Showing papers in "European Journal of Mechanics A-solids in 2020"
TL;DR: The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch.
Abstract: We present a deep energy method for finite deformation hyperelasticitiy using deep neural networks (DNNs). The method avoids entirely a discretization such as FEM. Instead, the potential energy as a loss function of the system is directly minimized. To train the DNNs, a backpropagation dealing with the gradient loss is computed and then the minimization is performed by a standard optimizer. The learning process will yield the neural network's parameters (weights and biases). Once the network is trained, a numerical solution can be obtained much faster compared to a classical approach based on finite elements for instance. The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch. Finally, we demonstrate the performance of our DNNs based solution for several benchmark problems, which shows comparable computational efficiency such as FEM solutions.
103 citations
TL;DR: In this paper, a coupled thermomechanical model is used for the FSW simulation and prediction of defect formation through the analysis of the material mixing during Friction Stir Welding (FSW).
Abstract: This work addresses the issue of the simulation and prediction of defect formation through the analysis of the material mixing during Friction Stir Welding (FSW). A coupled thermomechanical model is used for the FSW simulation. To follow the flow of the material, a tracing technique of the material particles is incorporated in the numerical model. A fast and accurate two-stage numerical strategy is adopted to analyse the FSW process. The speed-up stage intends to reach the steady state quickly. The material tracing is performed in the periodic stage where the rotation of the tool is modelled. The effect of the process parameters and the pin features on the defect formation is studied. The model is capable of predicting defects such as void, wormhole, flash and joint line remnant, as well as the formation of “onion rings” in a single simulation. The results show that the proposed model has significant capability to explain and predict the post-FSW defects.
62 citations
TL;DR: In this paper, the dynamic stability behavior of a nanocomposite sandwich truncated conical shells (NSTCS) is analyzed using the Kelvin-Voigt model.
Abstract: Present research is conducted in order to assess dynamic stability behavior of a nanocomposite sandwich truncated conical shells (NSTCS). In fact, graphene platelets (GPLs)-reinforced as core layer is encompassed through magnetostrictive layers as face sheets. For modeling the core layer and face sheets mathematically, higher order shear deformation theory (HSDT) besides first order shear deformation theory (FSDT) are utilized, respectively. To presume this sandwich structure much more realistic, Kelvin-Voigt model will be used. According to Hamilton's principle with respect to continuity boundary conditions, the governing equations are obtained. Utilizing differential cubature (DC) as well as Bolotin procedures, the governing equations will be solved and the region related to the dynamic instability is achieved. In this novel work, different variables covering various boundary edges, controller, cone's semi vertex angle, damping, feedback gain, proportion of core to face sheets thickness, dispersion kinds of GPLs and its volume percent will be studied. So as to indicate the accuracy of applied theories as well as methods, the results are collated with another paper. It is found that increment of GPLs volume percent leads to rise of excitation frequency.
49 citations
TL;DR: In this article, nonlinear theoretical models of two-dimensional and three-dimensional DVM based on a large beam deflection model are established to predict the normalized Young's modulus and Poisson's ratio in the principal directions.
Abstract: Double-V microstructure (DVM) is a type of auxetic cellular material with negative Poisson's ratio (NPR). Accurate predictions of the mechanical properties of these microstructures at large strains are critical for many engineering applications. In this paper, nonlinear theoretical models of two-dimensional (2D) and three-dimensional (3D) DVM based on a large beam deflection model are established to predict the normalized Young's modulus and Poisson's ratio in the principal directions. The theoretical solutions are compared to solutions obtained from numerical finite element analyses and quasi-static compression experiments of a 2D prototype manufactured using additive printing technique. It is found that there is good agreement between these results, validating the accuracy of the proposed theoretical model. Effects of geometry parameters on the mechanical properties of the DVM are also investigated to understand the mechanical behavior at large strains. This study provides validated models for predicting the behavior of these microstructures at large strains, useful for engineering designs.
49 citations
TL;DR: Three surrogate modeling approaches are compared in terms of accuracy, efficiency and calibration effort: the state-of-the-art mesoscopic plasticity model, regularized feed-forward neural networks and hyper-reduced-order models obtained by combining the Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) techniques.
Abstract: Although being a popular approach for the modeling of laminated composites, mesoscale constitutive models often struggle to represent material response for arbitrary load cases. A better alternative in terms of accuracy is to use the FE2 technique to upscale microscopic material behavior without loss of generality, but the associated computational effort can be extreme. It is therefore interesting to explore alternative surrogate modeling strategies that maintain as much of the fidelity of FE2 as possible while still being computationally efficient. In this work, three surrogate modeling approaches are compared in terms of accuracy, efficiency and calibration effort: the state-of-the-art mesoscopic plasticity model by Vogler et al. (Vogler et al., 2013), regularized feed-forward neural networks and hyper-reduced-order models obtained by combining the Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) techniques. Training datasets are obtained from a Representative Volume Element (RVE) model of the composite microstructure with a number of randomly-distributed linear-elastic fibers surrounded by a matrix with pressure-dependent plasticity. The approaches are evaluated with a comprehensive set of numerical tests comprising pure stress cases and three different stress combinations relevant in the design of laminated composites. The models are assessed on their ability to accurately reproduce the training cases as well as on how well they are able to predict unseen stress combinations. Gains in execution time are compared by using the trained surrogates in the FE2 model of an interlaminar shear test.
40 citations
TL;DR: In this paper, the impacts of temperature and moisture on the bending behavior of functionally graded porous plates resting on elastic foundations are taken into consideration, where the number of unknown functions involved here is only five as against six or more in case of other shear and normal deformation theories.
Abstract: The present paper deals with the impacts of temperature and moisture on the bending behavior of functionally graded porous plates resting on elastic foundations. The impacts of transverse shear deformation as well as the transverse normal strain are taken into consideration. The number of unknown functions involved here is only five as against six or more in case of other shear and normal deformation theories. The effects due to side-to-thickness ratio, aspect ratio, thermal and moisture loads, porosity factor and elastic foundation parameters as well as the volume fraction distribution on the functionally graded porous plates are investigated. Numerical outcomes are given and compared with those available in the literature. Discussions are made to show how the foundation stiffness and other parameters have significant effects on the bending response of the functionally graded porous plates under hygrothermal loading and porosities.
37 citations
TL;DR: In this article, the Gurson-Tvergaard-needleman (GTN) model damage mechanics parameters for 6061 Al alloys were determined by tensile tests.
Abstract: This research experimentally determines the Gurson-Tvergaard-Needleman (GTN) model damage mechanics parameters for 6061 Al alloys. Five different heat treatment conditions including T4 (natural aging) and T6 (peak strength) conditions of 6061 Al alloy were investigated. The GTN parameters considering different heat treatment conditions of the alloy were obtained by tensile tests. Scanning electron microscope (SEM) micrographs were used as inputs to determine initial and nucleated volume fractions. SEM and energy dispersive X-ray spectrography (EDX) analyses also revealed that the second-phase precipitates are the origin of the incipient voids. SEM analyses enabled the fractographic investigations where the primary and secondary voids were exhibited and thus showing nucleation strain. Density measurements clarify the critical and final void volume fractions and the standard deviation of the nucleated void volume fraction distribution. The results show that the void volume fraction increases exponentially along with increasing effective tensile plastic strain. Hence, a total of six different GTN parameters have been identified experimentally. Finite element method simulations based on GTN damage model were performed to verify the GTN model parameters. The results show that the experimentally obtained GTN model parameters could be used when performing tensile deformation simulations of 6061 Al alloys fabricated with different heat treatment conditions.
37 citations
TL;DR: In this article, a generalized nonlinear size-dependent curved beam model is established, which includes not only a nonlocal parameter and a material length scale parameter of NSGT but also three surface constants of the surface elasticity theory, which can explore the coupling effect of nonlocal stress, strain gradient and surface energy on the snap-buckling of nanoarches.
Abstract: We in this paper dedicate to study the snap-buckling of functionally graded multilayer graphene platelet-reinforced composite curved beams with geometrical imperfections on the nanometer length. It is supposed that graphene platelets (GPLs) are uniformly distributed and randomly oriented in each layer, while its weight fraction varies from one layer to another based on various functionally graded patterns. The effective material properties of functionally graded multilayer GPLRC beams are evaluated via the model of the Halpin-Tsa. In the theoretical framework of the nonlocal strain gradient theory (NSGT) and the surface elasticity theory, a generalized nonlinear size-dependent curved beam model is established. The novel model includes not only a nonlocal parameter and a material length scale parameter of NSGT but also three surface constants of the surface elasticity theory, which can explore the coupling effect of nonlocal stress, strain gradient and surface energy on the snap-buckling of nanoarches. Furthermore, the present model can be transformed into the Euler-Bernoulli shallow arch model, the Timoshenko shallow arch model as well as the Reddy's higher-order shear deformation shallow arch model by choosing the appropriated shape function. Next, On the basis of the principle of Hamilton, the nonlinear governing equations of curved nanobeams are derived. Then to obtain the analytical solution of snap-buckling of curved beams, the nonlinear equations are solved by a two-step perturbation method. Finally, a detailed parametric study is carried out based on the analytical solution, aiming at analyzing the influences of respective physical parameters on the snap-buckling of such nanostructure.
36 citations
TL;DR: In this paper, a robust control method is proposed for the vibration suppression of the piezoelectric laminated composite cantilever rectangular plate subjected to the aerodynamic force in the hygrothermal environment.
Abstract: In this paper, a robust control method is proposed for the vibration suppression of the piezoelectric laminated composite cantilever rectangular plate subjected to the aerodynamic force in the hygrothermal environment. The laminated composite cantilever rectangular plate is placed on the piezoelectric actuator and sensor for the upper and lower surfaces. The classical laminated composite plate theory and Hamilton's principle are applied to derive the dynamic equation of motion for the piezoelectric laminated composite cantilever rectangular plate under the aerodynamic force and hygrothermal loads. The structural damping is considered for the piezoelectric laminated composite cantilever rectangular plate. Galerkin method is used to obtain a two-degree-of-freedom discrete ordinary differential control equation of motion. For the active vibration suppression, a robust controller for the uncertain systems is designed through the obtained ordinary differential equation of motion. Moreover, the full-dimensional state observer is constructed to calculate the close-loop system. The influences of the moisture, temperature and geometric parameters on the dynamics behaviors of the piezoelectric laminated composite cantilever rectangular plate are investigated. The accuracy and effectiveness of the robust controller are verified in terms of the moisture concentration, temperature, aspect ratio, damping and parameter uncertainty by numerical simulations.
33 citations
TL;DR: In this paper, the thermally induced dynamic behaviors of functionally graded flexoelectric nanobeams (FGFNs) are analyzed theoretically while considering the neutral surface concept and the von Karman nonlinearity induced by thermal environment.
Abstract: In this work, thermally induced dynamic behaviors of functionally graded flexoelectric nanobeams (FGFNs) are analyzed theoretically while considering the neutral surface concept and the von Karman nonlinearity induced by thermal environment. The temperature field is assumed to vary only in the thickness direction by solving a simple steady state heat transfer equation and to be constant in the plane of the beam. The temperature-dependent material properties of FGFNs are assumed to vary continuously throughout the thickness according to a power-law form. For such FGFNs, the nonlocal simplified strain gradient elasticity theory to capture the effect of size-dependent and, the higher order shear deformation beam theory to account for rotary inertia and transverse shear strains are adopted to formulate the governing equations and associated boundary conditions, which are solved by using a two-step perturbation method. In the numerical part, comparison study is also performed to verify the present theoretical model and the parametric analysis is systematically studied. It is also found that the thermally induced bending amplitude, nonlinear frequency and frequency ratio depend enormously on the material distribution profile, the flexoelectricity, the size-dependent effect and the imposed temperature field.
32 citations
TL;DR: Based on the Timoshenko beam theory, von Karman geometric nonlinearity assumption and the modified couple stress theory, the authors presents linear and nonlinear free vibration analysis of rotating two-dimensional functionally graded micro-beam with even and uneven porous distributions.
Abstract: Based on the Timoshenko beam theory, von Karman geometric nonlinearity assumption and the modified couple stress theory, this paper presents linear and nonlinear free vibration analysis of rotating two-dimensional functionally graded micro-beam with even and uneven porous distributions. The material properties vary along the axial and thickness directions. The NURBS function is employed as the basic one to overcome the inherent difficulty of constructing higher order continuous displacement function for modified couple stress theory based finite element formulation. The validity of the present simulation is validated by comparing numerical results with those available literatures for rotating functionally graded micro-beams. Finally, the effects of several parameters such as porosity, power law index, material length scale parameter, rotational speed and hub radius on dimensionless frequencies and nonlinear frequency ratios are discussed.
TL;DR: In this paper, a stiffening method was proposed by adding inclined walls to the classical re-entrant honeycomb cell to boost the in-plane rigidity of the cell without significant loss from auxetic behaviour.
Abstract: This paper presents a stiffening method by which new inclined walls are added to the classical re-entrant honeycomb cell. This modification boosts the in-plane rigidity of the re-entrant cell without significant loss from auxetic behaviour. This study focuses on the in-plane elasticity moduli and negative Poisson's ratios along the principal axes. Analytical expressions that calculate the elasticity moduli and negative Poisson's ratios are derived; both finite element modelling and experiments reported in the literature validate the expressions of this work. Further, the variation in the in-plane elastic properties of the core cell is examined by altering the new wall's geometric, sectional, and material parameters. The results from the analytical expressions and the finite element models match very closely and demonstrate the boosted rigidity of the cell proposed in this work. This work also provides a benchmark of the new cell against the classical cell that can be used to tailor the in-plane elasticity moduli and negative Poisson's ratios to suit the needs of different applications.
TL;DR: In this article, a new fractional thermo-elasticity is established by directly extending classical thermoelasticness with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana-Baleanu and Tempered-Caputo definitions.
Abstract: Fractional thermoelastic models have been formulated from classical thermoelasticity or extended thermoelasticity, i.e. Lord-Shulman or Green-Naghdi theory. It seems different authors have different physical pictures on such topic, for instance, there exist several approaches from Lord-Shulman model to fractional order ones. This work is aimed to simplify the theoretical frameworks by clarifying connections between existed models. To this end, a new fractional thermoelasticity is established by directly extending classical thermoelasticity with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana–Baleanu and Tempered-Caputo definitions. All definitions are introduced into Fourier's law by a unified way with relaxation time incorporated. Theoretically, the present model may be simplified into existed fractional theory. Numerically, it has the capability of describing thermoelastic behaviors from fractional Lord-Shulman models. For numerical studies, Laplace transform method is adopted, and a two-layered structure subjected to thermal heating is considered, from which the effects of different fractional derivatives and relaxation time are firstly uncovered. And then, the influences of material constants of two layers, especially with interfacial conditions, are discussed in detail. Finally, some concluding remarks are made.
TL;DR: In this paper, the thermal properties of a composite cylindrical panel reinforced with graphene platelets distributed along the radial direction uniformly (UD) or functionally graded, FG − Δ, F G − ∇, F G− ∇, F g − ⋄ and F g− X pattern is studied in the frame work of elasticity theory.
Abstract: Thermoelastic behavior of composite cylindrical panel reinforced with graphene platelets distributed along the radial direction uniformly (UD) or functionally graded, F G − Δ , F G − ∇ , F G − ⋄ and F G − X pattern is studied in the frame work of elasticity theory. Functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical panel with simply supported boundary conditions is subjected to constant temperature at its inner and outer surfaces. By applying Fourier series expansion to the physical quantities along the axial and circumferential coordinates and using state space technique along the radial direction, state space governing differential equations can be derived and solved analytically. Parametric study is conducted by considering the effects of weight fraction as well as geometry and size of GPLs, pattern of graphene platelets distribution, applied temperature on thermoelastic behavior of GPLRC cylindrical panel. From numerical illustration it is evident that adding a little content GPLs affects thermoelastic behavior of GPLRC cylindrical panel significantly.
TL;DR: In this paper, a controllable electromagnetic force generated via a conventional proportional-derivative controller is utilized to stabilize the system lateral oscillations that excited by the rotating disk eccentricity when the spinning speed is close to or equal the system linear natural frequency.
Abstract: The present study is devoted to investigate the oscillatory behaviors of the 16-pole rotor active magnetic bearing system A controllable electromagnetic force generated via a conventional proportional-derivative controller is utilized to stabilize the system lateral oscillations that excited by the rotating disk eccentricity when the spinning speed ( Ω ) is close to or equal the system linear natural frequency ( ω ) The nonlinear dynamical equations governing the controlled system lateral vibrations at constant stiffness coefficients are derived in this article for the first time Then, four nonlinear autonomous first-order differential equations to describe the considered system oscillation amplitudes and the corresponding phase angles are obtained applying the asymptotic analysis Bifurcation behavior of the system periodic motions under varying the different control parameters is explored The main acquired results confirm that the 16-pole rotor-AMB system at constant stiffness coefficients can exhibit one of three oscillatory motions that are periodic, quasiperiodic, or chaotic motions depending on the derivative gain coefficient Moreover, the system may respond with one-stable solution, bi-stable solutions, tri-stable solutions, or quadri-stable solutions depending on the proportional gain coefficient Numerical simulations for different system motions are validated via the system time response, Poincare map, orbit plot, and frequency spectrum that are showed an excellent agreement with the obtained analytical results
TL;DR: In this paper, the postbuckling and geometrically nonlinear behaviors of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells under axial compression are investigated.
Abstract: The postbuckling and geometrically nonlinear behaviors of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells under axial compression are investigated in this paper. For the first time, a new type of instability named “snap-backward” with the presence of three limit points on the equilibrium path is proposed. A novel formulation based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT) using the von Karman assumption and considering the initial deformation of the shells is presented. In addition, the advantage of NURBS in modeling exactly geometries of shells is exploited. In numerical implementation, the discrete nonlinear equation system is iteratively solved by a modified Riks method. The rule of mixture is used to estimate the effective material properties of FG-CNTRC shells. Some benchmark problems are solved to verify the high reliability of the proposed formulation. Effects of geometrical imperfection, CNTs distribution, volume fraction, CNTs orientation, thickness, radius of shell on the postbuckling and geometrically nonlinear behaviors of FG-CNTRC shells are rigorously investigated. Especially, some new and complex load-deflection curves of imperfect FG-CNTRC shells under axial compression are first provided that could be useful for future references.
TL;DR: In this paper, analytical solutions for SH waves in transversely isotropic multilayered piezoelectric semiconductor (PSC) plates with imperfect interfaces are obtained. And the extended displacements and stresses are expressed in terms of the eigenvalues and eigenvectors by introducing the extended Stroh formalism.
Abstract: In this paper, analytical solutions for SH waves in transversely isotropic multilayered piezoelectric semiconductor (PSC) plates with imperfect interfaces are obtained. The extended displacements and stresses are expressed in terms of the eigenvalues and eigenvectors by introducing the extended Stroh formalism. Making use of the dual variable and position (DVP) method and the imperfect interface conditions, the transfer matrix which relates the extended displacement and traction on the lower and upper interfaces of the multilayered plates is derived. Then the dispersion relation is obtained by using the boundary conditions on the top and bottom surfaces of the multilayered plates. Effect of the steady-state carrier density in single-layer ZnO plate, and effect of stacking sequences and imperfect interfaces in sandwich plates are discussed via numerical examples. Particularly, the critical elastic (E), piezoelectric (PE), and PSC wave domains are identified for the given carrier density, plate thickness and frequency, which could be very helpful as theoretical guidance for the design of PSC devices.
TL;DR: In this paper, the Gent-Gent hyperelastic model is proposed for the nonlinear vibration of a dielectric elastomer balloon considering both the strain-stiffening and the second invariant of the Cauchy-Green deformation tensor.
Abstract: This paper studies the nonlinear vibration of a dielectric elastomer balloon considering both the strain-stiffening and the second invariant of the Cauchy-Green deformation tensor. To this end, the Gent-Gent hyperelastic model is proposed. The ordinary differential equation governing the motion of the system is derived using the Euler-Lagrange energy method. Then, it is solved with the application of a time integration-based solver. The chaotic interval for critical system parameters is identified, with and without considering the influence of the second invariant. This identification is conducted by depicting bifurcation diagrams of Poincare sections and the largest Lyapunov exponent criteria. In order to better analyse different motions of the system, time histories, phase-plane diagrams, Poincare maps, and power spectral densities are illustrated. Based on the obtained results, the second invariant parameter of the Gent-Gent model could suppress the chaotic motion of the system. Increasing this parameter, a transition from the chaos to the quasiperiodic attractor would happen.
TL;DR: In this article, a two-degree-of-freedom nonlinear Jeffcott-rotor system was modeled as a rotating shaft and the amplitude-phase modulating equations that govern the system lateral vibrations in the horizontal and vertical directions were derived.
Abstract: Nonlinear lateral vibrations and the corresponding whirling motions of asymmetric horizontally supported rotor system are investigated within this article. The rotating shaft is modeled as a two-degree-of-freedom nonlinear Jeffcott-rotor system. The nonlinear restoring force of the rotating shaft, asymmetry in both the linear and nonlinear stiffness coefficients, the disk weight, the disk eccentricity, and the eccentricity orientation angle are included in the studied model. The asymptotic analysis is utilized to derive the autonomous amplitude-phase modulating equations that govern the system lateral vibrations in the horizontal and vertical directions. Bifurcation diagrams of both the system vibration amplitudes and the corresponding phase angles are obtained. The main acquired results revealed that the existence of the asymmetry in the rotating shaft stiffness coefficients widens the spinning speed interval at which the system may have more than one stable solution. In addition, increasing the linear asymmetrical stiffness coefficient can eliminate the system backward whirling motion. Finally, numerical confirmations for the obtained analytical results are performed that illustrated their accuracy in the prediction of the system vibration amplitudes and the whirling direction whether forward, backward, or along a straight line.
TL;DR: In this paper, a dynamic analysis of a single rotating nonlocal cantilever nano-beam under external excitations is presented, where the cases of undamped and damped forced vibrations are analyzed.
Abstract: This study presents a dynamic analysis of a single rotating nonlocal cantilever nano-beam under external excitations. The cases of undamped and damped forced vibrations are analyzed. By employing Eringen's nonlocal elasticity theory and based on Euler–Bernoulli's beam theory, the governing equation of motion of the forced vibration rotating nonlocal cantilever nano-beam is derived. The mentioned equation of motion is discretized by the Galerkin method. In the paper, the standard modal analysis procedure is used for determining the forced responses. The effect of nonlocality on the forced vibrations of the rotating nano-beam is discussed. In the parametric study the influences of the varying angular velocity and varying hub radius effects are presented. The solutions for the natural frequencies of the rotating system are determined. Two interesting new phenomena are observed in the case of absence of the hub radius and an increase in the nonlocality effect. The undamped vibrations in the case without the hub radius become monotonic descending. In the same time interval, the existence of the hub radius leads to a different effect. An increase in nonlocality has a significant effect on the maximal amplitudes of the nano-beam's points that are located close to its midspan. Studies include and an influence of the axial extension load. Even though the qualitative impact of the axial external load is known, the quantitative effect will be shown here.
TL;DR: In this article, a theoretical method is proposed to improve the vibration attenuation characteristics of a finite hybrid piezoelectric phononic crystal beam utilizing the non-uniform distribution of shunting circuits.
Abstract: In this paper, a theoretical method is proposed to effectively improve the vibration attenuation characteristics of a finite hybrid piezoelectric phononic crystal (PC) beam utilizing the non-uniform distribution of shunting circuits. Considering the damping of resonators, the vibration transmissibility method (TM) for the finite electromechanical system is derived based on the Timoshenko beam theory. Numerical results are validated by the finite element method (FEM). Subsequently, a comprehensive study is conducted to investigate the influences of the structural and electrical parameters on the vibration attenuation property of the uniform PC. Furthermore, the organized disorder of the shunting circuits is introduced into the system. Combining with various types of non-uniform circuit configurations, the variation of the vibration attenuation is also examined. It is demonstrated that the hybrid PCs offer more tunable mechanisms to design target band-gaps, compared with the purely mechanical and piezoelectric PCs. The low-frequency vibration reduction over a broadband range could be achieved through the selective coupling ways of the mechanical local resonant band-gap (LRG), electromechanical LRG and Bragg band-gap (BG). It is expected to enhance the vibration attenuation and availability of hybrid PCs using the suitable distribution of shunting circuits in practice.
TL;DR: In this paper, the exact analytical solution for the static deflection analysis of fully coupled composite Timoshenko beams is derived from variational principles using the method of direct integration, and the results are compared to those obtained from classical Euler-Bernoulli theory by using different values of length-to-thickness ratio.
Abstract: The purpose of this paper is to present the exact analytical solution for the static deflection analysis of fully coupled composite Timoshenko beams. The system of governing equations and the boundary conditions are derived from variational principles. Using the method of direct integration, the exact analytical solution of the static deflection of a Timoshenko beam is obtained by solving this system of differential equations in terms of transverse displacements and cross-sectional rotations. Static deflection analyses of Timoshenko beams, subject to various boundary conditions and uniformly distributed and tip loads, are performed and the results are compared to those obtained from classical Euler–Bernoulli theory by using different values of length-to-thickness ratio. In addition, it is shown that for the case of a cantilevered composite beam subject to tip loads, the proposed exact analytical solution is equivalent to the exact solution from the intrinsic formulation. The Chebyshev collocation method is also employed to validate the obtained exact analytical solution. In the proposed formulation the stiffness properties of the composite beam are expressed by engineering constants, therefore is not limited by the cross-sectional shape of the beam, type of material and thus can be utilised for engineering applications and design purposes. The exact analytical solution can also be used as a benchmark for validating results obtained from various numerical methods.
TL;DR: This work investigates how the macroscale radial displacements are affected by the microscale solid matrix compressibility (MSMC), and suggests that parameter estimation based on techniques such as poroelastography should allow for a sufficiently long time in order to give a more accurate estimation of the mechanical properties of tissues.
Abstract: We present the macroscale three-dimensional numerical solution of anisotropic Biot's poroelasticity, with coefficients derived from a micromechanical analysis as prescribed by the asymptotic homogenisation technique. The system of partial differential equations (PDEs) is discretised by finite elements, exploiting a formal analogy with the fully coupled thermal displacement systems of PDEs implemented in the commercial software Abaqus. The robustness of our computational framework is confirmed by comparison with the well-known analytical solution of the one-dimensional Therzaghi's consolidation problem. We then perform three-dimensional numerical simulations of the model in a sphere (representing a biological tissue) by applying a given constant pressure in the cavity. We investigate how the macroscale radial displacements (as well as pressures) profiles are affected by the microscale solid matrix compressibility (MSMC). Our results suggest that the role of the MSMC on the macroscale displacements becomes more and more prominent by increasing the length of the time interval during which the constant pressure is applied. As such, we suggest that parameter estimation based on techniques such as poroelastography (which are commonly used in the context of biological tissues, such as the brain, as well as solid tumours) should allow for a sufficiently long time in order to give a more accurate estimation of the mechanical properties of tissues.
TL;DR: In this article, the effect of graphene nanoribbon twist on its lateral buckling resistance to axial compression and thermal conductivity is analyzed with the help of molecular dynamics simulations.
Abstract: The effect of graphene nanoribbon twist on its lateral buckling resistance to axial compression and on its thermal conductivity is analyzed with the help of molecular dynamics simulations. It is shown that the nanoribbon twisted by an angle close to π can withstand three times greater compressive force as compared to a flat nanoribbon. The explanation lies in the fact that such twist increases the effective area moment of inertia of the nanoribbon cross section. It is also found that the thermal conductivity coefficient of the nanoribbon increases monotonically up to 10% with increasing twist angle, in the regime of uniform twisting. This effect is due to the introduction of tensile strain in the twisted nanoribbon, which increases the contribution of the acoustic out-of plane (ZA) phonon modes to thermal conductivity. Our results demonstrate that twist deformation of nanoribbons can improve their mechanical and physical properties. The reported effects can be observed for 2D materials other than graphene because they have simple mechanical explanation not related to a particular crystal structure.
TL;DR: In this paper, a physically-based damage-hotspot formation framework incorporating multiple stress-state motivated evolution of microcracks and microvoids is developed to study the overall damage behavior of polymer-bonded explosives (PBXs).
Abstract: A physically–based damage–hotspot formation framework incorporating multiple stress–state motivated evolution–modes of microcracks and microvoids is developed to study the overall damage behavior of polymer–bonded explosives (PBXs). Localized heating sub-models of shear–crack friction and void collapse hotspot mechanisms are described to predict impact–shear ignition of PBXs. Several features of microdefect evolution under a combined shear and compression loading are predicted as follows. (i) Crack growth causes an elasticity deterioration and softening response; (ii) void distortion begins at the yield point and ends at the softening point; (iii) the softening stage will be interrupted if the increasing lateral pressure is sufficiently large to inhibit crack growth; and (iv) void collapse occurs if the lateral pressure continually increases to a critical high value. Simulated results of a punched PBX charge show that shear–crack friction heating plays a critical role in ignition under low–velocity impact ( 400 m/s), the heating due to void collapse dominates ignition because the timescale to void hotspot formation (~1 μs) is considerably shorter than that of crack hotspots (~10 μs).
TL;DR: In this article, a four-node Kirchhoff plate element was constructed considering dilatation, deviatoric stretch and rotation gradient effects to address the general boundary value problems of size-dependent isotropic thin micro-plates.
Abstract: This paper constructs a four-node Kirchhoff plate element considering dilatation, deviatoric stretch and rotation gradient effects to address the general boundary value problems of size-dependent isotropic thin micro-plates. This element benefits from the merits of differential quadrature method (DQM) and finite element method (FEM) and possesses four nodal displacement parameters at each node, i.e., deflection, its two first partial derivatives and one second mixed partial derivative with respect to two in-plane coordinates. To guarantee the C2 partial compatibility among neighboring elements, we establish a novel DQ-based geometric mapping scheme relating the deflection values at Gauss-Lobatto quadrature points to the displacement parameters at four nodes. By applying the DQ rule, the Gauss-Lobatto quadrature rule and the developed mapping scheme, the total potential energy of a generic gradient-elastic Kirchhoff plate element is represented as a function of nodal displacement parameters. The element formulation is derived using the minimum total potential energy principle. Several numerical examples are provided to demonstrate the validity of the proposed method and explore the static bending, free vibration and critical buckling behavior of thin micro-plates. It is validated that the size-dependence of vibration and critical buckling mode shapes of thin micro-plates can be observed in some cases.
TL;DR: In this paper, a new metamaterial plate (metaplate) made by a periodic repetition of "frame-springs-mass" systems for vibration isolation is presented, which shows a complete 3D phononic bandgap in the low-frequency range.
Abstract: This paper presents a new metamaterial plate (metaplate) made by a periodic repetition of ‘frame-springs-mass’ systems for vibration isolation. Numerical studies and experimental measurements demonstrate that the proposed structure show a complete 3D phononic bandgap in the low-frequency range. In the numerical computation of the transmission diagram, the self-weight gravity, the material damping, the geometry of the metaplate and different boundary conditions are considered. A prototype of the proposed metaplate, made of Polyamide, is fabricated by means of additive manufacturing and experimentally tested. The measured transmission diagram is in good agreement with numerical predictions, thus proving the proposed design and promoting potential applications such as low-frequency vibration isolation and stress wave mitigation.
TL;DR: In this article, the formulation for linear buckling and for geometrically nonlinear analysis of laminated composite and functionally graded material (FGM) plates under mechanical uniaxial in-plane uniform loads, and thermal loads is presented.
Abstract: In this work the formulation for linear buckling and for geometrically nonlinear analysis of laminated composite and functionally graded material (FGM) plates under mechanical uniaxial in-plane uniform loads, and thermal loads , is presented. An implemented finite element model based on a non-conforming triangular flat plate/shell element with three nodes and eight degrees of freedom per node, associated with a higher order shear deformation theory is used. The through the thickness variation of the material properties, discrete for laminated composite plates or continuous for FGM plates, as well as the through the thickness temperature distribution, originate a non-symmetry with respect to the middle-surface. Thus, in general, the occurrence of bifurcation-type buckling should be studied, and the transverse deflection at the centre of the plate could be a good indicator to anticipate this occurrence. The solutions of some illustrative examples involving different boundary conditions, composite lay-up, FGM variation of volume fractions, temperature distributions, material combinations, and boundary conditions are presented for benchmarking purposes, with emphasis for the plate transverse deflections. Linear solutions are compared with numerical alternative models. The occurrence of bifurcation-type buckling is discussed for several representative cases, the validity of the linear buckling solutions is addressed and nonlinear analyses have been performed for confirmation purposes.
TL;DR: In this paper, the reflection behaviors of elastic waves in the functionally graded piezoelectric (FGP) microstructures are studied based on the modified couple stress theory, and the extended Legendre orthogonal polynomial method (LOPM) is employed to obtain the analytical solutions of governing equations.
Abstract: The reflection behaviors of elastic waves in the functionally graded piezoelectric (FGP) microstructures are studied based on the modified couple stress theory. The extended Legendre orthogonal polynomial method (LOPM) is employed to obtain the analytical solutions of governing equations. The LOPM does not require delamination and calculation of the displacements of each partial wave. It is more suitable for solving FGP microstructure. The solutions of the incident P wave and SH wave with the consideration of open-circuit surface and short-circuit surface electrical boundaries are illustrated, respectively. The convergence of the polynomial series method is analyzed through numerical examples. The influences of the length scale parameters, gradient shapes and different electrical boundaries on the reflection behaviors are discussed. It is found that the couple stress can increase the propagation velocity of SH waves in the microstructures, and then reduce the critical angle of the total reflection of the incident SH wave.
TL;DR: In this paper, the Eringen result for random vibration of the simply-supported Bernoulli-Euler beam subjected to the "rain-on-the-roof" excitation is extended to the beam placed on Winkler elastic foundation.
Abstract: The Eringen's result for random vibration of the simply-supported Bernoulli-Euler beam subjected to the “rain-on-the-roof” excitation is extended to the beam placed on Winkler elastic foundation. The normal mode approach is utilized. The attendant infinite series are summed up in the closed form.