Showing papers in "Acta Mechanica in 2018"
TL;DR: In this article, the free vibration characteristics of a joined shell system that consists of three segments are considered, where two conical shells at the ends and a cylindrical shell at the middle are made from isotropic homogeneous material.
Abstract: The present research considers the free vibration characteristics of a joined shell system that consists of three segments. The joined shell system contains two conical shells at the ends and a cylindrical shell at the middle. All shell elements are made from isotropic homogeneous material. The shell elements are unified in thickness. With the aid of the first-order shear deformation shell theory and the Donnell type of kinematic assumptions, the equations of motion of a conical shell and the associated boundary conditions are obtained. These equations are valid for each segment. The obtained equations are then discreted using the generalised differential quadratures (GDQ) method. Applying the intersection continuity conditions for displacements, rotations, forces, and moments between two adjacent shells, and also boundary conditions at the ends of the joined shell system, a set of homogeneous equations is obtained, which governs the free vibration motion of the joined shell. Comparisons are made with the available data in the open literature for the case of thin conical–cylindrical–conical shells with special types of geometry or boundary conditions. Afterwards, numerical results are provided for moderately thick shells with different geometrical and boundary conditions.
73 citations
TL;DR: In this paper, a modified couple stress theory has been developed to capture the size effect in the small-size investigation of microbeams, where the microbeam is subjected to an inclined load of a linear combination of normal and tangential ones.
Abstract: This article presents a refined two-temperature multi-phase-lags thermoelasticity theory for the thermomechanical response of microbeams. The modified couple stress theory has been developed to capture the size effect in the small-size investigation. The microbeam is subjected to an inclined load of a linear combination of normal and tangential ones. Three partial differential equations of the modified couple stress microbeam are derived and solved exactly using the normal mode analysis. The influences of changing inclination angle, two-temperature parameter, and scale parameter on the field quantities like temperature, displacements, stresses, and couple stresses are investigated. Results of some earlier works are also deduced from the present investigation as special cases. Some comparisons are tabulated and presented graphically to estimate the effects of the scale parameter, the two-temperature parameter, the dual-phase-lags parameters, and the inclination angle. It is shown that the two-temperature parameter has a strong effect on the thermodynamic and conductive temperatures. However, the scale parameter and inclination angle have a very strong effect on all the field quantities of the microbeam.
67 citations
TL;DR: In this article, the roller length of a hydraulic jump on a rough channel bed is predicted using a novel, evolutionary, generalized structure design of a group method of data handling (GS-GMDH)-type neural network.
Abstract: Hydraulic jumps generally occur subsequent to structures such as ogee spillways, control gates, and weirs. The jump roller length is considered one of the main hydraulic jump parameters. In this study, the roller length of a hydraulic jump on a rough channel bed is predicted using a novel, evolutionary, generalized structure design of a group method of data handling (GS-GMDH)-type neural network. The topology of GMDH is designed with a genetic algorithm . Initially, the three most important non-dimensional parameters affecting hydraulic jump roller length, including the Froude number upstream of a hydraulic jump $$\left( {Fr} \right) $$
, the ratio of sequent depths $$\left( {{h_2 }/{h_1 }} \right) $$
, and the relative roughness $$\left( {{ks}/{h_1 }} \right) $$
were used to generate four different GS-GMDH models, and the most accurate model is identified. The best new GS-GMDH model prediction statistics, including RMSE, MARE, and correlation coefficient are 1.816, 0.081, and 0.966, respectively, while the scatter index and BIAS values are 0.084 and 1.45, respectively. A partial derivative sensitivity analysis of the input parameters for the new model is also performed. The new model predictions are then compared with predictions of a number of other models. The superior performance of the new GS-GMDH over these existing models is illustrated.
64 citations
TL;DR: In this article, an analytical approach to investigate the nonlinear dynamic response and vibration of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs) using first-order shear deformation theory and a stress function with full motion equations was presented.
Abstract: This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs) using first-order shear deformation theory and a stress function with full motion equations (not using Volmir’s assumptions). The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin–Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of the GPLRC layers. The plate is assumed to rest on a viscoelastic Pasternak medium and to be subjected to dynamic mechanical load in a thermal environment. Numerical results for the nonlinear dynamic response and vibration of functionally graded (FG) multilayer GPLRC plates are obtained by the Runge–Kutta method. The results show the influences of the GPL distribution pattern, weight fraction, geometry, foundation models, mechanical and temperature loads on the nonlinear dynamic response and vibration, natural frequencies and frequency–amplitude curves of FG multilayer GPLRC plates.
59 citations
TL;DR: In this article, the effects of vacancy defect on the elastic properties of carbon nanotubes (CNTs) were analyzed using molecular dynamics simulations with adaptive intermolecular reactive empirical bond order force fields.
Abstract: Molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order force fields were conducted to determine the transversely isotropic elastic properties of carbon nanotubes (CNTs) containing vacancies. This is achieved by imposing axial extension, twist, in-plane biaxial tension, and in-plane shear to the defective CNTs. The effects of vacancy concentrations, their position, and the diameter of armchair CNTs were taken into consideration. Current results reveal that vacancy defects affect (i) the axial Young’s and shear moduli of smaller-diameter CNTs more than the larger ones and decrease by 8 and 16% for 1 and 2% vacancy concentrations, respectively; (ii) the plane strain bulk and the in-plane shear moduli of the larger-diameter CNTs more profoundly, reduced by 33 and 45% for 1 and 2% vacancy concentrations, respectively; and (iii) the plane strain bulk and in-plane shear moduli among all the elastic coefficients. It is also revealed that the position of vacancies along the length of CNTs is the main influencing factor which governs the change in the properties of CNTs, especially for vacancy concentration of 1%. The current fundamental study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites.
58 citations
TL;DR: In this article, a nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of porous functionally graded nanoshells using nonlocal strain gradient theory.
Abstract: This paper studies the free vibrational behavior of porous functionally graded nanoshells using nonlocal strain gradient theory. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoshells. Porosities are evenly and unevenly distributed thorough the thickness of the nanoshell. The gradation of material properties having porosities is described using a modified power-law function. The nanoshell is modeled via first-order shear deformation theory, and Galerkin’s method is implemented to obtain vibration frequencies. Shape functions which satisfy available classical and nonclassical boundary conditions in nonlocal strain gradient theory are proposed. It is shown that the vibrational behavior of the nanoshell is influenced by the porosity volume fraction, porosity distribution, nonlocal coefficient, strain gradient coefficient, boundary conditions and radius-to-thickness ratio.
54 citations
TL;DR: In this paper, the size-dependent shear buckling force of FG nanoplates including porosities while resting on an elastic Kerr foundation and exposed to hygrothermal environment is analyzed.
Abstract: This article is motivated by the lack of a study on the size-dependent shear buckling force of functionally graded materials. In this study, the shear buckling force of imperfect FG nanoplates including porosities while resting on an elastic Kerr foundation and exposed to hygrothermal environment is analyzed. Three different templates of porosity distributions (even, uneven, and logarithmic-uneven distribution templates) are taken into account. Hamilton’s principle is employed to derive the governing equations based on a new polynomial quasi-three-dimensional (quasi-3D) shear deformation theory in conjunction with the Eringen nonlocal differential model (ENDM). Coupling effects between bending, shear, and thickness stretching are included by using the quasi-3D theory, and the size effects are considered by using the ENDM. Galerkin method is applied to find the shear buckling forces. A comparative study is given by using various structural models. By considering the size-dependent effects on the shear buckling of FG nanoplates, the influence of power-law index, porosity amount, and template, geometry, temperature, moisture, and elastic foundation components is explored.
53 citations
TL;DR: Considering its advantageous characteristics and its overall beneficial effects, TLCDs can be considered as practical and appealing means to control the seismic response of base-isolated structures.
Abstract: In this paper, the use of a tuned liquid column damper (TLCD) as a cost-effective means to control the seismic response of a base-isolated structure is studied. A straightforward direct approach for the optimal design of such a device is proposed, considering a white noise model of the base excitation. On this base, a direct optimization procedure of the TLCD design parameters is performed and optimal design charts are presented as a ready-to-use practical design tool. Comparison with the optimal parameters obtained considering a classical iterative statistical linearization technique proves the reliability of the proposed approach. The performance of the base-isolated TLCD-controlled structure is examined and compared with that of the simple base-isolated one (without TLCD), using a set of 44 recorded ground motions as base excitation. Theoretical and numerical results show that the TLCD is rather effective in reducing the response of base-isolated structures under strong earthquakes. Therefore, considering its advantageous characteristics and its overall beneficial effects, TLCDs can be considered as practical and appealing means to control the seismic response of base-isolated structures.
52 citations
TL;DR: In this article, the authors presented the vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak's medium using nonlocal plate theory.
Abstract: This article presents vibration characteristics of a piezoelectric viscoelastic nanoplate under various boundary conditions embedded in a visco-Pasternak’s medium using nonlocal plate theory. The piezo-hygrothermal effects are all included. The hygrothermal piezoelectric nanoplate is made of orthotropic viscoelastic material. Also, the visco-Pasternak’s medium is modeled according to a Kelvin–Voigt foundation. A Two-variable sinusoidal shear deformation plate theory is presented. The imaginary and real parts of the eigenfrequency of piezoelectric viscoelastic nanoplates which are associated with viscoelastic foundation, nonlocal parameter, as well as the viscoelastic structural damping coefficient, are obtained. The effects of other parameters such as aspect ratio, side-to-thickness ratio, temperature change, and moisture concentration are all investigated. The predicted results are compared with the corresponding ones in the literature to check their validation. Additional results are presented and suitable discussions are made.
52 citations
TL;DR: In this article, the effects of topography and inertia on gravity-driven film flows are discussed, and the effect of different types of topographies on creeping film flow and films in lubrication approximation is discussed.
Abstract: The present review deals with the effects of topography and inertia on gravity-driven film flows. The article is organized like a rope ladder, with the rungs of topography and inertia being scaled one after another. We begin with an introduction, where we specify the literature reviewed in our article and highlight the physical significance of this type of fluid motion. Next, we address the effects of different types of topographies on creeping film flow and films in lubrication approximation, and on inertial flow. Then, findings on inertial flow with sidewalls as bounding topography are reviewed. In all these cases, the impact of topography and inertia on both the free surface and the flow field structure is shown. Subsequently, we briefly highlight inverse problem theory. The following penultimate section focuses on the stability of film flows. After a short review on the stability of films over flat inclines which we give for convenience, the stability of films over topography is considered. A discussion on the stability of films with sidewalls as bounding topography follows. In each case, the interaction between topography, flow field, and free surface is shown with the theoretical and experimental methods being discussed. Finally, the paper closes with some concluding remarks and an outlook from the authors’ perspective—one century after the groundbreaking work of Wilhelm Nusselt.
50 citations
TL;DR: In this article, the effect of anisotropic distribution of reinforcing particles in a cubic representative volume element (RVE) of the carbon-polymer composite including stochastic interphases on its homogenized elastic characteristics is investigated.
Abstract: The main objective is to investigate an effect of anisotropic distribution of the reinforcing particles in a cubic representative volume element (RVE) of the carbon–polymer composite including stochastic interphases on its homogenized elastic characteristics. This is done using a probabilistic homogenization technique implemented using a triple approach based on the stochastic perturbation method, Monte Carlo simulation as well as on the semi-analytical approach. On the other hand, the finite element method solution to the uniform deformations of this RVE is carried out in the system ABAQUS. This composite model consists of two neighboring scales–the micro-contact scale relevant to the imperfect interface and the micro-scale—having 27 particles inside a cubic volume of the polymeric matrix. Stochastic interface defects in the form of semi-spheres with Gaussian radius are replaced with the interphase having probabilistically averaged elastic properties, and then such a three-component composite is subjected to computational homogenization on the microscale. The computational experiments described here include FEM error analysis, sensitivity assessment, deterministic results as well as the basic probabilistic moments and coefficients (expectations, deviations, skewness and kurtosis) of all the components of the effective elasticity tensor. They also include quantification of anisotropy of this stiffness tensor using the Zener, Chung–Buessem and the universal anisotropy indexes. A new tensor anisotropy index is proposed that quantifies anisotropy on the basis of all not null tensor coefficients and remains effective also for tensors other than cubic (orthotropic, triclinic and also monoclinic). Some comparison with previous analyses concerning the isotropic case is also included to demonstrate the anisotropy effect as well as the numerical effort to study randomness in composites with anisotropic distribution of reinforcements and inclusions.
TL;DR: The purpose of this investigation is to show that dealing with locking in fully parameterized ANCF elements is feasible and that several methods exist to effectively improve the AN CF element performance without sacrificing important ANCF element properties and features including position vector gradient continuity.
Abstract: This paper proposes a new locking alleviation technique for absolute nodal coordinate formulation (ANCF) beam and plate elements based on a strain split approach. The paper also surveys classical finite element (FE) and ANCF locking alleviation techniques discussed in the literature. Because ANCF beam elements, which allow for the cross-sectional stretch fully capture the Poisson effect, Poisson locking is an issue when such beam elements are considered. The two-dimensional fully parameterized ANCF beam element is primarily used in this investigation because such an element can serve as a good surrogate model for three-dimensional ANCF beams and plates as far as membrane, bending and transverse shearing behavior is concerned. In addition to proposing the strain split method (SSM) for ANCF locking alleviation, this work assesses the ANCF element performance in the cases of higher-order interpolation, enhanced assumed strain method, elastic line method, and the enhanced continuum mechanics approach, and demonstrates the design of the enhanced strain interpolation function by using the shape functions of higher-order ANCF elements. Additionally, a new higher-order ANCF two-dimensional beam element is proposed in order to compare its performance with other finite elements that require the use of other locking alleviation techniques proposed and reviewed in the paper. Finally, several numerical examples are shown to demonstrate the effectiveness of the locking alleviation methods applied to ANCF elements. The purpose of this investigation, apart from proposing a new locking alleviation technique, a new higher-order beam element, and comparing several existing locking alleviation techniques, is to show that dealing with locking in fully parameterized ANCF elements is feasible and that several methods exist to effectively improve the ANCF element performance without sacrificing important ANCF element properties and features including position vector gradient continuity. Because of the use of ANCF position vector gradients as nodal coordinates, complex stress-free initially-curved geometries can be systematically obtained. Such initially-curved geometries require special attention when attempting to solve locking problems, as will be discussed in this paper.
TL;DR: In this article, small-scale effects on the thermoelastic damping in microplates are studied and coupled governing equations of motion and heat conduction are obtained based on the non-classical continuum theory of the modified couple stress and the dual-phase-lag heat-conduction model.
Abstract: Thermoelastic damping (TED) is one of the main energy dissipation mechanisms in structures with small scales. On the other hand, the classical continuum theory is not capable of describing the mechanical behavior of small-scale structures. In this paper, small-scale effects on the thermoelastic damping in microplates are studied. To this end, the coupled governing equations of motion and heat conduction are obtained based on the non-classical continuum theory of the modified couple stress and the dual-phase-lag heat conduction model. By solving these coupled equations, an explicit expression including small-scale effects for calculating TED in microplates is derived. The results are compared with those given by the classical continuum and heat transfer theories. In addition, numerical results are presented to investigate the influences of some parameters on TED and critical thickness, such as microplate thickness, aspect ratio, boundary conditions, and the type of material.
TL;DR: In this paper, a dual-technique-based inline strategy was investigated as a sustainment to conventional techniques in terms of limitation of wave oscillation period spread-out, and the efficiency of the dual technique was considered for two operating conditions associated with up-and down-surge frames.
Abstract: A dual-technique-based inline strategy was investigated in this study as a sustainment to conventional-technique skills in terms of limitation of wave oscillation period spread-out. Instead of the single polymeric short section employed by the latter technique, the former is based on replacing an up- and downstream short section of the primitive piping system using another couple made of polymeric pipe-wall material. Numerical computations used the method of characteristics for the discretization of unconventional water-hammer model based on the Vitkovsky and the Kelvin–Voigt formulations. The efficiency of the dual technique was considered for two operating conditions associated with up- and downsurge frames. Moreover, two pipe-wall material types were utilized for short-section pipe wall, namely the HDPE or LDPE materials. Additionally, the conventional technique was also addressed in this study, for comparison purposes. First, analyses of pressure-head, circumferential-stress and radial-strain wave patterns, along with wave oscillation periods examination, confirmed that the dual technique could improve the efficiency of the conventional one, providing acceptable trade-off between the attenuation of pressure-head and circumferential-stress peaks (or crests), and limitation of period spreading and radial-strain amplification. Second, a parametric study of the sensitivity of the wave damping to the employed short-section dimensions was performed in terms of short-section length and diameter. This parametric study helped estimate the near-optimal values of the short-section dimensions.
TL;DR: In this article, the authors investigated the vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium based on nonlocal Euler-Bernoulli beam theory.
Abstract: In this study, vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium are investigated based on nonlocal Euler–Bernoulli beam theory In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived using Hamilton’s principle, where nonlocal effect, piezoelectric effect, flexoelectric effect, and viscoelastic medium are considered simultaneously Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient, and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium, and electrical loadings
TL;DR: In this paper, a thin-walled rotating pipe reinforced with functionally graded carbon nanotubes is modeled based on thinwalled Timoshenko beam theory and reinforced by singlewalled carbon nanotsubes with uniform distribution as well as three types of functionally graded distribution patterns.
Abstract: In this study, vibration and dynamic stability of fluid-conveying thin-walled rotating pipes reinforced with functionally graded carbon nanotubes are studied. The pipe is modeled based on thin-walled Timoshenko beam theory and reinforced by single-walled carbon nanotubes with uniform distribution as well as three types of functionally graded distribution patterns. The governing equations of motion and the associated boundary conditions are derived via Hamilton’s principle. The governing equations of motion are discretized via the Galerkin method, and the eigenfrequency and the stability region of the pipe are found using the eigenvalue analysis. Some numerical examples are presented to study the effects of length–radius ratio, carbon nanotubes distribution, volume fraction of carbon nanotubes, rotational speed and mass ratio on the non-dimensional eigenfrequency and critical flutter velocity of the thin-walled rotating pipe conveying fluid. The results show that the carbon nanotubes distribution has a significant effect on the non-dimensional eigenfrequency and critical flutter velocity. Also, it is found that the rotational speed has a stabilizing effect on the dynamic behavior of the system.
TL;DR: In this article, the buckling analysis of stiffened plates including curvilinear surfaces is carried out by an effective mesh-free model, which enables the assembly of curved shells for the modeling of more complex structures.
Abstract: A buckling analysis of stiffened plates including curvilinear surfaces is carried out by an effective meshfree model. The buckling loads and modes computed by the present method are analyzed. Six degrees of freedom (6-DOFs) curved shell meshfree formulation in a convected coordinate system including a drilling rotation component is employed, which enables the assembly of curved shells for the modeling of more complex structures. By this formulation, the assembly of any arbitrary shape of geometry can be modeled in convected coordinates, while the 5-DOFs shell formulation suffers from the modeling of shell assemblies. Particularly, curved shells with straight stiffeners and plates with curvilinear stiffeners are considered. Furthermore, a twisted T-shaped structure where both web and flange have curvilinear geometry is analyzed. A meshfree discretization is employed, with which the reproducing kernel particle method is used as the meshfree interpolant. A boundary singular kernel method is adopted to precisely impose an essential boundary condition and to model folded shell geometries. The accuracy and effectiveness of the proposed method are demonstrated by several shell buckling problems for stiffened plate structures with curvilinear surfaces. The obtained meshfree results are compared with the linear and quadratic shell element results of finite element method ANSYS and discussed.
TL;DR: In this paper, the authors used molecular mechanics/molecular dynamics (MM/MD) methods to fit the DREIDING force field parameters (see Mayo et al. 1990) to most closely reproduce the mechanical parameters of graphene (Young's modulus, Poisson's ratio, bending rigidity modulus and intrinsic strength).
Abstract: Molecular mechanics/molecular dynamics (MM/MD) methods are widely used in computer simulations of deformation (including buckling, vibration, and fracture) of low-dimensional carbon nanostructures (single-layer graphene sheets (SLGSs), single-walled nanotubes, fullerenes, etc). In MM/MD simulations, the interactions between carbon atoms in these nanostructures are modeled using force fields (e.g., AIREBO, DREIDING, MM3/MM4). The objective of the present study is to fit the DREIDING force field parameters (see Mayo et al. J Phys Chem 94:8897–8909, 1990) to most closely reproduce the mechanical parameters of graphene (Young’s modulus, Poisson’s ratio, bending rigidity modulus, and intrinsic strength) known from experimental studies and quantum mechanics simulations since the standard set of the DREIDING force field parameters (see Mayo et al. 1990) leads to unsatisfactory values of the mechanical parameters of graphene. The values of these parameters are fitted using primitive unit cells of graphene acted upon by forces that reproduce the homogeneous deformation of this material in tension/compression, bending, and fracture. (Different sets of primitive unit cells are used for different types of deformation, taking into account the anisotropic properties of graphene in states close to failure.) The MM method is used to determine the dependence of the mechanical moduli of graphene (Young’s modulus, Poisson’s ratio, and bending rigidity modulus) on the scale factor. Computer simulation has shown that for large linear dimensions of SLGSs, the mechanical parameters of these sheets are close to those of graphene. In addition, computer simulation has shown that accounting for in-layer van der Waals forces has a small effect on the value of the mechanical moduli of graphene.
TL;DR: In this paper, a four-variable plate model is successfully extended to investigate the thermal buckling analysis of advanced nanoplates, where the advanced nanoplate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the nanoplate thickness.
Abstract: A four-variable plate model is successfully extended here to investigate the thermal buckling analysis of advanced nanoplates. The advanced nanoplate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the nanoplate thickness. Two types of thermal loadings, uniform and nonlinear temperature rises along the nanoplate thickness are taken into consideration. The present model contains four unknown functions as against five or more in other alternative models. The through-the-thickness distributions of transverse shear stresses of the nanoplate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem-dependent shear correction factor. Comparison examples are made between results obtained via this model and those via available solutions in the literature.
TL;DR: In this article, an arbitrary Lagrangian-Eulerian (ALE) formulation of a Timoshenko beam based on geometrically exact beam theory, which considers the rotation around the axis of the beam, is presented.
Abstract: When a beam moves through a curved tube, there exists a large number of contacts between the beam and the inner wall of the tube. Usually, it is necessary to use fine Lagrangian meshes to discretize the beam for possible contact area in order to obtain sufficiently accurate results, even if the contact is only once for a very short time. Accordingly, the computation process is very time-consuming due to the large number of degrees of freedom (DOF) of the discretized system. To solve this problem, an Arbitrary Lagrangian–Eulerian (ALE) formulation of a Timoshenko beam based on geometrically exact beam theory, which considers the rotation around the axis of the beam, is presented in this paper. In this formulation, the mesh nodes of the beam are not associated with the material points, which provides the flexibility to mesh the beam freely. For this reason, the ALE mesh nodes can be arranged along the tube and constrained to move just within the corresponding tube cross section. The axial movement of the beam can be described by the material points flowing through the axially constrained mesh nodes. In so doing, only the beam in the high-curvature section of the tube needs to be finely meshed, resulting in a significant reduction of the DOF of the whole system. Several examples are presented and discussed to demonstrate the correctness and efficiency of the proposed method.
TL;DR: The size-dependent nonlinear instability of microtubules embedded in the biomedium of a living cell and under hydrostatic pressure is analyzed at different temperatures and it is observed that for a microtubule under hydro static pressure, an initial extension occurs in the prebuckling regime until the critical buckling pressure.
Abstract: As one of the most important components of a cytoskeleton, microtubules made from tubular polymers of tubulin can be found throughout the cytoplasm of eukaryotic cells. The role of microtubules in maintaining the structures of a living cell under external mechanical load is essential, so it is necessary to anticipate their size-dependent mechanical characteristics. In the present study, the size-dependent nonlinear instability of microtubules embedded in the biomedium of a living cell and under hydrostatic pressure is analyzed at different temperatures. For this objective, a more comprehensive size-dependent elasticity theory such as nonlocal strain gradient theory of elasticity is implemented to a refined hyperbolic shear deformation shell theory. Through deduction of the nonclassical governing equations to boundary layer-type ones and then employing a two-stepped perturbation solving process, explicit analytical expressions are established for nonlocal strain gradient stability paths of hydrostatic pressurized microtubules surrounded by the cytoplasm of a living cell. It is observed that for a microtubule under hydrostatic pressure, an initial extension occurs in the prebuckling regime until the critical buckling pressure. The nonlocality size effect decreases this initial extension, but the strain gradient size dependency increases it.
TL;DR: In this article, a geometrically nonlinear formulation for a six-node triangular shell element is proposed to avoid shear and membrane locking, a proper interpolation function for the strain field is implemented Both algorithm and flowchart of the nonlinear solution, which are utilized in the author's computer program, are presented to validate the suggested formulation.
Abstract: In this paper, a geometrically nonlinear formulation for a six-node triangular shell element is proposed Total Lagrangian formulation is utilized to consider large displacements and rotations in the shell analysis To avoid shear and membrane locking, a proper interpolation function for the strain field is implemented Both algorithm and flowchart of the nonlinear solution, which are utilized in the author’s computer program, are presented To validate the suggested formulation, several popular benchmark problems are solved Moreover, the obtained results are compared with those of the other well-known elements Findings demonstrate the ability of the suggested shell element
TL;DR: In this paper, new solutions are presented to examine large amplitude vibration of a porous nanoplate resting on a nonlinear hardening elastic foundation modeled by nonlinear four-variable plate theory, and the closed-form expression of the nonlinear frequency is obtained using a novel Hamiltonian approach as well as homotopy perturbation method for the first time.
Abstract: In this paper, new solutions are presented to examine large amplitude vibration of a porous nanoplate resting on a nonlinear hardening elastic foundation modeled by nonlinear four-variable plate theory. The closed-form expression of the nonlinear frequency is obtained using a novel Hamiltonian approach as well as homotopy perturbation method for the first time. Another novelty of these approaches is that they are needless of any iterative process. Based on a modified rule of mixture, the nanopores or nanovoids are considered in the model. Nonlinear governing equations of a four-variable nanoplate with von Karman geometric nonlinearity are obtained using Hamilton’s principle. The dependency of the nonlinear frequency on the porosities, scale parameter, maximum amplitude, material gradation, foundation parameters and geometrical parameters is explored. The proposed solution approach and also obtained results can be used in future investigations on nanostructures.
TL;DR: In this paper, the authors investigated the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads, and developed coupled and nonlinear equilibrium equations for the case of simply supported arches.
Abstract: The present investigation deals with the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads. The structure is resting on a three-parameter elastic foundation containing the Winkler springs, the shear Pasternak layer, and hardening nonlinear springs. The arch is made of a through-the-thickness functionally graded material. Except for Poisson’s ratio, the other properties of the arch are assumed to be temperature and position dependent. Each property is estimated according to the rule of mixtures in terms of the volume fraction of the constituents. The case of uniform temperature rise and uniform radial lateral load is considered. The governing equations of the arch are obtained with the aid of the third-order shear deformation arch theory and the von Karman type of geometrical nonlinearity. The developed coupled and nonlinear equilibrium equations are solved using the two-step perturbation technique for the case of simply supported arches. Closed-form expressions are developed for nonlinear bending equilibrium path of shallow arches under thermal and mechanical loads. Results are provided for different power law indices, geometrical parameters, and the foundation stiffness.
TL;DR: In this article, the authors analyzed the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams exposed to axial supersonic airflow in thermal environments.
Abstract: The purpose of this study is to analyze the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams exposed to axial supersonic airflow in thermal environments. The dynamic model of the FG-CNTRC beam is developed with regard to the first-order shear deformation theory incorporating the von Karman geometrical nonlinearity. The thermomechanical properties of the constituents are assumed to be temperature dependent. The third-order piston theory is adopted to estimate the nonlinear aerodynamic pressure induced by the supersonic airflow. Harmonic differential quadrature method is implemented to discretize the equations of motion in the spatial domain. A comprehensive parametric study is performed to expatiate on the effect of the distribution type and volume fraction of CNTs, boundary condition, slenderness ratio, and thermal environments on the aerothermoelastic responses of the FG-CNTRC beam. Simulation results indicate that the presence of the aerodynamic pressure not only increases the critical buckling temperature of the FG-CNTRC beam, but also changes the buckling mode shapes of the beam. Furthermore, the results show that aerothermoelastic characteristics of FG-CNTRC beams may be remarkably improved by the selection of a proper distribution of CNTs. Besides, it is found that FG-CNTRC beams with intermediate CNT volume fraction do not have an intermediate critical buckling temperature.
TL;DR: In this article, a size-dependent, nonlinear beam model for bending, buckling and free vibrations of electrically actuated viscoelastic clamped-clamped microbeams is presented.
Abstract: This paper presents a size-dependent, nonlinear beam model for bending, buckling and free vibrations of electrically actuated viscoelastic clamped–clamped microbeams. The modified couple stress theory is used to model the size effect. The Euler–Bernoulli beam model including von Karman geometric nonlinearity and intermolecular van der Waals and Casimir forces is adopted. The Boltzmann superposition viscoelastic model is used to simulate the linear behavior of the viscoelastic material. The governing integral–differential equation and corresponding boundary conditions are obtained using Hamilton’s principle. Galerkin’s discretization is used to obtain a reduced-order model of the problem. The quasi-elastic method is used to approximate the viscoelastic behavior. The model has been verified by comparing some results with those available in the literature, and a good agreement is obtained. The influence of the small size, creep modulus, relaxation time and intermolecular forces on the electrostatic bending, buckling and free vibrations are investigated and found significant.
TL;DR: In this article, a moving Kriging mesh free method based on a naturally stabilized nodal integration (NSNI) was proposed for bending, free vibration and buckling analyses of isotropic and sandwiched functionally graded plates within the framework of higher-order shear deformation theories.
Abstract: This paper presents a moving Kriging meshfree method based on a naturally stabilized nodal integration (NSNI) for bending, free vibration and buckling analyses of isotropic and sandwiched functionally graded plates within the framework of higher-order shear deformation theories. A key feature of the present formulation is to develop a NSNI technique for the moving Kriging meshfree method. Using this scheme, the strains are directly evaluated at the same nodes as the direct nodal integration (DNI). Importantly, the computational approach alleviates instability solutions in the DNI and significantly decreases the computational cost from using the traditional high-order Gauss quadrature. Being different from the stabilized conforming nodal integration scheme which uses the divergence theorem to evaluate the strains by boundary integrations, the NSNI adopts a naturally implicit gradient expansion. The NSNI is then integrated into the Galerkin weak form for deriving the discrete system equations. Due to satisfying the Kronecker delta function property of the moving Kriging integration shape function, the enforcement of essential boundary conditions in the present method is similar to the finite element method. Through numerical examples, the effects of geometries, stiffness ratios, volume fraction and boundary conditions are studied to prove the efficiency of the present approach.
TL;DR: In this article, the bi-Helmholtz operator was applied to the non-local integral model for the purpose of describing wave dispersion of atomic models, and the results showed that the Bi-Heltz operator is more suitable for the nonlocal integral form's suitability for dealing with problems in nanoscale.
Abstract: There are exhaustive reports revolving around the nonlocal differential beam models of micro- and nano-electromechanical systems (MEMS–NEMS), carbon nanotubes (CNTs), nanomaterials, etc., since the nonlocal continuum theory is considered a viable option for shedding light on size effect phenomena. A constitutive equation with a second-order differential operator, Helmholtz type, is employed in these studies. However, these models do not produce quadratic, self-adjoint energy functionals and give rise to paradoxes in static and dynamical problems. The transformation of Eringen’s integral constitutive equation into a differential one is not an injective process in a finite domain and that is probably responsible for the inconsistencies and paradoxes raised. This work researches into the adequacy of a higher-order differential operator, bi-Helmholtz type, applied to engineering problems. The bi-Helmholtz-type operator is more effective for describing wave dispersion of atomic models than the Helmholtz type. Eringen’s nonlocal integral stress model is also looked into beams for both types of kernels. The nonlocal integral model’s key benefit is the energy consistent formulas produced, whereas its main drawback lies in the handling of the 1st kind Fredholm governing equation. Exploiting the modified nonlocal attenuation function (kernel) normalized in a finite domain, the 1st kind Fredholm integral equation is directly transformed into a 2nd kind one. Furthermore, the modified kernel successfully handles the physical inconsistencies in a finite domain, such as the reversion of the nonlocal integral stress model to the classic-local model when the nonlocal parameter tends to zero. Our research objective is to explore bi-Helmholtz operator’s application and the corresponding kernel in the nonlocal integral model. The results deduced and the conclusions reached can be considered adequate for the nonlocal integral form’s suitability for dealing with problems in nanoscale.
TL;DR: In this paper, the authors investigated the size-dependent quality factor of microbeam damping in a microbeam resonator based on modified strain gradient elasticity theory and derived the governing differential equation of motion by using the principle of virtual displacements.
Abstract: The present study aimed to investigate the size-dependent quality factor of thermoelastic damping in a microbeam resonator based on modified strain gradient elasticity theory. The governing differential equation of motion is derived by using the principle of virtual displacements. The generalized thermoelasticity theory of the well-known Lord–Shulman model is also utilized to derive the equation of coupled thermoelasticity. The quality factor of thermoelastic damping in the microbeam is obtained based on both the complex frequency and the entropy generation methods. Further, by applying the generalized thermoelasticity theory and entropy generation method, explicit formulae for the quality factor of thermoelastic damping in the microbeam resonators are developed in the frameworks of both classical and modified couple stress elasticity theories. The effects of several parameters including size effect are investigated on thermoelastic damping in cantilever and clamped–clamped silicon microbeams as case studies. The results are validated by observing an excellent agreement regarding the comparison of the results of the present study and with previously published results.
TL;DR: In this article, a finite element method approach coupled with a direct integration algorithm is developed for efficiently tracing the nonlinear dynamic response of the beam-foundation system under the action of a transverse concentrated load, moving at a constant velocity along the beam, displaying an harmonic-varying magnitude in time.
Abstract: The present paper is concerned with the numerical modelization of the transient dynamic response of a simply supported Euler–Bernoulli elastic beam resting on a Winkler-type foundation, under the action of a transverse concentrated load, moving at a constant velocity along the beam, displaying an harmonic-varying magnitude in time. The elastic foundation, assumed as homogeneous in space, behaves according to a bilinear constitutive law, characterized by two different stiffness coefficients in compression and in tension. A finite element method approach coupled with a direct integration algorithm is developed for efficiently tracing the nonlinear dynamic response of the beam-foundation system. An original automated procedure is set, as being apt to resolve all required space/time discretization issues. Extensive parametric numerical analyses are performed to investigate how the frequency of the harmonic moving load amplitude and the ratio between the foundation’s moduli in compression and in tension affect the so-called critical velocities of the moving load, leading to high transverse beam deflections. Analytical interpolating expressions are proposed and fitted for the achieved two-branch critical velocity trends. The present outcomes shall reveal potential practical implications in scenarios of contemporary railway engineering, especially in terms of lowering down the admissible high-speed train velocities, as for structural requirement or preventing potential passenger discomfort.