Showing papers on "Orthotropic material published in 2016"

A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment

Abstract: In this paper, a new size-dependent plate model is developed based on the higher-order nonlocal strain gradient theory. The influences of higher-order deformations in conjunction with the higher- and lower-order nonlocal effects are taken into account. The presence of three different kinds of scale parameters in the formulation results in a theory which is capable of capturing both reduction and increase in the stiffness of structures at nanoscale. The governing differential equations are derived for the buckling of nanoplates resting on a two-parameter elastic foundation using the principle of virtual work. The nanoplate is assumed to be orthotropic with size-dependent material properties. The influence of thermal stress caused by a temperature change is taken into consideration. An exact closed-form solution is obtained for the critical buckling loads of graphene sheets. The higher-order governing differential equation is also solved by the differential quadrature method. The results of the two solution methods are compared with each other. Excellent agreement between the exact and numerical results is observed. For numerical results, three types of graphene sheets with different aspect ratio are considered. The effects of various scale parameters together with the other parameters such as the coefficients of the elastic medium, temperature change and the length of the nanoplate on the buckling behavior of graphene sheets are investigated.

An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment

Abstract: This study deals with the viscoelastic constitutive modeling and the respective computational analysis of the human passive myocardium. We start by recapitulating the locally orthotropic inner structure of the human myocardial tissue and model the mechanical response through invariants and structure tensors associated with three orthonormal basis vectors. In accordance with recent experimental findings the ventricular myocardial tissue is assumed to be incompressible, thick-walled, orthotropic and viscoelastic. In particular, one spring element coupled with Maxwell elements in parallel endows the model with viscoelastic features such that four dashpots describe the viscous response due to matrix, fiber, sheet and fiber-sheet fragments. In order to alleviate the numerical obstacles, the strictly incompressible model is altered by decomposing the free-energy function into volumetric-isochoric elastic and isochoric-viscoelastic parts along with the multiplicative split of the deformation gradient which enables the three-field mixed finite element method. The crucial aspect of the viscoelastic formulation is linked to the rate equations of the viscous overstresses resulting from a 3-D analogy of a generalized 1-D Maxwell model. We provide algorithmic updates for second Piola-Kirchhoff stress and elasticity tensors. In the sequel, we address some numerical aspects of the constitutive model by applying it to elastic, cyclic and relaxation test data obtained from biaxial extension and triaxial shear tests whereby we assess the fitting capacity of the model. With the tissue parameters identified, we conduct (elastic and viscoelastic) finite element simulations for an ellipsoidal geometry retrieved from a human specimen.

Web-flange behavior of pultruded GFRP I-beams: A lattice model for the interpretation of experimental results

Abstract: Glass fiber reinforced polymer (GFRP) I-beams have seen growing interest in the last decades, so that they are now being used in many civil applications. For this reason various experimental campaigns have been performed to study the structural response of such elements. In particular, experimental tests performed by Feo et al. [1] highlighted the need to study the local problem of the web-flange junction when pultruded I-beams are subjected to loads acting in the web plane: the experimental results dispersion stimulated numerical analyses and the need to study the problem by means of a nonlinear mesoscale lattice model approach that helped in the experimental result interpretation. The lattice model proposed has several appealing features that make it suitable for the simulation of orthotropic materials like GFRP. The different steps needed to build the model, and the constitutive law used will be explained and the achieved main results will be given in order to conclude that fluctuations in the effective contact area and local material non linearity can be the reasons for the measured dispersion for both element stiffness end strength.

Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method

Abstract: The stress and strain recovery procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of...

Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field

Abstract: In the present research, vibration and instability of axially moving single-layered graphene sheet (SLGS) subjected to magnetic field is investigated. Orthotropic visco-Pasternak foundation is developed to consider the influences of orthotropy angle, damping coefficient, normal and shear modulus. Third order shear deformation theory (TSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Motion equations are obtained by means of Hamilton’s principle and solved analytically. Influences of various parameters such as axially moving speed, magnetic field, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of SLGS on the vibration characteristics of moving system are discussed in details. The results indicated that the critical speed of moving SLGS is strongly dependent on the moving speed. Therefore, the critical speed of moving SLGS can be improved by applying magnetic field. The results of this investigation can be used in design and manufacturing of marine vessels in nanoscale.

Design of composite structures reinforced curvilinear fibres using FEM

Abstract: This paper describes a method of modelling a curvilinear reinforcement structure, for a composite plate with a hole that allows trajectories of fibres to be adapted to geometric discontinuities (holes, notches, bolts, etc.). For this method, it is assumed that the trajectories of fibres are curvilinear and continuous, as well as located along the trajectories of maximum principal stress. On the basis of these trajectories, the functionally graded material is simulated by means of the finite element method (FEM). Each element of this structure has its own mechanical properties, depending on the fibre direction and a change in the distance between the fibres. It is demonstrated that the maximum value of the stress concentration factor in the fibre direction for the plate with the curvilinear reinforcement structure reduces by 3.2 times in comparison with the same plate with a rectilinear reinforcement structure (orthotropic material).

Finite element analysis of surface milling of carbon fiber-reinforced composites

Abstract: Despite increased applications of carbon fiber-reinforced plastic (CFRP) materials in many industries, such as aerospace, their machining is still a challenge due to their heterogeneity and anisotropic nature. In this research, a finite element model is used to investigate the cutting forces, chip formation mechanism, and machining damage present during the flat end milling of unidirectional CFRP. The material is modeled as an equivalent orthotropic homogeneous material, and Hashin’s theory is used to characterize failure in plane stress conditions. The friction coefficient between the tool and the composite material was assumed to be dependent on the carbon fiber orientation. A comparison of modeling and experimental results indicates that the model successfully predicts the cutting forces. The numerical model predictions of machining damage around the cutting area due to fiber compression damage and matrix cracking and the relation between damage extension and fiber orientation are confirmed through a comparison with SEM images of machined edges and surfaces.

Experimental study on the mechanical properties of AZ31B-H24 magnesium alloy sheets under various loading conditions

Abstract: In order to fully characterize the plasticity and fracture of magnesium AZ31B-H24 sheets, a set of mechanical experiments (105 in total) were performed under different loading conditions, including monotonic uniaxial tension, notch tension, in-plane uniaxial compression, wide compression (or called biaxial compression), plane strain compression, through-thickness compression, in-plane shear, punch test, and uniaxial compression–tension reverse loading. Both the plastic strain histories and stress responses were obtained under the above loading conditions, which give a comprehensive picture of mechanical behaviors of this material. An orthotropic yield criterion involving two linear anisotropic transformation tensors, CPB06ex2, in conjunction with its associated flow rule, and a modified semi-analytical Sachs isotropic hardening model was fully calibrated to describe both the anisotropy in plastic flow and tension–compression asymmetry in stress–strain behaviors. An all-strain based modified-Mohr–Coulomb fracture model, transformed from a stress triaxiality based model, was applied to describe the calibrated fracture locus. Applying a linear transformation to the plastic strain tensor, a non-conjugated anisotropic equivalent strain was proposed to characterize anisotropic fracture behaviors. Good correlations were achieved between experimental results and model predictions in terms of material yield strengths, strain hardening curves, plastic flow directions and ductile fracture strains.

Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation

Abstract: The study intends to investigate the large amplitude vibration of functionally graded material (FGM) orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation in the framework of the Donnell's shell theory is investigated. To derivation of basic equations of FGM orthotropic cylindrical shells interacting with the nonlinear elastic foundation is used von-Karman type geometric nonlinearity. The superposition and Galerkin methods are used to convert the above equations into a nonlinear ordinary differential equation. The frequency-amplitude characteristics of functionally graded (FG) orthotropic cylindrical shell interacting with the nonlinear elastic foundation are obtained using the semi-inverse method. The accuracy of the current study is verified by comparing it other solutions available in the literature. Moreover, some new results are also presented for the nonlinear frequency parameters of the cylindrical shells to study the effects of the nonlinear elastic foundation, vibration amplitude, FG orthotropic profiles and shell characteristics.

Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory

Abstract: This research deals with the nonlocal wave propagation analysis of embedded nanocomposite polymeric piezoelectric micro plates reinforced by single-walled carbon nanotubes (CNTs). For the CNT-reinforced piezoelectric composite (CNTRPC) micro plate, uniform distribution (UD) and three types of functionally graded (FG) distribution patterns of single-walled CNT reinforcements are assumed. The material properties of FG-CNTRPC micro plate are assumed orthotropic viscoelastic based on Kelvin–Voigt model. The viscoelastic FG-CNTRPC micro plate subjected to 2D electro-magnetic fields is embedded in an orthotropic Visco-Pasternak foundation. Quasi-3D sinusoidal shear deformation theory is employed to establish the governing equations in which the size effects are considered using Eringen's nonlocal theory. Analytical solution is applied in order to obtain the dimensionless phase velocity, cut-off and escape frequencies. A detailed parametric study is conducted to elucidate the influences of the small scale parameter, magnetic fields, FG distributions of CNTs, damping coefficient, aspect ratio, applied voltage and elastic medium on the wave propagation behavior of viscoelastic FG-CNTRPC micro plate. Results indicate that the dimensionless cut-off and escape frequencies decrease with increasing the magnitude of small scale parameter. Furthermore, it can be concluded that CNT distribution close to top and bottom is more efficient than those distributed nearby the mid-plane for increasing the stiffness of plates. Results of this investigation can be applied for optimum design of smart composite plates as micro-electro-magneto-mechanical sensors and actuators.

A modified solution for the free vibration analysis of moderately thick orthotropic rectangular plates with general boundary conditions, internal line supports and resting on elastic foundation

Abstract: In this investigation, a unified solution procedure based on the first-order shear deformation theory is presented for the free vibration analysis of moderately thick orthotropic rectangular plates with general boundary restraints, internal line supports and resting on elastic foundation. Under the current framework, regardless of boundary conditions, each of the displacement and rotation components of the plates is described as a standard Fourier cosine series supplemented with some auxiliary functions introduced to eliminate any possible discontinuities of the original displacements and their derivatives throughout the entire plate area including the boundaries and then to effectively enhance the convergence of the results. All the unknown expansion coefficients are treated as the generalized coordinates and determined by using the Raleigh–Ritz method. The current method can be universally applied to a variety of boundary conditions including all classical boundaries and their combinations and arbitrary elastic restraints. The excellent accuracy and reliability of current solutions is demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the current method can also predict the vibration characteristics of the plate with internal line supports and elastic foundation. Comprehensive studies on the effects of elastic restraint parameters, locations of line supports and foundation coefficients are also reported. New results for plates subjected to elastic boundary restraints, arbitrary internal line supports in both directions and resting on elastic foundations are presented, which may serve as benchmark solutions for future researches.

Nonlinear vibration and instability analysis of functionally graded CNT-reinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium

Abstract: In this study, nonlinear vibration and instability of embedded temperature-dependent cylindrical shell conveying viscous fluid resting on temperature-dependent orthotropic Pasternak medium are investigated. The equivalent material properties of nanocomposites are estimated using rule of mixture. Both cases of uniform distribution and functionally graded distribution patterns of reinforcements are considered. Based on orthotropic Mindlin shell theory, the governing equations are derived. Generalized differential quadrature method is applied for obtaining the frequency and critical fluid velocity of a system. The effects of different parameters, such as distribution type of single-walled carbon nanotubes (SWCNTs), volume fractions of SWCNTs, and Pasternak medium are discussed.

Microplane triad model for simple and accurate prediction of orthotropic elastic constants of woven fabric composites

Abstract: An accurate prediction of the orthotropic elastic constants of woven composites from the constituent properties can be achieved if the representative unit cell is subdivided into a large number of finite elements. But this would be prohibitive for microplane analysis of structures consisting of many representative unit cells when material damage alters the elastic constants in each time step in every element. This study shows that predictions almost as accurate and sufficient for practical purposes can be achieved in a much simpler and more efficient manner by adapting to woven composites the well-established microplane model, in a partly similar way as recently shown for braided composites. The undulating fill and warp yarns are subdivided into segments of different inclinations and, in the center of each segment, one microplane is placed normal to the yarn. As a new idea, a microplane triad is formed by adding two orthogonal microplanes parallel to the yarn, one of which is normal to the plane of the laminate. The benefit of the microplane approach is that it is easily extendable to damage and fracture. The model is shown to give realistic predictions of the full range of the orthotropic elastic constants for plain, twill, and satin weaves and is extendable to hybrid weaves and braids.