A size-dependent model for a laminated microbeam with a partially covered flexoelectric layer is developed by using the isotropic flexoelectric theory. The static bending problem of the beam under ...the uniformly distributed load and the voltage with different boundary conditions is solved. The method of weighted residuals is applied to derive the analytical expressions of the charge, the potential, the polarization and the deflection. The size dependency of the charge, the potential, the polarization and the deflection is discussed. Results reveal that the charge, the potential, the polarization and the deflection is dependent on the ratio of beam thickness and material length-scale parameters. As the ratio increases, the charge, the potential, the polarization and the deflection gradually increase. In addition, the effects of length and thickness of flexoelectric layer on the induced charge and induced deflection are also studied. There is an optimum length and thickness of the flexoelectric layer to achieve the maximum induced charge and maximum induced deflection.
•A size-dependent flexoelectric response model of the laminated microbeam with a partially covered flexoelectric layer is developed.•The general isotropic flexoelectric theory is used to capture the strain gradient effects and flexoelectric effects.•The method of weighted residuals is applied to solve the governing equation.•The size dependency of the flexoelectric response is analysed.•The effects of laminated area of the beam on the flexoelectric response are discussed.
•A size-dependent partially covered laminated microbeam model incorporating strain gradient effects is developed.•The general strain gradient elasticity theory is used to describe the strain gradient ...effects.•The static bending behaviour of a partially covered laminated microbeam with different boundary conditions is studied.•The size-dependent responses of the deflection, the axial displacement and the neutral axis of the partially covered laminated beam are discussed.
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A size-dependent model for partially covered laminated microbeam is developed based on the general strain gradient elasticity theory. The governing equations and boundary conditions of the partially covered laminated beam are obtained by using the variational principle. The static bending behaviour of a partially covered laminated microbeam with different boundary conditions is studied. The size-dependent responses of the deflection, the axial displacement and the neutral axis of the partially covered laminated beam are analysed. Results reveal that the mechanical responses, including the deflection, the axial displacement and the neutral axis of the partially covered laminated beam, predicted by the strain gradient model and classical model are different when the ratio of the beam thickness and the material length scale parameter is small. As the ratio of the beam thickness and the material length scale parameter increases, the deflection predicted by the strain gradient model will gradually close to that of the classical model.
For static bending and free vibration analysis of functionally graded (FG) sandwich plates, a novel, enhanced first-order mixed plate element (IMQ4) is developed in this work. The transverse shear ...stresses are enhanced by assuming parabolic distribution shear stresses which satisfies the free condition of the transverse shear stresses on the upper and lower surfaces of the plates. Also, the shear correction factor is not required to calculate the shear strain anergy. To develop the basic equations of the proposed element, the mixed finite element formulation is used in conjunction with first-order shear deformation theory. Without the use of the reduced or selective integrations, the current IMQ4 is free of shear-locking phenomenon. For static bending and free vibration analysis, a variety of FG sandwich plates including hardcore, softcore and FG core types are investigated. By comparing the current results to previously published solutions, the performance and dependability of the IMQ4 are analyzed. The proposed element can be useful for analysis, design and testing of FG structures. Finally, detailed parametric analyses are conducted to illustrate the impacts of many factors, such as the layup scheme, the power-law index, and the side-to-thickness ratio on the bending and free vibration of FG sandwich plates.
RESUMO Depois de concluída a fase principal de exploração comercial do látex (cerca de 30 anos), os plantios de seringueira apresentam-se como fonte alternativa de madeira para serraria e para outros ...produtos à base de madeira com valor agregado superior ao da lenha, tendência já consagrada em países do sudeste asiático. O presente trabalho teve como objetivo principal avaliar a influência do módulo de elasticidade dinâmico (Ed) das lâminas no desempenho mecânico à flexão de painéis compensados de Hevea brasiliensis. Para este estudo, as lâminas de seringueira foram selecionadas em três classes de módulo de elasticidade dinâmico, definidas como baixo (de 4887-7323 MPa), médio (de 8200-8948 MPa) e alto (de 10979-13010 MPa) módulo de elasticidade. Foram confeccionados painéis compensados com cinco tratamentos, variando-se as classes das lâminas utilizadas e seus arranjos. Os resultados obtidos revelaram influência significativa dos tratamentos na resistência à flexão dos painéis. Os painéis com melhor desempenho mecânico foram confeccionados exclusivamente com lâminas de alto e médio módulo de elasticidade dinâmico. Os painéis que utilizaram lâminas com baixo módulo de elasticidade apresentaram menor desempenho mecânico, mesmo quando elas estavam combinadas com lâminas de alto módulo.
It has been common knowledge that as the density of wood increases, the mechanical properties also improve. In turn, the density of wood depends on many factors, including the wood moisture content, ...location and cross-section in the trunk, the type of treatment and the parameters of technological processes. There is a great deal of research reported in the scientific literature on the effect of solid wood density on mechanical properties for different wood species as well as for structural timber. However, no research data can be found related investigation of the influence of veneer density on the properties of the birch plywood.
In the present study, researching the properties of 7-ply birch plywood (thickness 9 mm), it was concluded that as the density of veneers increases, the bending properties of plywood in the direction of wood fibers (covered veneers) increases. When determining the plywood gluing quality, similar tendencies have been observed. For plywood with a lower density in all veneer plies the gluing quality (tensile-shear test) for perpendicular wood fiber veneers increases in the direction from the symmetry axis or middle veneer to the plywood outer plies, which can be explained by the fact that the outer plies become denser at the time of the hot pressing process. The results of the study will allow birch plywood manufacturers in direct production, sort veneers by density, to produce plywood with very predictable gluing quality, plywood thickness and mechanical properties in bending.
Effects of cyclic deformation and annealing treatment on conductive durability of indium tin oxide (ITO) thin film deposited on polyethylene terephthalate (PET) substrate are investigated. In-situ ...electrical and mechanical tests of ITO/PET sheet under various combinations of cyclic and static loadings are conducted at room temperature. Experimental results show that the number of cycles to failure is significantly decreased with an increase in displacement amplitude, given a specific extent of electrical resistance change of ITO/PET sheet. A static holding period of 1000s in various loading modes plays a role in influencing the failure of ITO/PET sheet. Cyclic bending combined with a static tensile holding generally generates more damages and a smaller number of cycles to failure than does that combined with a compressive holding, neutral holding, or no holding. Under a small fatigue loading, the conductive durability of ITO/PET sheet is increased with an increase in annealing temperature. However, there is little effect of annealing temperature on ITO/PET fatigue life under a larger displacement amplitude of fatigue loading. Using a surface-based cohesive modeling technique, a simplified three-dimensional finite element analysis micromodel subjected to tensile and compressive loadings is numerically analyzed to clarify the failure mechanism of interfacial and buckling-like delamination which governs the change in electrical conductivity of ITO/PET sheet. Modeling results indicate that buckle height of the ITO/PET micromodel subjected to tensile loading is significantly greater than that of compressive loading, providing more evidence of the aforementioned effect of loading mode.
•Effects of cyclic deformation on resistance change of ITO/PET are studied.•In-situ measurement and FEA analysis are built to assess ITO/PET conductivity change.•A greater cyclic deformation results in a larger increase of ITO/PET resistance.•Cyclic bending combined with tensile holding is more damaging than other holdings.•Annealing treatment enhances ITO/PET conductivity under small cyclic loading.
The article presents a numerical strength analysis of sandwich plates with solid face layers and tetrachiral honeycomb core layer under static bending conditions. An aluminum alloy was chosen as the ...material of plates. For honeycomb core layers, the discretization (number of unit cells) and the relative density were varied with a constant thickness. Calculations were performed for the case of bending with rigidly clamped ends and three-point bending within the framework of the theory of elasticity by the finite element method. The strength analysis enables one to determine the load values, at which the maximal stresses according to the von Mises criterion were equal to the conventional yield stress of the material. The aim of this work is to study the effect of discretization and relative density of honeycomb core layers of tetrachiral type on the str ength of sandwich plates.
This paper aims to carry out comprehensively the static bending, free vibration, and buckling analyses of two-layer FGM plates with shear connectors resting on elastic foundations, where two-layer ...FGM plates resting on Winker's-Pasternak elastic foundations taking into account relative sliding movements are analyzed by using the combination of Navier's solution and finite element method based on nth-order shear deformation plate theory. The plate is made up of two layers of FG materials joined by metal shear connectors. Lagrange and Hermitian shape functions are used to establish stiffness matrices, mass matrices, geometric stiffness matrices, and element force vectors. The suggested method and mechanical model are accurate when compared to the computed data from this research and reputable literature. The computed data accurately describes the mechanical response of the structure. Then a series of parameter investigations are conducted to capture the effects of the structure's geometrical and material features on the mechanical behavior of two-layer FG plates. The numerical results of this study may be utilized as a basis for future research, applications, and design of similar structures in mechanical and civil engineering practice. This is also a critical foundation for studying the dynamic behavior of structures with shear connectors.
This paper proposes a framework for physics-informed neural networks (PINNs) in the nonlinear bending of 3D functionally graded (FG) beams. Utilizing the underlying physical rules governing a 3D FG ...porous beam resting on a Winkler-Pasternak foundation and motivated by the advancements in the research area of machine learning, this paper develops a PINN framework to predict the nonlinear bending of the beam system. PINNs need much less training data and can achieve high accuracy using a more straightforward network. The powerful tool presented in this work is general enough to handle any class of PDEs. We also take advantage of the recently developed deep learning platform TensorFlow with the company of DeepXDE library to design our network. In this study, the PINN framework takes information from the governing equations and the data from boundary conditions. We developed a mathematical model using the Euler-Bernoulli beam theory and inhomogeneous beam model and validated the results with those extracted from the finite difference method. Furthermore, PINN is presented to accurately predict the nonlinear bending of the system up to 37 times faster than the numerical method.
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