter, K.
75 citations
TL;DR: In this paper, a non-probabilistic structural reliability analysis based on the multidimensional parallelepiped convex model is proposed, in which marginal intervals are used to express scattering levels for the parameters, and relevant angles are used for expressing the correlations between uncertain variables.
Abstract: Compared with a probability model, a non-probabilistic convex model only requires a small number of experimental samples to discern the uncertainty parameter bounds instead of the exact probability distribution. Therefore, it can be used for uncertainty analysis of many complex structures lacking experimental samples. Based on the multidimensional parallelepiped convex model, we propose a new method for non-probabilistic structural reliability analysis in which marginal intervals are used to express scattering levels for the parameters, and relevant angles are used to express the correlations between uncertain variables. Using an affine coordinate transformation, the multidimensional parallelepiped uncertainty domain and the limit-state function are transformed to a standard parameter space, and a non-probabilistic reliability index is used to measure the structural reliability. Finally, the method proposed herein was applied to several numerical examples.
72 citations
TL;DR: In this paper, a micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response.
Abstract: A micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response. Using a fiber–matrix concentric cylinder model as the basic repeat unit to represent the composite, micromechanics is used to relate the applied composite strains to the fiber and matrix strains by a six by six transformation matrix. The resolved spatial variations of the matrix fields are found to be in good agreement with corresponding finite element analysis results. The evolution of the composite nonlinear response is assumed to be governed by two scalar, strain-based variables that are related to the extreme value of an appropriately defined matrix equivalent strain, and the matrix secant moduli are used to compute the composite secant moduli for nonlinear analysis. The results from the micromechanics model are compared well with a full finite element analysis. The predictive capability of the proposed model is illustrated by two distinct fiber-reinforced material systems, carbon and glass, for the fiber volume fraction varying from 50 to 70 %. Since fully analytical solutions are utilized for the micromechanical analysis, the proposed method offers a distinct computational advantage in a multiscale analysis and is therefore suitable for large-scale progressive damage and failure analyses of composite material structures.
71 citations
TL;DR: In this paper, a quasi-3D hyperbolic shear deformation theory for functionally graded plates is developed, which accounts for both deformation and thickness-stretching effects by a Hyperbolic variation of all displacements across the thickness, and satisfies the stress free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor.
Abstract: A quasi-3D hyperbolic shear deformation theory for functionally graded plates is developed. The theory accounts for both shear deformation and thickness-stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The benefit of the present theory is that it contains a smaller number of unknowns and governing equations than the existing quasi-3D theories, but its solutions compare well with 3D and quasi-3D solutions. Equations of motion are derived from the Hamilton principle. Analytical solutions for bending and free vibration problems are obtained for simply supported plates. Numerical examples are presented to verify the accuracy of the present theory.
TL;DR: In this paper, a size-dependent, explicit formulation for coupled thermoelasticity addressing a Timoshenko microbeam is derived, which combines modified couple stresses and non-Fourier heat conduction to capture size effects in the microscale.
Abstract: A size-dependent, explicit formulation for coupled thermoelasticity addressing a Timoshenko microbeam is derived in this study. This novel model combines modified couple stresses and non-Fourier heat conduction to capture size effects in the microscale. To this purpose, a length-scale parameter as square root of the ratio of curvature modulus to shear modulus and a thermal relaxation time as the phase lag of heat flux vector are considered for predicting the thermomechanical behavior in a microscale device accurately. Governing equations and boundary conditions of motion are obtained simultaneously through variational formulation based on Hamilton’s principle. As for case study, the model is utilized for simply supported microbeams subjected to a constant impulsive force per unit length. A comparison of the results with those obtained by the classical elasticity and Fourier heat conduction theories is carried out. Findings indicate that simultaneous considering the length-scale parameter and thermal relaxation time has strong influence on the thermoelastic behavior of microbeams. In dynamic thermoelastic analysis of the microbeam, while the non-Fourier heat conduction model is employed, the modified couple stress theory predicts larger deflection compared with the classical theory.
TL;DR: In this paper, size and shape optimization of truss structures is performed using an efficient hybrid method that uses a particle swarm strategy and ray optimizer, and utilizes additional harmony search for a better exploitation.
Abstract: In this paper, size and shape optimization of truss structures is performed using an efficient hybrid method. This algorithm uses a particle swarm strategy and ray optimizer, and utilizes additional harmony search for a better exploitation. Here, multiple frequency constraints are considered making the optimization a highly nonlinear problem. Some basic benchmark problems are solved by this hybrid method, and the numerical results demonstrate the efficiency and robustness of this method compared to other mathematical and heuristic algorithms.
TL;DR: In this article, the authors show that the amount of solid grain in the fluid reservoir plays a significant role in controlling the overall dynamics of the submarine debris flow and the tsunami, and they investigate the complex interactions between the internal submarine debris wave and the surface tsunami wave.
Abstract: The general two-phase debris flow model proposed by Pudasaini (J. Geophys. Res. 117:F03010, 2012, doi:
10.1029/2011JF002186
) is employed to simulate subaerial and submarine two-phase debris flows and the mechanics of complex wave generation and interactions between the solid and the fluid phases. This includes the fluid waves or the tsunami generated by the debris impact at reservoirs, lakes, and oceans. The analysis describes the generation, amplification, and propagation of super tsunami waves and run-ups along coastlines, debris slide and deposition at the bottom floor, and debris shock waves. Accurate and advance knowledge of the arrival of tsunami waves in the coastal regions is very important for the design of early warning strategies. Here, we show that the amount of solid grain in the fluid reservoir plays a significant role in controlling the overall dynamics of the submarine debris flow and the tsunami. For very small solid particle concentrations in the reservoir, the submarine debris flow moves significantly faster than the surface tsunami wave. As the solid volume fraction in the reservoir increases, the submarine debris speed slows down. For relatively large solid volume fractions in the reservoir, the speed of the submarine debris becomes slower than the surface tsunami wave. This information can be useful for early warning strategies in the coastal regions. The fast or slow speed of the submarine wave can be attributed to several dynamical aspects of the model including the generalized drag, basal traction, pressure gradient, virtual mass force, the non-Newtonian viscous stress, and the strong phase interaction between the solid and the fluid as they enhance or diminish the motion of the solid phase. Solid particle concentration in the reservoir dam also substantially influences the interaction between the submarine debris flow and the frontal wall of the dam, and the interaction between the tsunami and the submarine debris wave. The tsunami wave impact generates a largely amplified fluid level at the dam wall. Submarine debris shock waves are observed for small solid volume fractions in the reservoir. Another important aspect of the simulation is to investigate the complex interactions between the internal submarine debris wave and the surface tsunami wave. Three complex waves occur simultaneously: the subaerial debris flow in the upstream region, submarine debris flow in the reservoir basin, and a super tsunami wave on the surface of the reservoir. This helps to develop insight into the basic features of the complex nonlinear solid and fluid waves and their interactions.
TL;DR: In this paper, the nonlinear oscillations and the steady-state responses of a thin-walled compressor blade of a gas turbine engines with varying rotating speed under high-temperature supersonic gas flow were investigated.
Abstract: This paper focuses on the nonlinear oscillations and the steady-state responses of a thin-walled compressor blade of gas turbine engines with varying rotating speed under high-temperature supersonic gas flow. The rotating compressor blade is modeled as a pre-twisted, presetting, thin-walled rotating cantilever beam. The model involves the geometric nonlinearity, the centrifugal force, the aerodynamic load and the perturbed angular speed due to periodically varying air velocity. Using Hamilton’s principle, the nonlinear partial differential governing equation of motion is derived for the pre-twisted, presetting, thin-walled rotating beam. The Galerkin’s approach is utilized to discretize the partial differential governing equation of motion to a two-degree-of-freedom nonlinear system. The method of multiple scales is applied to obtain the four-dimensional nonlinear averaged equation for the resonant case of 2:1 internal resonance and primary resonance. Numerical simulations are presented to investigate nonlinear oscillations and the steady-state responses of the rotating blade under combined parametric and forcing excitations. The results of numerical simulation, which include the phase portrait, waveform and power spectrum, illustrate that there exist both periodic and chaotic motions of the rotating blade. In addition, the frequency response curves are also presented. Based on these curves, we give a detailed discussion on the contributions of some factors, including the nonlinearity, damping and rotating speed, to the steady-state nonlinear responses of the rotating blade.
TL;DR: In this article, the effect of cross-linkers on density, glass transition temperature, elastic constants, and strength of a family of thermoset polymers was investigated. But the authors focused on the effect on the properties of crosslinkers.
Abstract: Molecular dynamics simulations are conducted to predict thermal and mechanical properties of a family of thermoset polymers. We focus on the effect of cross-linkers on density, glass transition temperature, elastic constants, and strength. The polymers are composed of the epoxy resin DGEBA (EPON825) and a series of cross-linkers with different number of active sites and rigidity 33DDS, 44DDS, APB133, TREN, and TAPA. Our simulations quantify effects of cross-linkers on thermal and mechanical properties.
TL;DR: In this article, the elastic response of dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy.
Abstract: Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.
TL;DR: In this paper, Weng et al. introduced weak non-locality in the constitutive equations through Laplacian terms and corresponding deterministic internal lengths (ILs) characterizing the dominant deformation mechanisms.
Abstract: This is a modest contribution dedicated to the work and virtue of George Weng, a prominent figure in material mechanics and a dear intellectual friend. The paper starts with the basics of gradient theory as applied to elasticity, plasticity and dislocation dynamics by introducing weak non-locality in the constitutive equations through Laplacian terms and corresponding deterministic internal lengths (ILs) characterizing the dominant deformation mechanisms. It then considers the interaction of such deterministic ILs with surface effects associated with internal or external surfaces, as well as stochastic effects associated with pre-existing or deformation-induced random microstructures. Experimentally observed stress drops and strain bursts are interpreted through combined gradient-stochastic models. Statistical features of corresponding deformation processes that cannot be fitted with Boltzmann–Gibbs–Shannon entropy statistics are interpreted by Tsallis q-entropy statistics. Some benchmark novel experiments for the direct determination of ILs for plasticity (by testing bulk specimens with gradient grain size) and dislocation dynamics (by testing thin films in TEM with gradient dislocation density) are proposed.
TL;DR: In this article, the vibration of functionally graded (FG) nanobeams subjected to a sinusoidal pulse-heating source is investigated, where the material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution in terms of the volume fractions of the metal and ceramic constituents.
Abstract: The vibration of functionally graded (FG) nanobeams subjected to a sinusoidal pulse-heating source is investigated. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is pure ceramic, whereas the lower surface is pure metal. The generalized nonlocal thermoelasticity model based on Lord and Shulman’s theory is used to solve this problem. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and temperature. The inverse Laplace transforms are computed numerically using Fourier expansion techniques. A comparison between the obtained results from the nonlocal theory and those from the local theory of coupled thermoelasticity is presented. The effect of the nonlocal parameter, the pulse width of the sinusoidal pulse, is studied on the lateral vibration, the temperature and the displacement of the nanobeam. Additional results across the thickness of the nanobeam are presented graphically.
TL;DR: In this paper, a general and efficient stress analysis strategy for hollow composite cylindrical structures consisting of multiple layers of different anisotropic materials subjected to different loads is presented, and the results are compared with numerical solutions.
Abstract: This paper presents a general and efficient stress analysis strategy for hollow composite cylindrical structures consisting of multiple layers of different anisotropic materials subjected to different loads. Cylindrical material anisotropy and various loading conditions are considered in the stress analysis. The general stress solutions for homogenized hollow anisotropic cylinders subjected to pressure, axial force, torsion, shear and bending are presented with explicit formulations under typical force and displacement boundary conditions. The stresses and strains in a layer of the composite cylindrical structures are obtained from the solutions of homogenized hollow cylinders with effective material properties and discontinuous layer material properties. Effective axial, torsional, bending and coupling stiffness coefficients taking into account material anisotropy are also determined from the strain solutions for the hollow composite cylindrical structures. Examples show that the material anisotropy may have significant effects on the effective stiffness coefficients in some cases. The stress analysis method is demonstrated with an example of stress analysis of a 22-layer composite riser, and the results are compared with numerical solutions. This method is efficient for stress analysis of thin-walled or moderately thick-walled hollow composite cylindrical structures with various multiple layers of different materials or arbitrary fiber angles because no explicit interfacial continuity parameters are required. It provides an efficient and easy-to-use analysis tool for assessing hollow composite cylindrical structures in engineering applications.
TL;DR: In this paper, the free vibration, mechanical buckling and thermal buckling analyses of multi-layered graphene sheets (MLGSs) are investigated, where Eringen's nonlocal elasticity equations are incorporated in new two-variable plate theories accounting for small-scale effects.
Abstract: In the present study, the free vibration, mechanical buckling and thermal buckling analyses of multi-layered graphene sheets (MLGSs) are investigated. Eringen’s nonlocal elasticity equations are incorporated in new two-variable plate theories accounting for small-scale effects. The MLGSs are taken to be perfectly bonded to the surrounding medium. The governing differential equations of this model are solved analytically under various boundary conditions and taking into account the effect of van der Waals forces between adjacent layers. New functions for the displacements are proposed here to satisfy the different boundary conditions. Comparison of the results with those being in the open literature is made. This comparison illustrates that the present scheme yields very accurate results. Furthermore, the influences of nonlocal coefficient, moduli of the surrounding elastic medium and aspect ratio on the frequencies and buckling of the embedded MLGSs are examined.
TL;DR: In this article, the buckling analysis of a solid circular plate made of porous material bounded with piezoelectric sensor-actuator patches is presented, and the results are verified with the known results in the literature.
Abstract: This study presents the buckling analysis of a solid circular plate made of porous material bounded with piezoelectric sensor–actuator patches. The porous material properties vary through the thickness direction of the plate following a given function. The general mechanical nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The buckling load is derived for solid circular plates under uniform radial compressive loading for the clamped edge condition. The effects of piezoelectric layers on the buckling load of the plate, piezoelectric layer-to-porous plate thickness ratio, feedback gain, and variation of porosity are investigated. The results are verified with the known results in the literature.
TL;DR: In this article, the effect of the graded interlayer on the band gap of a laminated piezoelectric/piezomagnetic phononic crystal with graded inter layer is studied.
Abstract: The band gaps of a laminated piezoelectric/piezomagnetic phononic crystal with graded interlayer are studied in this paper. First, the transfer matrix method and the Bloch theorem are used to derive the dispersion equation. Next, the graded interlayer with different gradient profiles between the piezoelectric and the piezomagnetic materials is considered. The graded interlayer is modeled as a system of homogenous sublayers with both piezoelectric and piezomagnetic effects simultaneously. The effect of the graded interlayer on the band gap is introduced by inserting an additional interlayer transfer matrix in the calculation of the total transfer matrix. Finally, the dispersion equation is solved numerically, and the dispersive curves are shown in the Brillouin zone. The band gaps of the phononic crystal with graded interlayer are compared with that without graded interlayer. The influences of the graded interlayer with different gradient profiles on the band gap of a laminated piezoelectric/piezomagnetic phononic crystal are discussed based on the numerical results.
TL;DR: In this paper, the authors applied the graded finite element method (GFEM) to solve the equations of two-dimensional functionally graded rotating annular and solid disks with variable thickness.
Abstract: Elasticity solutions of two-dimensional functionally graded rotating annular and solid disks with variable thickness are presented. Material properties vary through both the radial and axial directions contin- uously. Axisymmetric conditions are assumed for the two-dimensional functionally graded disk. The graded finite element method (GFEM) has been applied to solve the equations. The distributions of displacements and stresses in radial and axial directions for four different thickness profiles (constant, linear, concave and convex) and various power law exponents have been investigated. The achieved results show that by the use of functionally graded materials and variable thicknesses, the stresses are reduced, so a higher capability of angular velocity can be obtained. Also, using two-dimensional functionally graded materials leads to a more flexible design in comparison with conventional one-dimensional functionally graded materials. The GFEM solution of a functionally graded thin rotating annular disk has been compared with the published literature and it shows good agreement.
TL;DR: In this paper, an exact procedure for the reconstruction of multiple concentrated damages on a straight beam is proposed, where the concentrated damages are modelled as Dirac's delta distributions capturing the effect of concentrated stiffness reduction.
Abstract: In this paper, an exact procedure for the reconstruction of multiple concentrated damages on a straight beam is proposed. The concentrated damages are modelled as Dirac’s delta distributions capturing the effect of concentrated stiffness reduction. The presented procedure requires the knowledge of vibration mode shape displacements together with the relevant natural frequency, for the reconstruction of each damage position and intensity. The exact solution of the inverse problem at hand has been pursued by exploiting the analytical structure of the explicit closed form expressions provided for the vibration mode shapes of beams in the presence of an arbitrary number of cracks. The proposed procedure is first presented under the hypothesis that the displacements of a vibration mode shape are known at the cracked cross-sections. In this case, explicit closed form expressions of the crack severities are formulated. A further simple reconstruction approach allows the evaluation of the exact positions and intensity of the concentrated damages, if displacements of two vibration mode shapes are known at a single cross-section between two consecutive cracks. The proposed reconstruction procedure is applied for the identification of multiple cracks on a free–free beam where measurements have been simulated by means of a finite element analysis.
TL;DR: In this article, a unified analytical approach is applied for investigating the vibrational behavior of grid-stiffened composite cylindrical shells considering the flexural behavior of the ribs.
Abstract: A unified analytical approach is applied for investigating the vibrational behavior of grid-stiffened composite cylindrical shells considering the flexural behavior of the ribs. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of the shell in order to obtain the equivalent stiffness parameters of the whole panel. The stiffeners are modeled as a beam and considered to support shear loads and bending moments in addition to the axial loads. Therefore, the corresponding stiffness terms are taken into consideration while obtaining the stiffness matrices due to the stiffeners. Theoretical formulations are based on first-order shear deformation shell theory, which includes the effects of transverse shear deformation and rotary inertia. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes’ transformation. In order to validate the obtained results, a 3-D finite element model is also built using ABAQUS CAE software. Results obtained from two types of analyses are compared with each other, and good agreement has been achieved. Furthermore, the influence of variations in the shell thickness and changes of the boundary conditions on the shell frequencies is studied. The results obtained are novel and can be used as a benchmark for further studies.
TL;DR: In this paper, the frequency-dependent dielectric properties of a polymer-based BaTiO3 (BT) nanoparticles, BT/P(VDF-HFP) nanocomposites, and a soft mode theory have been investigated as functions of the volume fraction of the nanoparticles at room temperature by several theoretical models.
Abstract: In this paper, based on recent research on BaTiO3 (BT) nanoparticles, BT/P(VDF-HFP) nanocomposites, frequency-dependent dielectric properties of such a material system with high energy density have been investigated as functions of the volume fraction of the nanoparticles at room temperature by several theoretical models. For single domain and single crystals of BT, a Debye type of dissipation and soft mode theory have been adopted to obtain a more precise frequency-dependent dielectric spectrum of BT. For nanodielectric composites, among the others, Wiener Rule, Lichtenecker model, Maxwell–Wagner model, Yamada, and modified Kerner model were applied to evaluate the frequency-dependent dielectric spectrum of nanocomposites. A simple rule of mixture for the dielectric loss tangent was obtained using Lichtenecker logarithmic rule. The results from theoretical calculations are compared with the experimental data. For the dielectric constant, Lichtenecker model, Maxwell–Wagner model, and Yamada model show reasonable agreements with the experimental data up to 50 % volume fraction of the nanoparticles. At the higher volume fraction of the nanoparticles, the experimental data show a decreasing trend of the dielectric constant of the composites due to an increase in porosity of the system. In this case, a three-phase model (nanoparticles/pores/matrix) was developed to predict dielectric properties of the system at higher volume fraction of the nanoparticles (up to 80 %). The results showed reasonable agreements for a wide range of frequency. This theoretical study provides an essential information on dielectric properties of polymer-based BT nanocomposites with a wide frequency range instead of the trial-and-error strategy of experiments and can be used for designing high energy density dielectric materials in the future.
TL;DR: In this article, a mathematical model that describes the plane motion of the system is developed, taking into account the effects of the atmosphere and the rotary motion of a tethered space tug around the SLD center of mass.
Abstract: The problem of deorbiting large space debris (SLD) by means of a tethered space tug is considered A mathematical model that describes the plane motion of the system is developed The model takes into account the effects of the atmosphere and the rotary motion of the SLD around the SLD center of mass The effects of the moment of tension force, gravitational moment, and pitch moment on the SLD behavior are studied The evolution of the phase space of an angle of attack during the SLD descent is considered Singular points are found for special cases of motion It is shown that the effect of the atmosphere on the SLD dynamics can be neglected above an altitude of 300 km The situation that a tether becomes slack is observed In this case, the SLD can oscillate with increasing amplitude and even pass into rotation This is a dangerous situation that can lead to tether rupture A method of thrust control that provides tension in the tether during the SLD deorbiting is presented A slack tether is also observed at atmospheric entry This phenomenon is caused by the difference in drag forces that act on the SLD and on the space tug The obtained results can be used in the preparation of missions of space debris deorbiting
TL;DR: In this paper, the authors investigated the relationship between macro-scale, continuum-mechanical characteristics and the micro-scale characteristics at the particle and interparticle contact level in micromechanics of quasi-static deformation of granular materials.
Abstract: In micromechanics of quasi-static deformation of granular materials, relationships are investigated between the macro-scale, continuum-mechanical characteristics, and the micro-scale characteristics at the particle and interparticle contact level. An important micromechanical quantity is the fabric tensor that reflects the distribution of contact orientations. It also contains information on the coordination number, i.e. the average number of contacts per particle. Here, the focus is on characteristics of the critical state in the two-dimensional case. Critical state soil mechanics is reviewed from the micromechanical viewpoint. Two-dimensional discrete element method (DEM) simulations have been performed with discs from a fairly narrow particle-size distribution. Various values for the interparticle friction coefficient and for the confining pressure have been considered to investigate the effect of these quantities on critical state characteristics (shear strength, packing fraction, coordination number and fabric anisotropy). Results from these DEM simulations show that a limiting fabric state exists at the critical state, which is geometrical in origin. The contact network tessellates the assembly into loops that are formed by contacts. For each loop, a symmetrical loop tensor is defined, based on its contact normals. This loop tensor reflects the shape of the loop. An orientation is associated with each loop, based on its loop tensor. At the critical state, the frequencies with which loops with different number of sides occur depend on the coordination number. At the critical state, these loops have, on average, the following universal characteristics, i.e. independent of the coordination number: (1) loops with the same number of sides and orientation have identical anisotropy of the loop tensor, (2) the anisotropy of the loop tensor depends linearly on the number of sides of the loop, (3) the distribution of loop orientations is identical, (4) Lewis’s law for the loop areas, which is a linear relation between the number of sides of loops and their area, is satisfied (not exclusively at the critical state) and (5) the areas of the loops do not depend on their orientation.
TL;DR: In this paper, a simple model is presented for the fragmentation of rock avalanches, assuming that most of the fragmentation occurs along force chains in the granular medium, and the landslide motion is simulated along a curved bumpy profile path.
Abstract: Rock avalanches are the largest granular flows on Earth. In contrast to artificial, small-scale granular avalanches, they exhibit a large degree of fragmentation with reduction of average grain volume by a factor of up to 1015–1018. Even though fragmentation likely affects the whole dynamics of the rock avalanche, as yet the basic mechanics of the process is poorly known. In this work, a simple model is presented for the fragmentation of rock avalanches, assuming that most of the fragmentation occurs along force chains in the granular medium. The landslide motion is simulated along a curved bumpy profile path. The predicted grain spectra are found to agree reasonably with field data.