Showing papers in "European Journal of Mechanics A-solids in 2019"

Fatigue of hydrogels

Abstract: Hydrogels have been developed since the 1960s for applications in personal care, medicine, and engineering. Evidence has accumulated that hydrogels under prolonged loads suffer fatigue. Symptoms include change in properties, as well as nucleation and growth of cracks. This article is the first review on the fatigue of hydrogels. Emphasis is placed on the chemistry of fatigue—concepts and experiments that link symptoms of fatigue to processes of molecules. Symptoms of fatigue are characterized by testing samples with and without precut cracks, subject to prolonged static and cyclic loads. We describe the use of energy release rate for samples with precut cracks, under the conditions of large-scale inelasticity, for hydrogels of complex rheology. Highlighted are three experimental setups: pure shear, tear, and peel, where energy release rate is readily obtained for materials of arbitrary rheology. We describe chemistries of bonds and topologies of networks. Noncovalent bonds and some covalent bonds are reversible: they reform after breaking under relevant conditions. Most covalent bonds are irreversible. Each topology of networks is a way to connect reversible and irreversible bonds. We review experimental data of hydrogels of five representative topologies of networks. We compare the Lake-Thomas threshold, the cyclic-fatigue threshold, and the static-fatigue threshold. Fatigue is a molecular disease. All symptoms of fatigue originate from one fundamental cause: molecular units of a hydrogel change neighbors under prolonged loads. Fatigue correlates with rheology, according to which we distinguish poroelastic fatigue, viscoelastic fatigue, and elastic-plastic fatigue. Many hydrogels have sacrificial bonds that act as tougheners. We distinguish tougheners of two types according to their stress-relaxation behavior under a prolonged static stretch. A liquid-like toughener relaxes to zero stress, and increases neither static-fatigue threshold nor cyclic-fatigue threshold. A solid-like toughener relaxes to a nonzero stress, increases static-fatigue threshold, but does not increase cyclic-fatigue threshold. We outline a strategy to create hydrogels of high endurance. Because of the molecular diversity among hydrogels, the chemistry of fatigue holds the key to the discovery of hydrogels of properties previously unimagined. It is hoped that this review helps to connect chemists and mechanicians.

Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets

Abstract: This paper investigates the free vibrations of the rotating pretwisted functionally graded (FG) composite cylindrical panels reinforced with the graphene platelets (GPLs) by considering the cantilever boundary conditions. The weight fraction of the graphene platelets in each ply may be different, which leads to the layer-wise functionally graded composite cylindrical panels reinforced with the GPLs. The effective Young's modulus is calculated by the modified Halpin-Tsai model. The effective Poisson's ratio and mass density are derived by the rule of the mixture. The strain-displacement relationship is acquired by the Green strain tensor. Based on the first-order shear deformation theory, Chebyshev-Ritz method is used to obtain the natural frequencies of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs. The natural frequencies are discussed by considering different material and geometry parameters of the rotating pretwisted functionally graded composite cylindrical panel reinforced with the GPLs, such as the GPL distribution pattern, the GPL weight fraction, the geometries of the GPLs, the pretwisted angle, the presetting angle and the rotating speed. Several validations are carried out, the numerical results are in good agreement with the results of the literature and ANSYS.

An isogeometric approach of static and free vibration analyses for porous FG nanoplates

Abstract: This paper presents porosity-dependent analysis of functionally graded nanoplates, which are made of two kinds of porous materials, based on isogeometric approach for the first time. Material properties of the nanoplates are described by using a modified power-law function. The Eringen's nonlocal elasticity is used to capture the size effects. Using the Hamilton's principle, the governing equations of the porous FG nanoplates using the higher order shear deformation theory are derived. The obtained results demonstrate the significance effect of nonlocal parameter, material composition, porosity factor, porosity distributions, volume fraction exponent and geometrical parameters on static and free vibration analyses of nanoplates.

Actively controllable flexural wave band gaps in beam-type acoustic metamaterials with shunted piezoelectric patches

Abstract: In this paper, a tunable beam-type metamaterial composed of elastic base beams and periodically arrayed active beam-type resonators is designed and analyzed theoretically. The piezoelectric shunted array technique is applied to each engineered resonator, so that the band structure in the system can be actively controlled. Based on spectral element method, the dispersion relation of an infinite system as well as the transmission equation of a finite system are obtained explicitly. The effects of negative capacitance shunt and negative capacitance enhanced resonant shunt on band structures are considered numerically. It is shown that, on one hand, the negative capacitance shunts can sensitively control the widths and locations of local resonance band gaps. On the other hand, when a negative capacitance enhanced resonant shunt is applied, the enhanced meta-damping phenomenon emerges, leading to an extra wide and low-frequency band gap. The resistance in the shunt induces damping to the system, which together with the local resonance motion gives rise to meta-damping behavior. Such effect is further enhanced by negative capacitance, which increases the system electromechanical coupling property. Numerical simulations also show that such novel band gap can be realized only when the negative capacitance is close to the instability boundary and resistance in a certain region. In addition, the inductance of shunt can optimize the attenuation performance distribution in the extra broad band gap. Particularly, the transmission analyses show that the attenuation property of such extra wide band gap is as good as the general Bragg scattering band gaps. Such extremely wide and low-frequency band gap can be used for a wide range of engineering applications such as vibration suppression, sound absorption, acoustic filter, etc.

An improved coupled thermo-mechanic bond-based peridynamic model for cracking behaviors in brittle solids subjected to thermal shocks

Abstract: An improved coupled thermo-mechanical bond-based peridynamics with multirate time integration scheme is developed to study the thermal shock cracking behaviors in brittle solids. In the proposed numerical method, effects of the relative distance between material points on thermoelastic stiffness of a bond are considered in the deformed configuration . The periodical and hierarchical characteristics of thermal crack patterns of ceramics in quenching tests are accurately predicted in 2-D and 3-D cases. The present numerical results are in good agreement with the previous experimental observations and data. It is shown that the proposed numerical model is simple and efficient to simulate the periodical and hierarchical initiation and propagation of cracks in brittle solids under thermal shocks. The present numerical simulations provide direction observations on the whole processes of crack initiation and propagation , which is a quite difficult problem in the laboratory experiments.

Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory

Abstract: In the present study, based on the higher-order shear deformation plate theory, the unified numerical formulation is developed in variational framework to investigate the thermal buckling of different shapes of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates. Since the thermal environment has considerable effects on the material properties of carbon nanotubes (CNTs), the temperature-dependent (TD) thermo-mechanical material properties are taken into account. In order to present the governing equations, the quadratic form of the energy functional of the plate structure is derived and its discretized counterparts are presented employing the variational differential quadrature (VDQ) approach. The discretized equations of motion are finally obtained based on Hamilton's principle. In order to convenient application of differential quadrature numerical operators in irregular physical domain, the mapping procedure is considered in accordance to the conventional finite element formulation. Some comparison and convergence studies are performed to show validity and efficiency of the proposed approach. A wide range of numerical results are also reported to analyze the thermal buckling behavior of different shaped FG-CNTRC plates.

Mechanics of viscoelastic functionally graded microcantilevers

Abstract: An elastically supported viscoelastic functionally graded (FG) microcantilever is considered and its nonlinear mechanics is analysed for the first time. Moreover, for the first time, energy transfer via internal resonances and motion complexity are analysed. A nonlinear spring model is incorporated as an elastic support which is representative of elasticity induced from neighbouring devices. Size effects are incorporated using the modified couple stress theory (MCST). Mori-Tanaka formula is utilised for FG-material-property variations. Kinematics/kinetics for an infinitesimal beam elements in conjunction with Hamilton's method are used for large curvatures. Galerkin's technique is used for reductions and truncations of the dynamic model of elastically supported viscoelastic FG microsystem. Both base-excitation/frequency continuations are performed and the dynamics is investigated.

Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST

Abstract: The size dependent thermal buckling analysis of composite micro plate is studied in this paper based on modified couple stress theory (MCST) and sinusoidal shear deformation theory. The composite micro plate is composed of epoxy reinforced with functionally graded graphene nanoplatelets which is distributed along the thickness direction based on various distributions (parabolic, linear and uniform distributions). After calculation of effective material properties including modulus of elasticity and Poisson ratio of composite plate, Halpin-Tsai model and rule of mixture, the governing equations are derived based on principle of virtual work. The in-plane mechanical and thermal loads are included in the work of external loads. The novelty of this work is the application of a modified couple stress theory to predict the mechanical and thermal buckling loads of micro plate reinforced composites. The effect of weight fraction of graphene nanoplatelets and various distributions of reinforcement was studied on the mechanical and thermal buckling loads. It is concluded that with increase of weight fraction of graphene nanoplatelets, the mechanical buckling loads are increased for all distributions, while the thermal buckling loads are increased for parabolic distribution, are decreased for linear distribution and are insensitive for uniform distribution.

Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces

Abstract: The paper analyses the wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. The two piezoelectric half-spaces (left and right) are both AlN materials, the middle piezoelectric semiconductor slab is ZnO material and is assumed to be transversely isotropic. The semiconductor effect is emphasized by considering the coupling mechanical displacement, electric potential and the carrier in the slab. The state transition differential equation is derived based on the reduction of order of the governing equations and the transfer matrix of state is obtained by solving the state transition equation. The present method can deal with not only the homogeneous slab but also the heterogeneous slab. Two cases (incident QP wave and incident QSV wave) are considered, and the energy reflection and transmission coefficients varying with the incident angle are calculated. The results show that the steady carrier density and the exterior biasing electric field have obvious influences on the reflection and transmission coefficients. This investigation provides a new thought for the adjustment and controlling of elastic wave propagation in the laminated structures.

A comparative study of EMD and EEMD approaches for identifying chatter frequency in CNC turning

Abstract: Tool chatter identification is one of the most important issues for today's researchers; as it adversely affects the tool life and surface finish which in turn reduces the overall productivity. In the past, researchers have proposed various techniques to compensate the effect of chatter. Signal processing is one such emerging technique that has proved to be quite efficient in exploring chatter. There are various approaches within this domain. Hilbert-Huang transform (HHT) is one of them. HHT is composed of empirical mode decomposition (EMD) and classical Hilbert transform (HT). EMD decomposes nearly any signal into a finite set of functions and a residue, whose Hilbert transform gives physical instantaneous frequency . However, there is a critical problem of mode mixing in EMD. To overcome this problem, a suitable EEMD approach has been adopted on experimentally acquired raw chatter signals in order to identify chatter frequency which has not been done by the previous researchers. In the present work, time-frequency analysis of experimentally acquired raw chatter signals have been done considering both EMD and EEMD techniques and thereafter their results have been compared to ascertain the suitability of each approach. It has been inferred from the present analysis that EEMD is quite apt in detecting chatter in turning operation with utmost accuracy.

Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation

Abstract: The main purpose of this paper is to provide a semi analytical method to analyze the free vibration of spherical-cylindrical-spherical shell subject to arbitrary boundary conditions. The formulations are established based on energy method and Flugge thin shell theory. The displacement functions are expressed by unified Jacobi polynomials and Fourier series . The arbitrary boundary conditions are simulated by penalty method about spring stiffness . The final solutions of spherical-cylindrical-spherical shell are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical example about spring stiffness, Jacobi parameters etc. are carried out. In addition, to verify the accuracy of this method, the results are compared with those obtained by FEM, experiment and published literature. The results show that the proposed method has ability to solve the free vibration behaviors of spherical-cylindrical-spherical shell.

Chaotic motion analysis of fluid-conveying viscoelastic nanotubes

Abstract: In the current analysis, an attempt is made to develop a nonlinear size-dependent fluid-structure interaction model for the chaotic motion of nanofluid-conveying nanotubes subject to an external excitation. The material properties of the nanotube are assumed to be viscoelastic. Size effects in both solid and fluid nanoscale parts are taken into consideration. In addition, the effects of both centripetal and Coriolis accelerations are incorporated in the model. Using Hamilton's principle , the nonlocal strain gradient elasticity and the Beskok-Karniadaki theory, the nonlinear size-dependent governing equation is derived. For developing a precise solution approach, Galerkin's procedure and a direct-time-integration method are eventually used. Different parameters of the nanosystem are taken into consideration to study the size-dependent chaotic motion of the viscoelastic nanotube conveying nanofluid subject to a harmonic excitation .

Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads

Abstract: Nonlinear free and forced vibration behavior of a porous functionally graded Euler-Bernoulli nanobeam subjected to mechanical and electrical loads is studied based on the nonlocal strain gradient elasticity theory. It is assumed that the porous functionally graded (FG) nanobeam is resting on a nonlinear foundation. Also, material properties of the nanobeam are assumed to vary in the thickness direction. Equations of motion are derived using Hamilton's principle. Galerkin method along with variation iteration method (VIM), Homotopy perturbation method (HPM), Hamiltonian approach method (HAM) and multiple scale method are employed to solve the governing equations based on clamped-clamped, simply-simply and clamped-simply boundary conditions. For verification purposes, the results of this study are compared with those of other studies. The effects of different parameters such as type of porosity distribution, nonlinear foundation, boundary conditions, electrical voltage and size effect parameters on the primary and secondary resonances were investigated. It was found that length-scale parameters have a crucial role on the nonlinear vibration behavior of such structures.

Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates

Abstract: This paper addresses the thermal buckling of actuated functionally graded piezoelectric porous nanoplates. Eringen's nonlocal elasticity theory with a higher-order shear deformation theory are used to obtain the analytical solution. The FGP porous nanoscale plate material possesses smooth continuous gradient transition of properties between materials as the dimension varies according to a modified power law function. The plate is under the influence of several thermal loadings (uniform, linear, nonlinear thermal difference) and electric voltages. A closed form solution of simply-supported FGP porous nanoplates is obtained using Navier's method. The critical thermal buckling of FGP porous nanoplates subjected to several thermal loadings and electric voltages is investigated. Numerical examples are presented to validate the present formulation. The influence of several porosity coefficients, small-scale parameters, thermal loadings, geometric parameters, power law exponents and external electrical voltages on the thermal buckling of FGP porous nanoplates are discussed.

A semi-analytical approach to analyze vibration characteristics of uniform and stepped annular-spherical shells with general boundary conditions

Abstract: In this paper, the free vibration characteristics of uniform and stepped annular-spherical shells are investigated by using a semi-analytical approach with general boundary conditions. The theoretical model of annular-spherical shell is established by using Flugge's thin shell theory, and the annular-spherical shells are divided into their segments along the axial direction. The displacement functions of shell segments are consist of the Jacobi polynomials along the axial direction and the standard Fourier series along the circumferential direction. The boundary conditions at the ends of the shells and the continuity conditions at two adjacent segments were enforced by penalty method of spring stiffness technique. Then, the accurate solutions about the vibration characteristics of uniform and stepped annular-spherical shells were solved by method of Rayleigh–Ritz. The accuracy and reliability of the proposed method are verified with the results of FEM and published literatures. The results show that the present method has good convergence ability and excellent accuracy. In addition, some numerical results of uniform and stepped annular-spherical shells with various geometric parameters and boundary conditions are reported, which can be used as reference data for future researchers.

Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment

Abstract: Analytical solutions for the nonlinear vibration of imperfect functionally graded nanocomposite (FG-CNTRC) double curved shallow shells on elastic foundations subjected to mechanical load in thermal environments are introduced in this paper. The double curved shallow shells are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction according to the different types of linear functions. Motion and compatibility equations are derived using Reddy's higher order shear deformation shell theory and taking into account the effects of initial geometrical imperfection and temperature – dependent properties. The deflection – time curve and the natural frequency are determined by using Galerkin method and fourth – order Runge – Kutta method. The effects geometrical parameters, elastic foundations, initial imperfection, temperature increment, mechanical loads and nanotube volume fraction on the nonlinear thermal vibration of the nanocomposite double curved shallow shells are discussed in numerical results. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory

Abstract: Based on nonlocal strain gradient theory (NSGT), transient behavior of a porous functionally graded (FG) nanoplate due to various impulse loads has been studied. The porous nanoplate has evenly and unevenly distributed pores inside its material structure. Impulse point loads are considered to be rectangular, triangular and sinusoidal types. These impulse loads lead to transient vibration of the nanoplate which is not studied before. NSGT introduces a nonlocal coefficient together with a strain gradient coefficient to characterize small size influences due to non-uniform stress and strain fields. Galerkin's approach has been performed to solve the governing equations and also inverse Laplace transform method is used to obtain transient response due to impulse loads. It is explained in this research that the transient response of a nanoplate is dependent on nonlocal coefficient, strain gradient parameter, pore dispersion, pore amount, type of impulse load and loading time.

Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load

Abstract: In this study, an improved finite element method is presented which can be used to analyse the transverse and axial vibrations of the functionally graded material (FGM) beams in a thermal environment and exposed to a mass moving at variable speed. The motion equations of the FGM beam were obtained using first order shear deformation theory (FSDT). In these equations, the interaction terms of the mass inertia are derived from the exact differential of the displacement functions of the beam relative to the mass contact point. For various temperature loads (homogeneous, linear and non-linear), thermal stresses are converted to mechanical stresses and then the thermal rigidity matrix is combined with the stiffness matrix of the beam. After verification of the method, the novel findings of the interaction of the moving mass with the FGM beam in different ceramic and metallic compositions are presented for uniform, linear and non-linear thermal loads and the variable speed of the mass.

Effect of radially graded porosity on the free vibration behavior of circular and annular sandwich plates

Abstract: Porous materials with functionally graded porosity are achieved by tailoring the size and density of the internal pores in one or more directions that leads the desired mechanical properties. Thus, due to the promotion of porous materials in engineering applications such as the foam core in sandwich plates, the compact heat exchangers , lightweight structures, biomedical systems and separation processes, in this paper, the free vibration of sandwich circular and annular plates with a core made of materials with functionally graded porosity are investigated. Different porosity distributions through the radial direction are introduced for the core of the plate. The governing equations of motion for the free vibration of a plate are obtained based on the first order shear deformation plate theory (FSDT). Clamped and simply supported edges are assumed for the plates. The collocation version of spectral method called the pseudo-spectral (PS) method using Chebyshev polynomials as the basis function is adopted to solve the equations of motion. Validation studies are also done to demonstrate the accuracy of the results. The natural frequencies of the clamped and simply-supported sandwich circular and annular plates with a porous core are calculated. The effects of different porosity distributions, porosity parameter, core thickness and geometric parameters on the results are investigated.

Nonlinear dynamic analysis of sandwich S-FGM plate resting on pasternak foundation under thermal environment

Abstract: In the present study, stress-function Galerkin (SFG) method is employed to investigate the dynamic characteristics of a new sigmoid law based sandwich functionally graded plate (S-FGM) plates resting of Pasternak elastic foundation in the thermal environment . For modified sigmoid law, a new temperature profile is derived considering 1D steady state heat conduction equation . The Hamiltonian formulation is done to derive governing equations and nonlinearity, due to Von- Karman strains, is worked out using Airy's function in conjunction with Galerkin's method. The time and frequency domain analysis is then performed using a numerical integration scheme and harmonic balance method, respectively. The nonlinear rise in temperature is considered across the thickness due to the temperature difference between the top and the bottom surface of the simply supported plate with immovable edges. Wide-Ranging parametric studies for, linear and nonlinear, frequency and time domain analysis have been performed by taking into consideration the effect of thickness ratio , inhomogeneity parameter, thermal load , and foundation parameter for various configurations of the sandwich plates. Poincare maps , phase-plane plots and time responses are demonstrated to study the nonlinear dynamics behavior of sandwich S-FGM plate under harmonic excitation . The variation of aspect ratios shows the route to chaos. With the Winkler foundation, the response is chaotic but becomes weakly chaotic with the introduction of the Pasternak type foundation. The dynamic response clearly shows the route to chaos with the varying thermal load from ΔT = 0–600 K. It is observed that the periodicity of the plate behavior is primarily affected by considering different configurations of the sandwich S-FGM plate. The computed results and observations can be utilized as a validation study for future examination for sandwich S-FGM plates.

Nonlinear vibrations of carbon fiber reinforced polymer laminated cylindrical shell under non-normal boundary conditions with 1:2 internal resonance

Abstract: In this paper, the nonlinear vibrations of a carbon fiber reinforced polymer (CFRP) laminated cylindrical shell are investigated with 1:2 internal resonance , primary parametric resonance and 1/2 subharmonic resonance. The radial line load and axial excitation are acting on the two free ends of the CFRP laminated cylindrical shell. The partial differential governing equations of motion for the CFRP laminated cylindrical shell are derived by utilizing the von-Karman type nonlinear geometric relationship, the first-order shear deformation theory and Hamilton principle . Galerkin method is used to obtain two-degrees-of-freedom nonlinear ordinary differential governing equations of motion along the radial displacement of the CFRP laminated cylindrical shell under the non-normal boundary conditions. The ordinary differential governing equations are solved as a system of four-dimensional average equations by the second-order approximate multiple scale method. The first two order dimensionless natural frequencies versus the ratio of length to thickness L / h , the frequency-response curves, the force-response curves, the bifurcation diagrams , the three-dimensional bifurcation diagrams, the maximum Lyapunov exponent diagrams, the phase portraits, the time history diagrams and the Poincare maps are obtained by numerical calculations. The influences of the radial line load, the axial excitation as well as the detuning parameter of the CFRP laminated cylindrical shell on the 1:2 internal resonant behaviors are investigated.

Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method

Abstract: One of the most important issues in the design of engineering structures is the prevention of structural failure due to the stress caused by geometric discontinuities . Hole geometry is one of the effective parameters in the distribution of stress and displacement around it. In this study, using the two-dimensional thermoelastic theory and based on the Likhnitskiiʼ complex variable technique, the stress analysis of orthotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a rectangular hole. To achieve this goal, a conformal mapping function is used to map an infinite plate containing a rectangular hole into the outside of a unit circle. Stress and displacement distributions around the rectangular hole in an orthotropic infinite plate are investigated in thermal steady state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition at the edge of the hole are considered. The rotation angle of the hole, fiber angle, the flux angle, bluntness and the aspect ratio of hole size are important parameters investigated in the present study. The obtained results show that these parameters have a significant effect on the stress and displacement distributions around the rectangular hole.

A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams

Abstract: In this study, for the first time, a nonlocal finite element model is proposed to analyse thermo-elastic behaviour of imperfect functionally graded porous nanobeams (P-FG) on the basis of nonlocal elasticity theory and employing a double-parameter elastic foundation. Temperature-dependent material properties are considered for the P-FG nanobeam, which are assumed to change continuously through the thickness based on the power-law form. The size effects are incorporated in the framework of the nonlocal elasticity theory of Eringen. The equations of motion are achieved based on first-order shear deformation beam theory through Hamilton's principle. Based on the obtained numerical results, it is observed that the proposed beam element can provide accurate buckling and frequency results for the P-FG nanobeams as compared with some benchmark results in the literature. The detailed variational and finite element procedure are presented and numerical examinations are performed. A parametric study is performed to investigate the influence of several parameters such as porosity volume fraction, porosity distribution, thermal loading, material graduation, nonlocal parameter, slenderness ratio and elastic foundation stiffness on the critical buckling temperature and the nondimensional fundamental frequencies of the P-FG nanobeams. Based on the results of this study, a porous FG nanobeam has higher thermal buckling resistance and natural frequencies compared to a perfect FG nanobeam. Also, the format of the porosity distribution is important, that uniform distributions of porosity result in greater critical buckling temperatures and vibration frequencies, in comparison with functional distributions of porosities.

Shape optimization of structures with cutouts by an efficient approach based on XIGA and chaotic particle swarm optimization

Abstract: Structural shape optimization is one important and crucial step in the design and analysis of many engineering applications as it aims to improve structural characteristics, i.e., reducing stress concentration and structural weight, or improving the stiffness, by changing the structural boundary geometries. The goal of this paper is to present an efficient approach, which goes beyond limitations of conventional methods, by combining extended isogeometric analysis (XIGA) and chaotic particle swarm optimization algorithm for shape optimization of structures with cutouts. In this setting, mechanical response of structures with cutouts is derived by the non-uniform rational B-spline (NURBS) and enrichment techniques. The computational mesh is hence independent of the cutout geometry, irrelevant to the cutout shape during the optimization process, representing one of the key features of the present work over classical methods. The control points describing the boundary geometries are defined as design variables in this study. The design model, analysis model, and optimization model are uniformly described with the NURBS, providing easy communication among the three aforementioned models, resulting in a smooth optimized boundary. The chaotic particle swarm optimization (CPSO) algorithm is employed for conducting the optimization analysis. Apart from that, the CPSO has some advantages as it includes: (i) its structure is simple and easy to implement; (ii) without the need for the complicated sensitivity analysis as compared with the traditional gradient-based optimization methods; and (iii) effectively escaping from the local optimum. The accuracy and performance of the developed method are underlined by means of several representative 2-D shape optimization examples.

Experimental and numerical investigations of the electro-viscoelastic behavior of VHB 4905TM

Abstract: Dielectric elastomers are a class of electro-active polymers (EAPs) that can be used for the development of simple soft actuators, sensors and energy harvesters. Their operation principle is based on the interaction of quasi-static electric charges in combination with soft dielectrics and deformable electrodes. Due to their ability to undergo large deformations with a time dependent material response of the underlying polymer, the mechanical behaviors of EAPs can be described by a finite strain viscoelastic material model [1]. This model is here augmented in order to account for the influence of the electro-mechanical coupling. In this contribution we pursue a comprehensive electro-mechanical characterization of the popular dielectric polymer VHB 4905™. In contrast to the results of the electro-mechanical experiments published previously [2] all of these experiments are conducted without the application of a pre-stretch and are therefore well suited for the identification of the coupling parameters of the material model. The presented model shows excellent agreements with experimental findings.

Modeling and simulation of droplet impact on elastic beams based on SPH

Abstract: Theoretical formulation of droplet impact on elastic beams is relatively difficult, due to its transient, non-stationary, and elasto-capillarity nature. In this study, a numerical model is proposed based on the smoothed particle hydrodynamics (SPH) method to simulate the impact process of a droplet on elastic beams. Both of the liquid droplet and the elastic substrate are modeled by SPH, and this feature ensures that the fluid-solid interaction can be solved in a unified framework. In addition, the continuum surface force (CSF) method is adopted to simulate the surface tension effect on the droplet impact. Robustness, concision and validity of the model are validated by simulating a single water drop impact on elastic super-hydrophobic beams. Interesting phenomena of droplet bouncing and beam vibrations are reproduced following the experiment. These analyses may be beneficial to engineering new materials and new devices in such areas as fabrics, agriculture, petroleum, and micro/nano technology.

Experimental investigation and theoretical modelling on nonlinear dynamics of cantilevered microbeams

Abstract: The nonlinear vibration of cantilever nickel microbeams with thickness in micron level is investigated through experiment and theory. A non-contact dynamic vibration measurement system is built to test the fundamental linear frequency and the nonlinear amplitude-frequency curves near the primary resonance . Experimental result reveals the nonlinear amplitude-frequency curves exhibit a marked weak softening-type behavior as well as hysteresis behavior . To elucidate the experimental observations, a modified couple stress-based Euler-Bernoulli beam model incorporating geometric and inertial nonlinearities is established. The derived partial differential equation of motion is converted into a set of ordinary differential equations (ODEs) by employing the Galerkin method. And then, the multi-dimensional Lindstedt-Poincare (L-P) method is applied to solve these ODEs. By comparing these analytical and experimental results, a good agreement is observed. Besides, a p -version Ritz method is combined with the iteration algorithm to reveal the close similarity of the beam and plate models and to further demonstrate the size-dependency in the nonlinear regime. Meanwhile the size-dependency in nonlinear regime is demonstrated. The effects of different order nonlinear terms , length scale parameter and damping coefficients on the system are investigated. It is illustrated that the period-doubling bifurcation occurs when imposing sufficiently large excitations, and it turns into chaos with increasing the excitations continuously.

Microscopic instabilities and elastic wave propagation in finitely deformed laminates with compressible hyperelastic phases

Abstract: In this paper, we study the elastic instability and wave propagation in compressible layered composites undergoing large deformations . We specifically focus on the role of compressibility on the onset of instability, and elastic wave band gaps (forbidden frequency ranges) in finitely deformed buckled laminates. We employ the Bloch-Floquet analysis to study the influence of compressibility on the onset of instability and the corresponding critical wavelengths . Then, the obtained information about the critical wavelengths is used in the subsequent numerical postbuckling simulations. By application of the Bloch wave numerical analysis implemented in the finite element code, we investigate the elastic wave band gaps of buckled layered composites with compressible phases. The compressible laminates require larger strains to trigger mechanical instabilities. This results in lower amplitudes of instability induced wavy patterns in compressible laminates as compared to incompressible layered materials. The instability induced wavy patterns give rise to tunability of the widths and locations of shear wave band gaps (that are not tunable by deformation in LCs with neo-Hookean phases in the stable regime); this tunability, however, is not significant in comparison to the tunability of the pressure wave band gaps. Thus, the complete band gaps (frequency ranges where neither shear nor pressure wave can propagate) can be controlled by deformation in both stable and post-buckling regimes.

Closed-form solution for nonlinear buckling analysis of FG-CNTRC cylindrical shells with initial geometric imperfections

Abstract: The circular cylindrical shells have been widely used in modern engineering structures, especially in the aerospace industry such as the oil pipeline, the missile, spacecraft hull, storage tanks. In recent years, functionally graded carbon nanotube composites (FG-CNTRCs) have emerged, as a promising type of composites. Due to the increasing demands for high structures performance, this research paper proposes a closed-form solution to investigate the nonlinear buckling behavior of the FG-CNTRC cylindrical shells subjected to compressive load. The small initial imperfections of the FG-CNTRC cylindrical shells are also considered through analytical modeling. Effective properties of materials of the shells reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micro-mechanical model based on the extended rule of mixtures. The Donnell shell theory and von-Karman nonlinear kinematics are used for nonlinear equilibrium equations. The novelty of this work is to exploit an exact solution via Galerkin procedure and term of the Airy stress function in order to reveal the impacts of the imperfection parameter, different types of CNTs distribution, the volume fraction of CNTs on nonlinear behavior and compressive equilibrium paths of FG-CNTRC cylindrical shells.

Influence of strain rate on fracture behavior of sandwich composite T-joints

Abstract: Applications of sandwich-structured composites gained increasing interest in aviation and aerospace industries as well as in modern lightweight design. In order to improve the reliability of computational models for the dimensioning of such structures, experimental data are indispensable prerequisites. In the current manuscript, the essential outcomes of experimental and numerical investigations of strain rate effects on the stiffness of honeycomb sandwich T-joints are presented. A series of static and dynamic tensile tests is carried out to understand the influence of different loading conditions on failure and fracture of honeycomb sandwich T-joints within strain rates up to 5000 s−1. A digital image correlation technique was employed to characterize the fracture behavior as well as to verify the strain gauges measurements. Failure modes of adhesively bonded sandwich T-joints are determined by a detailed fractographic analysis. In addition, numerical simulation was performed via three-dimensional finite element models using ABAQUS software, which exhibit excellent agreement with experimental results.