Showing papers on "Orthotropic material published in 2017"
TL;DR: In this article, a linear elastic second gradient orthotropic two-dimensional solid that is invariant under 90-degree rotation and for mirror transformation is considered, and analytical solutions for simple problems, referred to the heavy sheet, to the nonconventional bending, and to the trapezoidal cases, are developed and presented.
Abstract: A linear elastic second gradient orthotropic two-dimensional solid that is invariant under $$90^{\circ }$$
rotation and for mirror transformation is considered. Such anisotropy is the most general for pantographic structures that are composed of two identical orthogonal families of fibers. It is well known in the literature that the corresponding strain energy depends on nine constitutive parameters: three parameters related to the first gradient part of the strain energy and six parameters related to the second gradient part of the strain energy. In this paper, analytical solutions for simple problems, which are here referred to the heavy sheet, to the nonconventional bending, and to the trapezoidal cases, are developed and presented. On the basis of such analytical solutions, gedanken experiments were developed in such a way that the whole set of the nine constitutive parameters is completely characterized in terms of the materials that the fibers are made of (i.e., of the Young’s modulus of the fiber materials), of their cross sections (i.e., of the area and of the moment of inertia of the fiber cross sections), and of the distance between the nearest pivots. On the basis of these considerations, a remarkable form of the strain energy is derived in terms of the displacement fields that closely resembles the strain energy of simple Euler beams. Numerical simulations confirm the validity of the presented results. Classic bone-shaped deformations are derived in standard bias numerical tests and the presence of a floppy mode is also made numerically evident in the present continuum model. Finally, we also show that the largeness of the boundary layer depends on the moment of inertia of the fibers.
151 citations
TL;DR: In this article, the bending, buckling and buckling of embedded nano-sandwich plates are investigated based on refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first order shear deformability theory (FSDT), and classical plate theory (CPT).
124 citations
TL;DR: In this paper, the Dragonfly Algorithm (DA) was used to calculate the stress distribution based on Lekhnitskii's analytical solution for perforated orthotropic plates.
Abstract: This paper aims at optimizing the parameters involved in the stress analysis of perforated orthotropic plates, to achieve the lowest value of stress around the quasi-triangular cut-out located in an infinite orthotropic plate by using the Dragonfly Algorithm (DA) method. This method is used to calculate the stress distribution based on Lekhnitskii's analytical solution. The study design variables include fiber angle, load angle, bluntness, orientation angle of cut-out and the material properties. In addition, the performance of the DA algorithm is compared with the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The comparison of these methods indicates the appropriateness of the DA algorithm in optimizing the perforated plates. The finite element method has been used to verify the accuracy of the analytical results. The results indicate that by selecting the aforementioned parameters properly, we can increase the structural load-bearing capacity.
113 citations
TL;DR: In this paper, a piezoelectric sandwich plate is used to simulate the orthotropic visco-Pasternak model and a proportional-derivative (PD) controller is employed to control the phase velocity in the structure.
111 citations
TL;DR: In this paper, the surface energy effect on the nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells was investigated using the electro-elastic surface/interface model.
Abstract: In this paper, the electro-elastic surface/interface model is introduced to investigate the surface energy effect on the nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. On the basis of classical shell theory and von-Karman-Donnell-type geometric nonlinearity, the fundamental equations for vibration are given. By considering the constitute relations for surfaces, the total energy of the orthotropic piezoelectric cylindrical nano-shell is obtained. The governing equations of motion are derived from Hamilton's principle and solved by using the homotopy perturbation method (HPM). Afterwards, the results without surface effect are compared and validated with the datum available in the literature, and the influences of surface parameters and geometric characteristics on the nonlinear free vibration of the orthotropic piezoelectric cylindrical nano-shell are examined.
88 citations
TL;DR: In this article, a unified formulation which is based on a general refined shear deformation beam theory is presented to conduct free vibration analysis of composite laminated beams subjected to general boundary conditions.
Abstract: In this paper, a unified formulation which is based on a general refined shear deformation beam theory is presented to conduct free vibration analysis of composite laminated beams subjected to general boundary conditions. In the refined theory model, the displacement fields are chosen by including the high-order variation of transverse shear strain through the thickness of the beam and meeting the stress-free boundary conditions on both the top and bottom surfaces. With considering the material couplings and the Poisson's effect, the governing equations and appropriate boundary conditions are derived from the Hamilton's principle. Exact solutions are obtained by employing the method of reverberation ray matrix (MRRM). In order to implement general boundary conditions, the artificial spring boundary technique is introduced in the MRRM to make it suitable for different boundary cases. The present solutions are compared with those available in the literature to confirm their validity. A systematic parameter study for composite beams with various boundary conditions, fiber orientations, lamina numbers and orthotropic ratios is also performed. New results for free vibration involving composite laminated beams with various boundary constraints are also presented for the first time and they may be served as benchmark for researchers in this field.
83 citations
TL;DR: This work proposes a novel metamaterial with controllable, freely orientable, orthotropic elastic behavior - orthotropy means that elasticity is controlled independently along three orthogonal axes, which leads to materials that better adapt to uneven, directional load scenarios, and offer a more versatile material design primitive.
Abstract: Additive manufacturing enables the fabrication of objects embedding meta-materials. By creating fine-scale structures, the object's physical properties can be graded (e.g. elasticity, porosity), even though a single base material is used for fabrication. Designing the fine and detailed geometry of a metamaterial while attempting to achieve specific properties is difficult. In addition, the structures are intended to fill comparatively large volumes, which quickly leads to large data structures and intractable simulation costs. Thus, most metamaterials are defined as periodic structures repeated in regular lattices. The periodicity simplifies modeling, simulation, and reduces memory costs - however it limits the possibility to smoothly grade properties along free directions. In this work, we propose a novel metamaterial with controllable, freely orientable, orthotropic elastic behavior - orthotropy means that elasticity is controlled independently along three orthogonal axes, which leads to materials that better adapt to uneven, directional load scenarios, and offer a more versatile material design primitive. The fine-scale structures are generated procedurally by a stochastic process, and resemble a foam. The absence of global organization and periodicity allows the free gradation of density, orientation, and stretch, leading to the controllable orthotropic behavior. The procedural nature of the synthesis process allows it to scale to arbitrarily large volumes at low memory costs. We detail the foam structure synthesis, analyze and discuss its properties through numerical and experimental verifications, and finally demonstrate the use of orthotropic materials for the design of 3D printed objects.
72 citations
TL;DR: In this paper, the non-linear free vibration behavior of functionally graded (FG) orthotropic cylindrical shells interacting with the two-parameter elastic foundation is investigated, and the results are compared and validated with the results available in the literature.
Abstract: The non-linear free vibration behavior of functionally graded (FG) orthotropic cylindrical shell interacting with the two-parameter elastic foundation is investigated. The major goal of this research was to obtain a solution for the non-linear frequencies associated with the problem outlined above. The dynamic stability and compatibility equations of FG orthotropic cylindrical shells surrounded by an elastic foundation are derived within the first order shear deformation theory (FSDT) and von Karman strain displacement relationships, and then superposition and Galerkin methods are adopted to convert the above equations into a nonlinear ordinary differential equation. The expression for non-linear frequency of FG orthotropic cylindrical shell surrounded by an elastic foundation within the FSDT is obtained using the homotopy perturbation method (HPM). In particular, similar expression in the framework of the classical shell theory (CST) is obtained, also. The results are compared and validated with the results available in the literature. Finally, the calculation and presentation of the effect of many parameters included in the analysis conclude the goals to be reached in the study.
69 citations
TL;DR: It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them.
67 citations
TL;DR: In this paper, the dynamic behavior of double layered nanoplate systems (DLNPS) with respect to a moving nanoparticle is investigated, where both layers of DLNPS are assumed to be orthotropic and each layer is bearing a biaxial load while internal damping effects are also taken into account.
59 citations
TL;DR: In this article, the effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) are studied considering five different boundary conditions.
Abstract: In this paper, the small scale effect on the vibration behavior of orthotropic single layered graphene sheets is studied based on the nonlocal Reddy's plate theory embedded in elastic medium with considering initial shear stress. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. To simulate the interaction between the graphene sheet and surrounding elastic medium we used both Winkler-type and Pasternak-type foundation models. The effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) are studied considering five different boundary conditions. Numerical approach of the obtained equation is derived by differential quadrature method (DQM). Effects of shear stress, nonlocal parameter, size of the graphene sheets, stiffness of surrounding elastic medium and boundary conditions on vibration frequency rate are investigated. ...
TL;DR: In this article, a spherocylindrical microplane constitutive model was proposed for the inelastic fracturing behavior of orthotropic materials, and particularly the shale, which is transversely isotropic and is important for hydraulic fracturing (aka fracking) as well as many geotechnical structures.
Abstract: Constitutive equations for inelastic behavior of anisotropic materials have been a challenge for decades. Presented is a new spherocylindrical microplane constitutive model that meets this challenge for the inelastic fracturing behavior of orthotropic materials, and particularly the shale, which is transversely isotropic and is important for hydraulic fracturing (aka fracking) as well as many geotechnical structures. The basic idea is to couple a cylindrical microplane system to the classical spherical microplane system. Each system is subjected to the same strain tensor while their stress tensors are superposed. The spherical phase is similar to the previous microplane models for concrete and isotropic rock. The integration of stresses over spherical microplanes of all spatial orientations relies on the previously developed optimal Gaussian integration over a spherical surface. The cylindrical phase, which is what creates the transverse isotropy, involves only microplanes that are normal to plane of isotropy, or the bedding layers, and enhance the stiffness and strength in that plane. Unlike all the microplane models except the spectral one, the present one can reproduce all the five independent elastic constants of transversely isotropic shales. Vice versa, from these constants, one can easily calculate all the microplane elastic moduli, which are all positive if the elastic in-to-out-of plane moduli ratio is not too big (usually less than 3.75, which applies to all shales). Oriented micro-crack openings, frictional micro-slips and bedding plane behavior can be modeled more intuitively than with the spectral approach. Data fitting shows that the microplane resistance depends on the angle with the bedding layers non-monotonically, and compressive resistance reaches a minimum at 60°. A robust algorithm for explicit step-by-step structural analysis is formulated. Like all microplane models, there are many material parameters, but they can be identified sequentially. Finally, comparisons with extensive test data for shale validate the model.
TL;DR: In this article, a bond-based peridynamic model was developed to study in-plane dynamic fracture process in orthotropic composites and the model was extended to a continuous micromodulus C θ for orthotropic materials.
TL;DR: In this paper, the authors investigated the plane frictional contact problem of a cylindrical punch on a functionally graded orthotropic medium (FGOM) and developed analytical and computational methods to obtain the contact stresses.
TL;DR: An analytical solution of the buckling problem formulated for a composite cylindrical shell with its ends closed by rigid disks and subjected to hydrostatic pressure is presented in this article, where the problem is solved using Fourier decomposition and the Galerkin method.
TL;DR: In this article, a viscoelastic model for single-ply cylindrical shells (tape springs) that are deployed after being held folded for a given period of time is presented.
Abstract: The viscoelastic behavior of polymer composites decreases the deployment force and the postdeployment shape accuracy of composite deployable space structures. This paper presents a viscoelastic model for single-ply cylindrical shells (tape springs) that are deployed after being held folded for a given period of time. The model is derived from a representative unit cell of the composite material, based on the microstructure geometry. Key ingredients are the fiber volume density in the composite tows and the constitutive behavior of the fibers (assumed to be linear elastic and transversely isotropic) and of the matrix (assumed to be linear viscoelastic). Finite-element-based homogenizations at two scales are conducted to obtain the Prony series that characterize the orthotropic behavior of the composite tow, using the measured relaxation modulus of the matrix as an input. A further homogenization leads to the lamina relaxation ABDABD matrix. The accuracy of the proposed model is verified against the experimentally measured time-dependent compliance of single lamina in either pure tension or pure bending. Finite element simulations of single-ply tape springs based on the proposed model are compared to experimental measurements that were also obtained during this study.
TL;DR: In this article, the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of a three-phase-lag model of thermo-elasticity is studied.
Abstract: The present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The freq...
TL;DR: In this paper, the free vibration analysis of rotating truncated conical conical shells, circular shells and panels was performed using the discrete singular convolution (DSC) method.
TL;DR: In this article, an isogeometric finite element method on the basis of non-uniform rational B-spline (NURBS) basis functions is developed for the in-plane vibration problems of various orthotropic shaped plates with general boundary restraints, which include rectangular plate with hole, rhombic, trapezoidal and quadrilateral plates.
TL;DR: In this article, the authors investigated the stochastic dynamic response and reliability analysis of membrane structure under impact load obeying Gaussian distribution, and the model proposed provides some theoretical basis for the stochiastic vibration control and dynamic design of orthotropic membrane structure based on reliability theory.
Abstract: Orthotropic membrane structure is widely applied in construction buildings, mechanical engineering, electronic meters, space and aeronautics, etc. During their serving period, membrane structure is prone to vibrate stochastically and seriously under stochastic dynamic loads, which may lead to structural failure. For this purpose, this paper investigates the stochastic dynamic response and reliability analysis of membrane structure under impact load obeying Gaussian distribution. The equation of stochastic motion of membrane structure is established by Von Karman's large deformation theory. The results of stochastic dynamic response are obtained with perturbation method solving the equation. Then, reliability parameters of extreme value of dynamic response are calculated by Moment method based on first-passage probabilities of level crossing. Furthermore, the theoretical model proposed is validated by experimental study using Monte Carlo method. The effects of parameters including impact velocity, pretension force and radius on structural reliability are discussed in addition. The model proposed herein provides some theoretical basis for the stochastic vibration control and dynamic design of orthotropic membrane structure based on reliability theory.
TL;DR: In this paper, an exact 3D static analysis of one-layered and multilayered isotropic, orthotropic, sandwich and composite structures is proposed in terms of displacements and in-plane and out-of-plane stresses through the thickness direction.
Abstract: This new work proposes an exact three-dimensional static analysis of plates and shells. One-layered and multilayered isotropic, orthotropic, sandwich and composite structures are investigated in terms of displacements and in-plane and out-of-plane stresses through the thickness direction. Proposed structures are completely simply-supported and a transverse normal load is applied. The proposed method is based on the 3D equilibrium equations written using general orthogonal curvilinear coordinates which are valid for spherical shells. Cylindrical shell, cylinder and plate results are obtained as particular cases of 3D spherical shell equations. All the considered structures are analyzed without any geometrical approximation. The exact solution is possible because of simply-supported boundary conditions and harmonic form for applied loads. The shell solution is based on a layer-wise approach and the second order differential equations are solved using the redouble of variables and the exponential matrix method. A preliminary validation of the model is made using reference results in the literature. Thereafter, the proposed exact 3D shell solution is employed with confidence to provide results for one-layered and multilayered plates, cylinders, cylindrical shell panels and spherical shell panels. All these geometries are analyzed via a unified and general solution, and the obtained results can be used to validate future numerical methods proposed for plates and shells (e.g., the finite element method or the differential quadrature method). Proposed results allow to remark substantial features about the thickness of the structures, their geometry, the zigzag effects of displacements, the interlaminar continuity of displacements and transverse stresses, and boundary loading conditions for stresses.
TL;DR: In this paper, the perforation process of a target AA5754-O Aluminum plate when subjected to normal impact at low (up to 25ms − 1 ) and moderate velocities (ranged between 25 − 50 ǫm − 1 ).
TL;DR: In this paper, free vibration of composite beams under axial load using a four-unknown shear and normal deformation theory is presented, where the constitutive equation is reduced from the 3D stress-strain relations of orthotropic lamina.
TL;DR: This paper describes the extension of a wave and finite element (WFE) method to the prediction of noise transmission through, and radiation from, infinite panels, and various example applications are presented to illustrate the approach.
Abstract: This paper describes the extension of a wave and finite element (WFE) method to the prediction of noise transmission through, and radiation from, infinite panels. The WFE method starts with a conventional finite element model of a small segment of the panel. For a given frequency, the mass and stiffness matrices of the segment are used to form the structural dynamic stiffness matrix. The acoustic responses of the fluids surrounding the structure are modelled analytically. The dynamic stiffness matrix of the segment is post-processed using periodic structure theory, and coupled with those of the fluids. The total dynamic stiffness matrix is used to obtain the response of the medium to an incident acoustic pressure. Excitation of the structure by oblique plane waves and a diffuse sound field are considered. The response to structural excitation and the consequent radiation are determined. Since the size of the WFE model is small, computational times are small. Various example applications are presented to illustrate the approach, including a thin isotropic panel, an antisymmetric, cross-ply sandwich panel and a symmetric panel with an orthotropic core.
TL;DR: In this article, an analytical approach is adopted to investigate Rayleigh waves in a layered composite structure with corrugated boundaries, where the structure of the model has been taken in such a way that the pre-stressed piezoelectric layer with rotation is lying over a rotating, gravitational orthotropic substrate.
Abstract: An analytical approach is adopted to investigate Rayleigh waves in a layered composite structure with corrugated boundaries. The structure of the model has been taken in such a way that the pre-stressed piezoelectric layer with rotation is lying over a pre-stressed, rotating, gravitational orthotropic substrate. The frequency equations of the considered wave have been obtained in the form of a determinant for both electrically open and short cases. Notable effects of various parameters (piezoelectric constant, initial stress, rotation, undulation parameter and position parameter) on Rayleigh wave velocity have been observed. Numerical computation and graphical demonstration have been carried out. The obtained results are matched with existing results, under certain conditions. Also, the analytical solution of the problem is matched and found in good agreement with the solution obtained by the finite element method. The outcomes are widely useful for the development and characterization of rotation sensors and SAW devices.
TL;DR: An orthotropic constitutive model is developed in order to capture the complex response of unidirectional fibrous materials with arbitrary orientation under a three-dimensional (3D) stress state and it is utilised to analyse the non-linear mechanical response of bulk or laminated timber.
TL;DR: In this article, the authors used the shear deformation theory to obtain the basic equations of orthotropic cylindrical shells on the nonlinear elastic foundations within the Donnell's shell theory.
01 Mar 2017-Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems
TL;DR: In this paper, the authors derived the governing equations for bulk and surface of double-layer orthotropic nanoplate using refined plate theory, and the results showed that by augmenting nonlocal parameter, the surface effects on the vibration and buckling modes of both out-of-phase and in-phase increase.
Abstract: In this article, shear vibration and buckling of double-layer orthotropic nanoplates resting on elastic foundations are analyzed subjected to in-plane loadings including surface and nonlocal effects. These effects are considered by Gurtin---Murdoch's theory. Using the principle of virtual work, the governing equations for bulk and surface of double-layer orthotropic nanoplate are derived using refined plate theory. Differential quadrature method (DQM) is implemented. DQM solutions are validated by Navier's method and journal references. The influences of nonlocal parameter, van der Waals, Winkler, shear modulus, orthotropic material properties, boundary conditions, and in-plane biaxial, uniaxial, and shear loadings, are investigated on the surface effects of buckling and vibration modes of out-of-phase and in-phase. Results demonstrate that by augmenting nonlocal parameter, the surface effects on the vibration and buckling modes of both out-of-phase and in-phase increase. This result is in contrast with the works of other researchers in the field. Moreover, by enhancing in-plane loadings, the degree of surface effects on the vibration increase. On the other hand, the effects of nonlocal parameter on the vibration and buckling under in-plane shear load are more influential than those of biaxial and uniaxial, while the surface effects on the biaxial vibration and buckling are more remarkable than those of shear vibration and buckling.
TL;DR: In this paper, the displacement-based free vibration analysis of functionally graded (FG) open cylindrical shells is presented using various refined higher order theories, including higher order shear and normal deformation theory (HOSNT), along with first-order shear deformation theories (FOST) and higher order HSDT, and the Navier method of solution with double trigonometric functions for displacement terms is used to analytically reduce the given set of partial differential equations to an eigenvalue problem.
Abstract: Free vibration analysis of functionally graded (FG) open cylindrical shells is presented here using various refined higher order theories. Present study undertakes the displacement based approach including higher order shear and normal deformation theory (HOSNT) along with first order shear deformation theory (FOST) and higher order shear deformation theory (HSDT) models. Difficulty of obtaining three dimensional (3D) solutions and errors associated with classical shell theory (CST) necessitates the requirement of higher order models. Present study takes into account moderately thick shells unlike CST, by considering square of ratio of thickness to radius of shell less than unity, instead of the classical assumption of considering ratio of thickness to radius less than unity. Here Navier method of solution with double trigonometric functions for displacement terms is used to analytically reduce the given set of partial differential equations (PDEs) to an eigenvalue problem. Results are computed using MATLAB and comparison between various higher order models is discussed based on the consideration of middle surface displacement parameters. Present results should establish benchmark solutions for free vibration analysis of isotropic/orthotropic FG cylindrical panels. Functionally graded material properties are graded according to power law variation in thickness direction. Various shell solutions, based on other theories and 3D solutions available in the literature are compiled along with present solutions.
01 Jul 2017-Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems
TL;DR: In this article, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and nonlinear strains of Von-Karman was studied.
Abstract: In this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets was modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear deformation theory. For calculation of critical temperature and critical shear load, the equations were divided for two states via adjacent equilibrium criterion, pre-buckling and stability. The stability equations were discretized by differential quadrature method which is a high accurate numerical method. The equations were solved for various boundary conditions, such as free edges. Finally, the small scale parameter effect due to length to the width ratio, stiffness of elastic medium on the critical load was considered. The shear buckling results showed that the effect of type of shear loading on the nonlocal results is more than local results. Also, in thermal buckling analysis, the most important results being that whether the boundary conditions have more flexibility, by increasing the dimensions ratio, the results of critical temperature were tightly close together in nonlocal and local analysis.