Multilayered Plates Research Articles

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

The Legendre polynomial series approach (LPSA) has been widely used to solve guided wave propagation in various structures since 1999. The LPSA directly introduces the boundary conditions into the control equations through the rectangular window function. However, in the solving process, the Legendre polynomial series, the rectangular window function, and their derivatives are introduced into the integral kernel functions, which results in a lot of CPU time on the abundant numerical integration calculations. To overcome this defect, an analytical integration Legendre polynomial series approach (AILPSA) is presented and is used to solve the Lamb waves in fractional order thermoelastic multilayered plates. Coupled wave equations and heat conduction equation are solved by the AILPSA and the LPSA, respectively. Comparison between two approaches indicates the computational efficiency of the AILPSA is improved by more than 90%. In addition, a backward error estimation is given in the convergency analysis to make up for the deficiency of the numerical experiments. Finally, the influence of fractional order on the thermoelastic Lamb wave is discussed.

Dynamic Behavior of Kinetic Projectile Impact on Honeycomb Sandwich Panels and Multi-Layer Plates

In order to study the dynamic response associated with the impact of a kinetic projectile on the internal structure of an artificial satellite, we propose a kinetic projectile configuration with non-metallic material wrapping and multiple damage elements. The artificial satellite is simplified as a honeycomb sandwich panel and multi-layer plates. We carried out a ground damage test and finite element dynamic simulation, and we determined the lateral effect and penetration performance of the projectile. Then, we studied the dynamic behavior of the projectile penetrating the honeycomb sandwich panel using a theoretical model. We found that its ballistic limit velocity was 150 m/s, and the deformation of the opening had little relationship with the projectile velocity. Finally, we studied the dynamic response of the kinetic projectile impacting the multi-layer plates under various launch parameters. We found that the launch velocity required to meet the damage requirements was within 325 ± 25 m/s. Projectiles with a higher initial velocity had a stronger ability to penetrate the plates, but initial velocities higher than 325 m/s led to a reduced damage area. The kinetic projectile could adapt to incident angles less than 5° when damaging the plates. With the increasing incident angle, the penetration ability was reduced, and the damage area increased.

The depolarization effect of microwave in multilayer plate dielectric beam combiner

Beam combiner was the key component of compound guidance hardware-in-the-loop simulation system, which was used to synthesize microwave signal and infrared signal in a common aperture. In this paper, the depolarization effect of microwave caused by beam combiner was studied, and the standard equation of linear polarization wave depolarization into elliptic polarization wave was derived. The reason of depolarization was analyzed, which was that the cross-polarization component perpendicular to the main-polarization component was generated after the microwave passed through the beam combiner. The condition to avoid depolarization was given. A polarization-insensitive beam combiner composed of three-layer dielectric working in X, Ku and K bands was designed. Its microwave transmittance was greater than 96% and the polarization angle deviation was less than 0.1°.

Optimization of Rectangular Articulated Reinforced Concrete Smooth and Ribbed Slabs Using Resource Reduction Method

The paper considers the optimization problem of hinged reinforced concrete rectangular smooth and ribbed slabs. The static calculation of the slabs has been performed while using the finite element method. The model is built from rectangular finite elements containing four nodes each and having twelve degrees of freedom. The load is presented in the form of nodal vertical forces. To take into account the nonlinearity of the deformation of reinforced concrete, the finite elements are taken as inhomogeneous multilayer plates. The modulus of elasticity changed according to the hyperbolic dependence. The determination of the stress-strain state has been carried out by the iterative method. For optimization, a method has been used to reduce resources for strength, stiffness, and crack opening with gradient descent along the boundary of the allowable area. The cost of the material spent on the manufacture of the slab and the volume of concrete are taken as objective functions. Restrictions on strength, stiffness and width of cracks are set. By scanning, the boundaries of the admissible search area for the optimal solution are set; the boundary of this region has a curvilinear outline. According to the results of the calculation, the trajectories of the search for optimal solution are obtained. Examples are given and optimal solutions are found for various starting points. It has been established that for the accepted conditions of the problem, the extreme points are located near the boundaries of the admissible region. The speed of gradient descent and the location of the starting points do not significantly affect the results. Due to the fact that the objective function can have several minima, a method is proposed to search for a global minimum by preliminary scanning and analysis of extrema values. It is confirmed that the applied method ensures the stability of the optimal solution.

Appearing ZGV point in the first flexural branch of Lamb waves in multilayered plates

Appearing the zero group velocity (ZGV) point belonging to the first quasi flexural branch (A1) of Lamb waves propagating in the multilayered traction-free plates containing homogeneous isotropic layers is observed and analyzed; in contrast to the previously studied homogeneous isotropic plates admitting ZGV points that may belong to the higher flexural modes (A2, A3, …) and higher symmetric modes. The detected ZGV point in a multilayered traction-free plate leads to the transverse quasi resonance occurred at the lower frequency than the previously studied resonance associated with the first symmetric mode (S1) and especially higher symmetric and flexural modes. The analysis is done by the combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method.

Experimental research of main characteristics in a complex multi-layer plate heat exchanger

Abstract The objective of this paper is research of main heat exchange characteristics in a complex multi-layer heat-exchanger with the purpose of determining heat exchanging process intensification dependencies and conditions during utilization of ventilation gas and emission low-grade heat with associated recovery of thermoelectricity.

Vibration analysis of a composite magnetoelectroelastic bimorph depending on the volume fractions of its components based on applied theory

Introduction. Transverse vibrations of a bimorph consisting of two piezomagnetoelectric layers and located in the alternating magnetic field are investigated. Piezomagnetoelectric layers are multilayer composites with alternating piezoelectric and piezomagnetic layers. The mechanical and physical properties of such a composite are given by known effective constants.Materials and Methods. The applied theory of multilayer plate vibrations takes into account the nonlinear distribution of electric and magnetic potential in piezoactive layers in the longitudinal and transverse directions. On the basis of this theory, the stress-strain state, the dependences of deflection, electric and magnetic potentials on the volume ratio of the composition of the hinged bimorph, are investigated. The electric potential is assumed to be zero at all electrodes, while the magnetic potential is zero at the inner boundary and unknown at the outer boundaries. Therefore, the distribution of electric and magnetic potentials in the middle of the layer are unknown functions. In the case of the magnetic potential, the distribution at the outer boundary is also unknown. In the problem, the Kirchhoff hypotheses for mechanical characteristics were accepted. The use of the variational principle and the quadratic dependence of the electric and magnetic potentials on the thickness of piezoactive layers made it possible to obtain a system of differential equations and boundary conditions.Results. When the volume ratio of the composition of piezoactive bimorph materials changes, the electric potential in the middle of the layer changes nonlinearly. The magnetic potential in the middle of the layer and at the outer boundary increases almost linearly with an increase in the volume percentage of BaTiO3. The dependence of the deflection in the middle of the layer is determined.Discussion and Conclusions. An applied theory for calculating transverse vibrations of a bimorph with two piezomagnetoelectric layers is constructed. The dependence of the characteristics of the stress-strain state, electric and magnetic fields on the volume fractions of piezomagnetic and piezoelectric materials, is investigated.

Free vibration analysis of multi-layer rectangular plate containing magnetorheological fluid and flexible core layers rested on Winkler-Pasternak foundation

Magneto-rheological (MR) fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they can improve structural rigidity and damping property. The current study presents a free vibration analysis of a multilayer rectangular plate with two layers of MR fluid and a flexible core layer, rested on a Winkler-Pasternak foundation based on exponential shear deformation theory (ESDT). In this theory, the exponential functions are applied in terms of thickness coordinates to include the effect of transverse and inertial rotational shear deformation. The flexible core displacement is modeled via the second-order Frostig model. The Hamilton’s principle is used to derive the equations of motion. These equations are solved using the Navier method to obtain the natural frequencies of the plate. The accuracy of the derived equations is validated, and the obtained results are compared with a specific case. Finally, the results show that by applying and increasing the magnetic field intensity, the natural frequencies and loss factor increase. With the increase in the mode number for each specific magnetic field intensity, the natural frequency increases and the loss factor decreases. The natural frequencies and loss factor decrease with the increase of the MR layer thickness to overall thickness ratio and the flexible core layer thickness to overall thickness ratio. The natural frequencies increase when the parameters of the foundation increase.

Guided Wave Propagation in Multilayered Two-dimensional Quasicrystal Plates with Imperfect Interfaces

Guided Wave Propagation in Multilayered Two-dimensional Quasicrystal Plates with Imperfect Interfaces

3D progressive damage analysis of a unidirectional multi-layered composite for mechanical joints

ABSTRACT Due to the presence of holes in composite mechanical joints, stresses around the holes are increased, and they may cause failure in the composites. Analysis of the composite behaviour after damage initiation around the holes is important, complex, and mostly three-dimensional. In order to achieve accurate results about the composite failure modes, damage analysis using a modern criterion is needed. In this research, to investigate the damage behaviour of a unidirectional multi-layered composite plate of a mechanical joint under pure tension, three codes are prepared in the USDFLD, VUSDFLD and VUMAT subroutines based on the Hashin criterion and implemented in ABAQUS software. These codes, using the methods of suddenly and gradually degradation in composite properties, progressively simulate the three-dimensional damage behaviour of the composite plate after damage initiation. The results show that, when a mechanical joint is under pure tension, the adequate distance from the edge of a hole to the edge of a composite plate is about two times the hole diameter. Furthermore, it is found that to rapidly investigate and analyse a mechanical joint in the composite structures, the USDFLD subroutine, which uses suddenly decreased material properties after damage initiation, is reasonable and more efficient.

Multiferroic laminated composites with interfacial imperfections and the nonlocal effect

In this study, we investigate multiferroic magneto-electro-elastic (MEE) laminated plates with interfacial imperfections by using nonlocal theory. The multilayered MEE plate is considered a simply supported rectangular plate subjected to appropriate boundary conditions. Generalized membrane-type and generalized linear-spring-type imperfect interfaces are considered. We extend the pseudo-Stroh formalism and propagator matrix method to derive analytical solutions for an orthotropic and multilayered MEE plate with interfacial imperfections and the nonlocal effect. The key step is first to observe that the equilibrium equations and interface conditions are equivalent to those in the classical MEE multilayered problem. Next, we derive the relationship between nonlocal and classical tractions. The derived solutions are then applied to BaTiO3−CoFe2O4 sandwich plates. Numerical calculations show that interfacial imperfections and the nonlocal effect can be used to tune the field distribution and ME effect. The findings can provide insights for the application and design of various nanodevices.

Some improvements on the energy absorbed in composite plate resting on the viscoelastic substrate

The vibration, as well as energy of a reinforced three-phase hybrid composite plate resting on a viscoelastic foundation subjected to initial stress, is examined with the aid of three-dimensional elasticity theory. The two-parameter viscoelastic Winkler–Pasternak foundation is formulated. The multilayer plate with three, five, and seven layers are modeled with the aid of compatibility conditions. The state-space-based analytical method is utilized as the solution procedure to extract the results. To attain the composite material properties, the rule of the mixture alongside modified Halpin–Tsai model is incorporated. The distribution of the carbon nanotubes is supposed to be nonuniform. The parametric examination on the impacts of the sequence of the composite layers, initial stresses, foundation coefficients, and nanocomposite related constants on the vibration frequency as well as energy stored in the system is carried out. The extracted results indicate that the initial stresses and foundation parameters play a significant role in determining the frequency value along with the energy of the system.

Numerical Investigation of Multi-scale Characteristics of Single and Multi-layered Woven Structures

Resin flow through multi-ply woven fabrics is affected by the fibre orientation and laminate stacking sequence during the impregnation process. This is characterised by permeability, which measures the ability of transferring fluids within a 2D or 3D layered woven fibre architecture (i.e., through a porous medium). The work aims to investigate the feasibility of characterising macro-scale flow permeability via the micro-meso-scale (dual-scale) permeability across and along woven yarns, with different structures of yarn nesting, non-shifting, and ply orientation. The permeability characterisation is performed using Ansys-Fluent software package where textile architectures and resin flow in porous media are simulated. The results show that in- and out-plane permeability of the nested, non-shifted and oriented single-ply woven preforms are different than that corresponding to multi-layered plates, making them only applicable for dual-scale permeabilities. However, with a number of plies in the multi-ply woven fabrics — e.g., 9-ply and 5-ply, for in- and out-of-plane flows, respectively — the dual-scale permeabilities can be extended to macro-flow making them applicable at all scales (multi-scale flow). The calculated in-plane multi-scale permeabilities are then used in the 2D simulations and compared with the analytical solution of the Darcy’s equation, which resulted in a very good agreement.

3D hygro-elastic shell model for the analysis of composite and sandwich structures

The present work proposes the study of the hygrometric loading effects in the static analysis of multilayered composite and sandwich plates and shells. The employed model is based on a general exact 3D shell theory valid for one-layered and multilayered sandwich and composite plates, cylinders and cylindrical/spherical shell panels. The employed 3D equilibrium equations are developed in an orthogonal mixed curvilinear coordinate system for spherical shells in order to obtain the other simpler geometries as particular cases. A layer-wise approach is employed and equilibrium equations are solved in the thickness direction via the exponential matrix method. The partial derivatives in the in-plane directions are exactly calculated by assuming simply-supported edges and harmonic forms for the variables. The presented 3D shell model is extended to hygro-elastic cases by considering moisture content amplitudes imposed at the external surfaces of the structures in steady-state conditions. The moisture content profile through the thickness of the structures can be included in the 3D shell model using three different methodologies: it can be calculated by solving the steady-state 3D or 1D version of the Fick diffusion law, or it can be “a priori” assumed as linear through the thickness. Therefore, the developed system includes three non-homogeneous second order differential equilibrium equations that are solved after the introduction of opportune mathematical layers to consider the curvature effects through the thickness. The reduction to a first order differential equation system is obtained by redoubling the number of variables. The exponential matrix method is employed to accurately define both general and particular solutions. The implemented 3D hygro-elastic shell model is firstly validated and then it is employed with confidence for new benchmarks where the effects of thickness ratio, geometry, lamination scheme, material, thickness layer and imposed moisture content values at the external surfaces are investigated for composite and sandwich plates and shells. Showed results demonstrate the importance of an accurate developing of the elastic part of the 3D shell model combined with an appropriate evaluation of the moisture content profile through the thickness. Assumed linear moisture content profiles are correct only for thin one-layered isotropic structures, the use of the 1D Fick diffusion law allows only the correct definition of the material layer effect, the use of its 3D version allows the correct definition of both material and thickness layer effects.

Multi-layer TiC nanosheets-decorated TiB2 plates for enhanced microwave absorption

Searching for microwave absorbers with excellent microwave absorption performance in harsh environments is still a huge challenge. Here, a novel hybrid of TiB2 plates decorated by multi-layer TiC nanosheets (TiB2/TiC hybrids) was fabricated via a molten salt-mediated carbothermal reduction. Due to the increase of the reflective interface, the TiB2/TiC hybrids exhibited improved microwave absorption performance with a minimum reflection loss (RLmin) value of −52.5 dB (13.1 GHz, 5.2 mm). The reasonable dielectric loss, higher dipole moments and interface effect whereas brought by the three-dimensional multilayer network formed by TiC nanosheets together promoted the improvement of the microwave absorption capacity of TiB2/TiC hybrids.

Static and dynamic NURBS-based isogeometric analysis of composite plates under hygrothermal environment

In this paper, a computationally efficient isogeometric plate model, employing nonpolynomial shear deformation theory (NPSDT), for static and dynamic analysis of laminated and sandwich composite plates under hygrothermal environment is presented. Transient and steady-state response using Rayleigh damping model and fast Fourier transformation of transient response have also been obtained for the hygrothermal environment. The non-uniform rational B-splines (NURBS) based formulation has been considered, which attribute only five-degree of freedom and satisfies the stringent continuity requirement of the NPSDT model (C1-continuity) without any additional variables. A total Lagrangian approach in conjunction with Hamilton’s principle is utilized to formulate the governing equations for thermal bending and subsequent dynamic analysis of multilayered composite plates. To model stress stiffening effect due to hygrothermal load, both von Kármán and Green–Lagrange strain displacement relations are incorporated and obtained solutions are compared. It has been shown that at higher temperature (around one fourth of the critical buckling temperature), the consideration of Green–Lagrange strain relationship for modeling stiffening effect due to hygrothermal load is important for better accuracy. Further, it has been shown that bending strip is essential in case of higher-order shear deformation theory (HSDT) to get more accurate solution. In addition, the obtained transient damped/undamped solutions may be used to get the natural frequency from their FFT solution.

3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

Mechanical properties of carbon/glass fiber reinforced polymer plates with sandwich structure exposed to freezing-thawing environment: Effects of water immersion, bending loading and fiber hybrid mode

In this article, two kinds of carbon/glass fiber hybrid rod with the sandwich structures were designed and developed through the pultrusion technology, including the fiber random hybrid (RH) mode with multi-layer sandwich structure and fiber core-shell hybrid (CH) mode with single-layer sandwich structure. The hybrid sandwich-structure plates were prepared from the rod and immersed in bending loading, temperature alternating and sustained water immersion as long as 360 days. The effect of fiber hybrid mode/sandwich structure on the degradation mechanism of mechanical properties was revealed through the digital image correlation and thermogravimetric analysis. Through the fiber hybrid design, the strength improvement percentages of RH plates with multi-layer sandwich structure were up to ∼50% (tensile strength), 30 ∼ 40% (flexural strength) and 18% (in-plane shear strength) compared to CH plates with single-layer sandwich structure. Higher bending loading level brought about the decrease of flexural strength and in-plane shear strength close to 18% and 19%, respectively. During the immersion, microcracks or microvoids formed and expanded in the resin tensile area under the bending loading and water diffusion, leading to the uncoordinated stress concentration for single-layer sandwich-structure CH plate. By uniformly dispersing carbon fibers into glass fibers, the uneven interface stress concentration can be effectively alleviated for multi-layer sandwich-structure RH plates. The comparison of mechanical properties with the others’ work showed the interface shear strength was more sensitive to the bending loading and immersion temperature. The long-term life prediction showed the maximum increase percentages of mechanical properties of multi-layer sandwich structure were 435.4% (tensile strength) and 149.2% (flexural strength) and 110.7–114.2% (shear strength) compared to the single-layer sandwich structure.

Возможности использования математических моделей для теплового контроля дефектов многослойных биметаллических пластин

There is an actual task of delamination detection in multilayer bimetallic materials. Various methods of nondestructive testing (NDT) are used to solve it, including the method of transient thermal NDT. This method consists in remote registration, visualization and analysis of thermal (temperature) fields, which depend on thermophysical and geometric characteristics, thermal effect capacity and internal structure features of the object. The internal structure defects cause the appearance of abnormal temperature zones on the object surface. Their analysis allows us to judge the presence of changes in the material as a whole or in individual areas. It is possible to understand whether there is a defect under the anomalous site, and what its parameters are, if there is an adequate mathematical model that theoretically describes the dependence of the measuring results on the properties of the object and the selected technological modes. This model is a significant component of thermal NDT systems. For the same object or process, a certain set of mathematical models can be compiled, differing in the number of factors taken into account, the assumptions made, the completeness and accuracy of the description of the state of the object or the conditions of the process. The set of factors is determined by the purpose of the study, and in order to unambiguously determine the model of the thermal state, it is necessary to describe the characteristics of the object (geometric shape and thermophysical characteristics of the material) and the heat exchange process (characteristics of heat sources, initial and boundary conditions). Aim. To analyze the existing mathematical models for the research object – a multilayer bimetallic plate with delaminations between the outer and inner layers, and to identify common approaches to modeling the processes of thermal NDT of multilayer objects. Materials and methods. The structure of the mathematical model of the thermal state of the object is determined. An analytical review of mathematical models of thermal NDT of multilayer objects is performed. Results. The requirements, assumptions and limitations for a mathematical model of thermal NDT of a multilayer bimetallic plate with delamination defects are formulated. Conclusion. On the basis of the considered approaches to the mathematical modeling of the thermal state of multilayer objects with ideal layers contact and delamination defects, the necessary factors for the development of a model for the transient thermal NDT processes of the studied objects are determined.

Эллиптические уравнения со сдвигами произвольных направлений в полупространстве

In this paper, we investigate the half-space Dirichlet problem for elliptic differential-difference equations with superpositions of differential operators and translation operators acting in arbitrary directions parallel to the boundary hyperplane. The summability assumption is imposed on the boundary-value function of the problem. The specified equations, substantially generalizing classical elliptic partial differential equations, arise in various models of mathematical physics with nonlocal and (or) heterogeneous properties or the process or medium: multi-layer plates and envelopes theory, theory of diffusion processes, biomathematical applications, models of nonlinear optics, etc. The theoretical interest to such equations is caused by their nonlocal nature: they connect values of the desired function (and its derivatives) at different points (instead of the same one), which makes many classical methods unapplicable. For the considered problem, we establish the solvability in the sense of generalized functions, construct Poisson-like integral representations of solutions, and prove the infinite smoothness of the solution outside the boundary hyperplane and its uniform convergence to zero (together with all its derivatives) as the timelike variable tends to infinity. We find a power estimate of the velocity of the specified extinction of the solution and each its derivative.