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This paper presents an asymptotic two-dimensional (2D) finite-deformation theory for a thin magnetoelastic sheet starting from a three-dimensional (3D) variational form. This theory is used to model wrinkling phenomena under applied traction and external magnetic field. The resulting 2D potential energy is specialized to an isotropic, in compressible material, and the expressions for material constants, i.e., elasticity tensor, magnetoelastic coupling constant, and permeability, are obtained as a function of the applied magnetic field. The formulation is further simplified assuming reflection symmetry about the mid-surface of the sheet. Strong form of the resulting 2D governing equations are obtained by setting the first variation of potential energy functional to zero. The resulting governing equations are used to analyze wrinkling in a stretched rectangular sheet placed in a uniform magnetic field. Approximate analytical solutions are obtained by linearizing the 2D plate equation for small slopes. The effect of magnetic field and applied stretch on onset of wrinkling and amplitude of wrinkles is studied. [ABSTRACT FROM AUTHOR]

The present paper introduces the development of dynamic stiffness method for analyzing small-scale sandwich functionally graded nanoplates resting on elastic foundation in thermal environments. The mathematical formulation is based on classical plate theory in conjunction with nonlocal elasticity theory. The governing equation is derived using Hamilton’s principle. The dynamic stiffness matrix is obtained through the application of the Levy displacement approach and assembled to form the global stiffness matrix. The final matrix is solved for natural frequency of the plates using the Wittrick–Williams algorithm. The proposed methodology is validated against existing literature, demonstrating a strong agreement. Various parametric studies explore the effects of thermal environments, volume fraction index, sandwich configurations, elastic foundation characteristics, nonlocal parameter and boundary conditions. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of sandwich functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices. [ABSTRACT FROM AUTHOR]

Fine particle content significantly affects the in situ leaching of ion-adsorption-type rare earth ores. This study investigated the effect of fine particle content on solution flow and mass transfer in leaching. The results showed that with the increase in fine particle content, the peak concentration and peak time of rare earth increased. When the fine particle content exceeded 20%, all ion-exchangeable-phase rare earth ions could be replaced with a low dosage of the leaching solution. The leachate flow rate exhibited multi-stage variation, influenced by solution permeation, ion exchange, and fluctuations in accumulated liquid height. A mass transfer analysis showed that a higher fine particle content corresponded to a smaller plate height and a larger plate number of theoretical plates. As fine particle content increased, the final rising height of capillary water decreased, with rising rates varying across different stages for the samples. Moreover, an increase in fine particle content from 5% to 20% resulted in a 94% decrease in the samples' permeability coefficients. A mechanism analysis showed that when the fine particle content was higher, the fine particles were embedded in the gaps between coarse particles, and the ore particles in the sample were arranged continuously, resulting in a lower permeability coefficient. Then, the leaching solution could penetrate uniformly, which was beneficial for reducing leaching blind spots and improving leaching efficiency. However, excessive fine particle content might have detrimental effects. Based on these results and considering actual mining conditions, the optimal fine particle content for rare earth leaching is 20%. [ABSTRACT FROM AUTHOR]

Recently, capacitive micromachined ultrasound transducers (CMUTs) with long rectangular membranes have demonstrated performance advantages over conventional piezoelectric transducers; however, modeling these CMUT geometries has been limited to computationally burdensome numerical methods. Improved fast modeling methods, such as equivalent circuit models, could help achieve designs with even better performance. The primary obstacle in developing such methods is the lack of tractable methods for computing the radiation impedance of clamped rectangular radiators. This paper presents a method that approximates the velocity profile using a polynomial shape model to rapidly and accurately estimate radiation impedance. The validity of the approximate velocity profile and corresponding radiation impedance calculation was assessed using finite element simulations for a variety of membrane aspect ratios and bias voltages. Our method was evaluated for rectangular radiators with width:length ratios from 1:1 up to 1:25. At all aspect ratios, the radiation resistance was closely modeled. However, when calculating the radiation reactance, our initial approach was only accurate for low aspect ratios. This motivated us to consider an alternative shape model for high aspect ratios, which was more accurate when compared with FEM. To facilitate the development of future rectangular CMUTs, we provide a MATLAB script that quickly calculates radiation impedance using both methods. [ABSTRACT FROM AUTHOR]

Abstract The present paper introduces the development of dynamic stiffness method for analyzing small-scale sandwich functionally graded nanoplates resting on elastic foundation in thermal environments. The mathematical formulation is based on classical plate theory in conjunction with nonlocal elasticity theory. The governing equation is derived using Hamilton’s principle. The dynamic stiffness matrix is obtained through the application of the Levy displacement approach and assembled to form the global stiffness matrix. The final matrix is solved for natural frequency of the plates using the Wittrick–Williams algorithm. The proposed methodology is validated against existing literature, demonstrating a strong agreement. Various parametric studies explore the effects of thermal environments, volume fraction index, sandwich configurations, elastic foundation characteristics, nonlocal parameter and boundary conditions. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of sandwich functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices.

The present paper deals with the development of a dynamic stiffness matrix to evaluate the free vibration response of functionally graded nanoplate (FG-nP) resting on the Winkler-Pasternak elastic foundation. The complete mathematical modeling of the dynamic stiffness matrix for nanostructures is given for the first time. The equation of motion for rectangular FG-nP plates supported on an elastic foundation is derived using Hamilton’s principle in conjunction with nonlocal elasticity theory. The non-local theory is incorporated to account for the size effect in the small-scale plate. The effective material property of the porous FG-nP has been calculated using three recently developed models of porosity. The developed dynamic stiffness matrix is solved using the Wittrick-Williams algorithm to extract the natural frequencies of the FG-nP. The variation of natural frequencies with the change of numerical values, such as nonlocal parameter, aspect ratio, elastic foundation parameters, and porosity volume fraction is analyzed. The validity and accuracy of the results are confirmed through comparison with the available literature. The use of non-local theory in dynamic stiffness analysis is shown to be effective in predicting the natural frequency of the FG-nP on a Winkler-Pasternak elastic foundation, providing new insights into the dynamic behavior of small-scale structures. [ABSTRACT FROM AUTHOR]

Advancements in non-destructive evaluation systems for predicting mechanical properties of cross-laminated timber appear to have been limited to laboratory scale, reduced sample sizes, or difficult practical solutions for industry implementation. This study has developed classical vibration analysis methods for industry adoption in large-scale, rapid panel characterisation through frequency analysis. The non-destructive method allowed for the prediction of the elastic moduli in both axial directions (Ex and Ey) and shear moduli (Gxz, Gyz, and Gxy) for thin or thick plates. The comparison with the static reference method and non-destructive technique showed a good consistency for predicting the elastic and shear moduli of the cross-laminated timber with mean percentage differences for Ex, Ey, and Gxy of 5.2%, 7.9%, and 18.9%, respectively. An observation was made that the accurate determination of the mechanical properties required enough correctly identified frequencies/modes. Mode shapes generated from experimental data through modal assurance criterion were compared with finite element analysis to confirm the assessment method yielded frequencies specific to the panel, rather than other contributing effects (environment, boundary conditions, panel variability, mesh resolution). [ABSTRACT FROM AUTHOR]

Denticle microstructures in shark skin have intrigued researchers since they can be prospective for various marine applications due to their inherent properties which help in reducing drag as well as do not allow barnacles to form on its surface. However, any such alterations to create surface rivulets will invariably lead to changes in mass and stiffness, and thereby natural frequencies. Subsequently, the dynamic response will also be influenced as these hydrodynamic phenomena are strongly dependent on the natural frequencies. Therefore, in this work, an investigation of the effect of shark skin type biomimetic surface modifications on the free vibration response is investigated. The free vibration response of plates with shark skin is computed first using a high-fidelity numerical simulation in a commercial finite element package ABAQUS and then compared against a simplified semi-analytical model proposed herein. Results from both these methods agreed quite well. It is observed that shark skin denticles significantly influence the natural frequency without altering its mode shapes. It appears that adding shark skin like dermal denticles on the surface of a bare plate as an appendage helps in reducing the natural frequencies in each mode. The study also reveals that the reduction in the spacing between denticles reduces natural frequency even further. Therefore, the effect of these wettability altercations on free vibration response should be known apriori for efficient design. [ABSTRACT FROM AUTHOR]

A piezoelectric composite circular plate energy harvester is modeled and analyzed based on a nonlinear plate theory. The harvester consists of a bimorph piezoelectric circular plate and a rigid body. The nonlinear electromechanical coupling equations are derived from the Hamilton principle and the von Karman plate theory with the account for the structural weight. The equations are discretized via the Galerkin truncation method (GTM) for the vibration around the equilibrium configuration. The discrete equations are approximately solved via the harmonic balance method (HBM) with the convergence considerations. Moreover, the solutions are validated by the Runge–Kutta method (RKM) and the finite element simulations. The account for the structural weight leads to the asymmetricity in the relation of the restoring force and the deformation. The amplitude-frequency response curves display a typical hardened nonlinear behavior in the first-order vibration mode and a linear behavior in the second-order vibration mode. Parametric studies demonstrate the effects of the rigid body mass, the external excitation amplitude, the load resistance, and the piezoelectric composite plate size on harvesting the performance. [ABSTRACT FROM AUTHOR]

Recently, capacitive micromachined ultrasound transducers (CMUTs) with long rectangular membranes have demonstrated performance advantages over conventional piezoelectric transducers; however, modeling these CMUT geometries has been limited to computationally burdensome numerical methods. Improved fast modeling methods, such as equivalent circuit models, could help achieve designs with even better performance. The primary obstacle in developing such methods is the lack of tractable methods for computing the radiation impedance of clamped rectangular radiators. This paper presents a method that approximates the velocity profile using a polynomial shape model to rapidly and accurately estimate radiation impedance. The validity of the approximate velocity profile and corresponding radiation impedance calculation was assessed using finite element simulations for a variety of membrane aspect ratios and bias voltages. Our method was evaluated for rectangular radiators with width:length ratios from 1:1 up to 1:25. At all aspect ratios, the radiation resistance was closely modeled. However, when calculating the radiation reactance, our initial approach was only accurate for low aspect ratios. This motivated us to consider an alternative shape model for high aspect ratios, which was more accurate when compared with FEM. To facilitate the development of future rectangular CMUTs, we provide a MATLAB script that quickly calculates radiation impedance using both methods.

The need for smooth, gapless mechanisms that offer superior aerodynamic performance has been the prime mover for a wide range of studies on the morphing concepts from the early years of the twenty-first century. In light of the importance of novel analytic means for inspecting such structures, this article describes a comprehensive dynamic model for the flexural vibration of a special type of morphing structure known as fish bone active camber (FishBAC). In view of the shortcomings of previous models, the developed procedure considers the variable thickness of the central spine of FishBAC as well as the possibility of arbitrary truncations in its numerous partitions to offer more accurate results. A general idea is first proposed based on the assumptions of classical plate theory for such partitioned structures. The equations are derived using the energy method and the assumption of artificial springs to satisfy the continuity of shear force and bending moment along the connecting lines between partitions. A robust Rayleigh-Ritz method along with a set of fast-converging admissible functions is presented to solve the governing equations of motion. Combined with the power of Mathematica and validated by other analytic models and finite element codes, this technique can be used to deal with a plethora of similar systems while paving the path for the dynamic analysis of FishBAC built around various airfoils. [ABSTRACT FROM AUTHOR]

This article presents a comprehensive investigation into the thermomechanical analysis of glass powder as an additive in concrete. The efficient Eshelby's model is utilized to determine the relevant composite properties, considering the spherical shape of the glass powder. A higher-order shear deformation plate theory is employed to theoretically simulate the reinforced concrete panel, ensuring accuracy and simplicity. Equilibrium equations are derived using the virtual work concept, and energy equations are derived using Hamilton's principle. Navier's analytical techniques are applied to obtain closed-form solutions for simply supported plates. A comprehensive parametric study is conducted, analyzing the impact of factors such as glass powder volume, geometric parameters, and thermal loading on the thermomechanical behavior of the panel. The findings highlight the challenges associated with using glass powder in concrete for thermomechanical applications and suggest the need for alternative approaches to optimize its effectiveness in such scenarios, also the study provides first-time numerical results that serve as guidelines for further research on reinforced concrete. [ABSTRACT FROM AUTHOR]

This study aims at improving the empirical correlation for estimating the yield strength from small punch tests. The currently used procedure in the European standard EN 10371 to determine the elastic–plastic transition force—based on bi-linear fitting—involves a dependency not only on the onset of plastic flow but also on the work hardening of the material. Consequently, the yield strength correlation factor is not universal but depends on the material properties and on the geometry of the small punch set-up, leading to a significant uncertainty in the yield strength estimation. In this study, an alternative definition of the elastic–plastic transition force is proposed, which depends significantly less on the work hardening of the material and on the small punch geometry. The approach is based on extensive elastic–plastic finite element simulations with generic material properties, including a systematic variation of the yield strength, ultimate tensile strength, and uniform elongation. The new definition of the transition force is based on the deviation of the force-deflection curve from the analytical elastic slope derived by Reissner's plate theory. A significant reduction of the uncertainty of the yield strength estimation is demonstrated. [ABSTRACT FROM AUTHOR]

Deflection and stress calculated from an experimentally validated, high-fidelity finite element model (FEM) of a photovoltaic module experiencing mechanical load was compared to results from a simplified FEM treating the module laminate as a homogenized composite using a rule of mixtures approach, and further compared to analytical calculations treating the module as a Kirchoff-Love flat plate. The goal of this study was to determine the error incurred by analyzing module mechanics with varying levels of simplification, since resolving the aspect ratios of a module is computationally expensive. Homogenized FEMs were found to underpredict peak deflection under a 1.0 kPa load by between 13 and 19% for lower and upper bound application of the rule of mixtures. However, module shape was captured, implying that a useful replication of a resolved model could be achieved with a reduced, calibrated material stiffness. Homogenized stress results captured glass layer tensile stress components to within 46 to 52% at a sample location of interest, though agreement was poor through the remainder of the laminate due to the lack of material resolution. For plate theory, deflection was overpredicted by 45 to 67% for upper and lower bound homogenizations, and frame-adjacent module shapes were not adequately replicated. Stress results mirrored FEM trends but magnitudes were not well correlated to resolved model values. These results support the use of homogenized laminate models for module shape derivation, though resolved models remain necessary for stress analyses. The accuracy of plate theory was found to be inadequate for most applications. [ABSTRACT FROM AUTHOR]

In this work, a fifth-order shear deformation theory is computed using the layer-wise model to determine non-dimensional fundamental frequencies. The theoretical, experimental, and finite element analysis (FEA) results are compared for a standard isotropic material. Hand layup technique is used to prepare glass fiber reinforced polymer composites (GFRPC) with selective layers filled with graphene and flyash. This technique helps to reduce the fabrication cost as the whole structure is not to be strengthened by the fillers. Six classes of the laminated-composite-plate (LCP) such as outer layer graphenated LCP (O-LCP), core layer graphenated LCP(C-LCP), functionally graded LCP (FG-LCP), LCPs only rich in graphene (G-LCP), LCPs only rich in flyash (F-LCP) along with a neat epoxy-glass LCP (N-LCP) are fabricated. A low-cost frequency measurement module is set-up to measure the fundamental frequency (FF) of the fabricated LCPs. FFs, amplitudes, non-dimensional stress parameters, and central deflection of the LCPs under harmonic load, the buckling strength, and displacements of the LCPs are calculated. It is found that harmonically excited C-LCP and O-LCP have better stability accompanied by lower deflections, followed by G-LCP as compared to other kinds of LCPs. Also, the addition of graphene increases the buckling strength of LCPs, which portrays that the local layer filling is a useful technique to enhance the strength of the LCPs. [ABSTRACT FROM AUTHOR]

Nanoparticles, by virtue of their amorphous nature and high specific surface area, exhibit ideal pozzolanic activity which leads to the formation of additional C-S-H gel by reacting with calcium hydroxide, resulting in a denser matrix. The proportions of ferric oxide (Fe2O3), silicon dioxide (SiO2), and aluminum oxide (Al2O3) in the clay, which interact chemically with the calcium oxide (CaO) during the clinkering reactions, influence the final properties of the cement and, therefore, of the concrete. Through the phases of this article, a refined trigonometric shear deformation theory (RTSDT), taking into account transverse shear deformation effects, is presented for the thermoelastic bending analysis of concrete slabs reinforced with ferric oxide (Fe2O3) nanoparticles. Thermoelastic properties are generated using Eshelby's model in order to determine the equivalent Young's modulus and thermal expansion of the nano-reinforced concrete slab. For an extended use of this study, the concrete plate is subjected to various mechanical and thermal loads. The governing equations of equilibrium are obtained using the principle of virtual work and solved using Navier's technique for simply supported plates. Numerical results are presented considering the effect of different variations such as volume percent of Fe2O3 nanoparticles, mechanical loads, thermal loads, and geometrical parameters on the thermoelastic bending of the plate. According to the results, the transverse displacement of concrete slabs subjected to mechanical loading and containing 30% nano-Fe2O3 was almost 45% lower than that of a slab without reinforcement, while the transverse displacement under thermal loadings increased by 10%. [ABSTRACT FROM AUTHOR]

In this article we solve a few problems of shell and plate theory with py-pde package. The shell has a shape of elliptic paraboloid. Only membrane shell theory is considered. Both shell and plate have a rectangular boundary and are subjected to the uniform vertical load. The paper includes distributions of internal forces in the shell and bending moments in the plate obtained with the help of the py-pde program.

This study presents a method for level ice-structure interaction analysis to estimate the fatigue damage of arctic structures by applying plate theory to the behavior of level ice. The boundary element method (BEM), which incurs a lower computational cost than the finite element method (FEM), was introduced to solve the plate bending problem. The BEM formulation was performed by applying the BEM to plate theory. Finally, to check the validity of the proposed method, the BEM results and FEM results obtained using the ABAQUS commercial software were compared. The response results of the BEM analysis agreed well with those of the FEM analysis. Based on the results of the analysis, the BEM approach is considered to be very powerful in level ice-structure interaction analysis for estimating level ice-induced fatigue damage. Further work is being conducted to perform level ice fracture analysis based on the stress field calculated using the boundary element method.

As an aircraft or spacecraft ascends, the atmospheric pressure drops. If the internal pressure is not released, a pressure differential develops on the facesheet. With an in-plane load from vehicle acceleration as well, the pressure and in-plane load may cause failure. Vented sandwich structures are strongly preferred since they release the internal pressure; however, special cases still require an unvented design. This paper provides an analysis and test methodology for unvented sandwich structures. Parametric studies of facesheet-core debonding and buckling were conducted via finite element analysis, considering geometric, material, and load parameters. Design curves based on the key nondimensional parameters were tuned to the data from the parametric study, providing a tool to predict facesheet-core debond failure. Examples of how to use the design curves in practical applications are provided. [ABSTRACT FROM AUTHOR]

Modeling and Methods: This work is devoted to the numerical dynamic bending characterization of delaminated multi-walled carbon nanotubes (MWCNTs) reinforced epoxy/glass fiber-based hybrid composite plate based on finite element method with displacement fields derived from classical laminated plate theory (CLPT). Verification: The accuracy and performance of the developed method were confirmed by a validation study with reference solutions available in the literature. Results: Various parametric studies were carried out to study the influence of MWCNTs content, delamination location, delamination interface, ply orientation, and end condition on the dynamic bending characteristics of the intact and delaminated hybrid laminated composite plate. Conclusion: The weight fraction of MWCNTs, delamination location, and clamping condition significantly influences the natural frequency. The natural frequencies also depended upon the ply configuration and delamination interface irrespective of the MWCNT loadings. However, anomalous trends were observed as far as the influence of end conditions is concerned. [ABSTRACT FROM AUTHOR]

This study aims at improving the empirical correlation for estimating the yield strength from small punch tests. The currently used procedure in the European standard EN 10371 to determine the elastic–plastic transition force—based on bi-linear fitting—involves a dependency not only on the onset of plastic flow but also on the work hardening of the material. Consequently, the yield strength correlation factor is not universal but depends on the material properties and on the geometry of the small punch set-up, leading to a significant uncertainty in the yield strength estimation. In this study, an alternative definition of the elastic–plastic transition force is proposed, which depends significantly less on the work hardening of the material and on the small punch geometry. The approach is based on extensive elastic–plastic finite element simulations with generic material properties, including a systematic variation of the yield strength, ultimate tensile strength, and uniform elongation. The new definition of the transition force is based on the deviation of the force-deflection curve from the analytical elastic slope derived by Reissner’s plate theory. A significant reduction of the uncertainty of the yield strength estimation is demonstrated.

Due to its special geometry, plate (shell) elements are usually used for structural analysis, which is more efficient than solid elements. Finite elements analysis based on MATLAB programming of a plate structure made of particleboard materials and static load test were carried out. Firstly, the transversely isotropic material constitutive equation was applied to plate-form members, the constitutive relationship and mechanical properties of three-layer composite laminate (represented by particleboard) was obtained. Secondly, the construction methods of discrete Kirchhoff triangle (DKT), discrete Kirchhoff quadrilateral ( DKQ), discrete shear triangle (DST), discrete shear quadrangle(DSQ) plate elements based on Kirchhoff thin plate and Mindlin-Reissner thick plate theories were introduced in detail, and the convergence performance between finite elements numerical solution and accurate theoretical solution of each plate element was verified. By assembling the plate members in space, law of change of reference for material parameters and nodal degrees of freedom between the element local and spatial global coordinate systems was explained. Finally, the influence of different plate elements on the numerical results of the finite elements model was analyzed by comparing with the measured value of the static load test of plate structure. The results show that the DST element has better calculation accuracy for the mechanical properties simulation of composite laminate structure due to the consideration of transverse shear effect. [ABSTRACT FROM AUTHOR]

Chiral growth is ubiquitous in nature and has always been of great interest in the field of biomimetic and man-made materials, but its formation mechanism is complex. In order to clarify this mechanism, with the help of the plate theory and the theory from differential geometry, we established a new theoretical model that can be used to describe the interaction between anisotropic elasticity and anisotropic residual stress of slender biomaterials and provide additional insight onto the mechanical mechanism of biomaterial's morphological chiral growth. Based on these results, it appears that misfit of material properties and residual stresses may create various chiral morphologies, like helices and twisting belts. It is found here that the cooperative and competitive interactions between anisotropic elasticity and anisotropic residual stress can also give rise to chiral morphologies, and macro shapes, sizes, and handedness of chiral morphologies can be designed by residual stresses orientation angles and elastic parameters of biomaterials. This theoretical model is in good agreement with the recent experiments and can provide theoretical guidance for the design of medical-assisted soft robots. [ABSTRACT FROM AUTHOR]

Plate-like structures had been thoroughly studied in literature over years to reduce the computational space from 3D to 2D. Many of these theories suffer either from satisfying the free traction condition or thickness extensibility in addition to the consistency of transverse shear strain energy. This work presents a higher order shear deformation thickness-extensible plate theory (eHSDT) for the analysis of plates. The proposed eHSDT satisfies the condition of free traction as other theories do but it also satisfies the condition of consistency of transverse shear strain energy which is neglected by many theories in the area of plates and shells. The implementation of the proposed theory in displacement-based finite element procedure requires continuity of derivatives across elements. This necessary condition was achieved using the penalty enforcement method for derivative-based nodal degrees of freedom across the standard 9-nodes Lagrange element. The theory was tested for elastic bending deformation of Polyether-ether-ketone (PEEK) which is one of the basic materials for medical implants. The theory showed good accuracy compared to experimental data of the three-points bending test. The present eHSDT was also tested for different conditions with a wide range of aspects ratios (thin to thick plates) and different boundary conditions. The accuracy of the proposed eHSDT was verified against exact solutions for these conditions which showed the advantage over other approaches and commercial finite element packages., (Creative Commons Attribution license.)

We study the propagation of bending waves along the free edge of a semi-infinite piezoelectric plate within the framework of two-variable refined plate theory (TVPT, a high-order plate theory), Reissner-Mindlin refined plate theory (RMPT, a first-order plate theory), and the classical plate theory (CPT). The piezoelectric plate has macroscopic symmetry of orthogonal mm2 The governing equations are derived using Hamilton principle. The dispersion relations for electrically open and shorted boundary conditions at the free edge are obtained analytically. The difference in dispersion property between the three plate theories is analyzed. The numerical results show that the dispersion curves predicted by TVPT and RMPT are similar and have small difference over the complete frequency range, which means both the two theories are valid for the analysis of edge waves in a piezoelectric plate. But the wave velocity calculated by CPT is much larger than the two theories above and is no longer valid for high frequency and thick plate. The electrical boundary condition at the free edge has an insignificant effect on phase velocity and group velocity which can be ignored for the analysis of edge waves in a piezoelectric plate governed by bending deformation. The velocity of bending edge waves in a semi-infinite piezoelectric plate is positively related to that of Rayleigh surface wave in a traction-free piezoelectric half-space. The edge wave velocity can be enhanced when the piezoelectric plate is considered as one with weaker anisotropy.

Background: The impact of power and signal cable harnesses on the dynamic behavior of lightweight space structures has come into the spotlight in the recent past. The previous analytical modelling efforts in this area have primarily focused on either periodically wrapped beam structures or plate structures of parallel cable wrapping patterns. Objective: The presented paper aims at experimental validation for an analytical model developed by the authors for cable harnessed plate structures with periodic patterns such as zigzag and diagonal. The work includes an extensive analysis of the vibration behavior of cable-harnessed plates in comparison to their host plates with no cables attached. Methods: An energy equivalence homogenization technique is developed to model the vibrations behavior of the cable harnessed plates of periodic patterns. Experimental modal analysis is performed on cable-harnessed plates using impact hammer excitation and laser doppler vibrometry. The natural frequencies, mode shapes, and frequency response functions are obtained for comparisons with the model predictions. Results: The impacts of the harnessing cables on plate dynamics are modeled and compared to the experimental frequency response functions for periodically wrapped cabled plates in four different test structures. The impact of the cable wrapping directions along the length and width on the modes that experience the largest stiffening effects are clearly discussed and validated with the test results for the two major wrapping patterns, diagonal and zigzag. It is shown that for a given number of fundamental elements and cable wrapping rows along the length, the parallel pattern experiences the largest stiffening along the length followed by the diagonal and zigzag patterns respectively. Also, the twist mode was stiffened the most for the zigzag pattern and the least in the parallel cabled plate. Finally, the wrapping angle for which the torsional frequency is maximum for each of the diagonal and zigzag patterns is found to be the same. A computational study is also performed to further analyze the system dynamics by varying the host plate dimensions. Conclusions: The model and test results are shown to be in very good agreement. The analytical model is found to well predict the cables' mass and stiffening effects for all the wrapping patterns studied in this research. [ABSTRACT FROM AUTHOR]

Thin films may experience wrinkling instability when two clamped ends are stretched uniaxially. For a fiber-reinforced anisotropic thin film, the wrinkling distributions and evolutions can be significantly affected by the fiber orientation and the anisotropic parameters. In this paper, we study the stretch-induced wrinkling of anisotropic thin films based on a uniformly-valid asymptotic plate equation for anisotropic materials derived from the three-dimensional field equations. A numerical model is established in COMSOL Multiphysics by virtue of the weak form of plate equations and by employing the Holzapfel–Gasser–Ogden model. The effects of fiber orientations and anisotropic parameters on wrinkling evolutions are unraveled from various case studies. In particular, we find that there exists a critical fiber orientation interval where the usual isola-center bifurcation will give way to the pitchfork bifurcation, and the associated amplitude against strain curve presents an N shape. A phase diagram for different bifurcation types is characterized as well. Our numerical model is validated by three-dimensional numerical simulations. It is expected that the results in this paper will offer useful insight into pattern formation in anisotropic soft materials. • The wrinkling responses of anisotropic parameters and fiber orientation are analyzed. • Stretch-induced wrinkling could be an N-shaped pitchfork bifurcation. • A phase diagram for different bifurcation types is provided. • The numerical model is validated by 3D numerical simulations. [ABSTRACT FROM AUTHOR]

A multi-objective optimization of a sandwich structure is presented to maximize the fundamental frequency and the critical buckling temperature while minimizing the cost of the laminate, alongside with keeping the weight lower than a preset value. The sandwich structure was chosen to be made of a high-stiffness, relatively expensive material (carbon/epoxy), and a low-stiffness, relatively low-cost material for the core (glass/epoxy). The governing equations are derived using the principle of virtual work, based on the first-order shear deformation plate theory. MATLAB Genetic Algorithm toolbox is used to find the optimum stacking sequence and ply thicknesses to achieve the optimal solution. The ground structure was used to set the initial ply stacking sequence and then the algorithm assumes the existence or absence of each ply and their thicknesses. The optimum buckling temperature and natural frequency values are introduced for different aerodynamic pressure values and under simply supported boundary condition. [ABSTRACT FROM AUTHOR]

Even though micropolar theories are widely applied for engineering applications such as the design of metamaterials, applications in the study of the Earth's interior still remain limited and in particular in seismology. This is due to the lack of understanding of the required elastic material parameters present in the theory as well as the eigenfrequency ω r which is not observed in seismic data. By showing that the general dynamic equations of the Timoshenko's beam is a particular case of the micropolar theory we are able to connect micropolar elastic parameters to physically measurable quantities. We then present an alternative micropolar model that, based on the same physical basis as the original model, circumvents the problem of the original eigenfrequency ω r laking in seismological data. We finally validate our model with a seismic experiment and show it is relevant to explain observed seismic dispersion curves. [ABSTRACT FROM AUTHOR]

This study presents the quasi-three-dimensional, higher-order shear-deformation theory for the stress and displacement analysis of sandwich plate subjected to concentrated force. Using expansion of thickness coordinate in the displacement field, the effects of both transverse shear and normal deformations are included. The theory satisfies the zero shear stress conditions on the top and bottom surfaces of sandwich plate. Hence, the shear correction factor is not required, generally associated with the First order shear deformation theory (FSDT). The boundary-value problem of the theory is derived using the principle of virtual work. Transverse shear and normal stresses are recovered from the stress-equilibrium equations of the theory of elasticity, and the continuity condition is satisfied at the interface between layers and stress boundary condition at the external surfaces. In addition, this study provides the effects of transverse normal strain on flexural response of sandwich plate. Closed-form solutions for simply supported sandwich plate subjected to concentrated force are obtained for various side-to-thickness ratios. The results of the present theory are compared with third-order shear and normal deformation theory, first-order shear-deformation theory, and the classical plate theory. The inclusion of the effect of transverse normal strain in the theory showed significant deviations in displacements and stresses. [ABSTRACT FROM AUTHOR]

The paper investigates the post-buckling response of web-core sandwich plates through classical continuum mechanics assumptions. The compressive loading is assumed to be in the direction of the web plates. Equivalent Single Layer (ESL) plate formulation is used with the kinematics of the First order Shear Deformation Theory (FSDT). During the initial, membrane-dominated loading stages, it is observed that the effect of finite size of the periodic microstructure is barely influences the plate responses. At the higher loads, when bending is activated, the finite size of the microstructure activates secondary shear-induced bending moments at the unit cells of the plate. A method to capture the envelope of the maximum values of these bending moments is presented. The findings are validated with the shell element models of the actual 3D-geometry. Finally, the physical limits of the classical continuum mechanics are discussed in the present context. [ABSTRACT FROM AUTHOR]

• A new isogeometric analysis model for MEEFG microplate is proposed. • Static and dynamic responses with square and elliptical plates are investigated. • The accuracy and convergence of the numerical solution are verified. • The microstructure effect becomes more pronounced as the structure size and stiffness decrease. • Adjusting the graded index can improve the mechanical and electromagnetic properties of the plate. In this study, an accurate numerical method for the static and dynamic response analysis of magneto-electro-elastic functionally graded (MEEFG) microplates with complex geometries is proposed with the application of isogeometric analysis (IGA). Leveraging Hamilton's principle and the extended modified couple stress theory, the weak form of motion equations is derived. By performing convergence analysis, the accuracy of the proposed numerical method is verified. To show the applicability of the new method, the influences of the microstructure effect and gradient index on the static and dynamic behaviors of both the MEEFG square and elliptical microplates with various boundary conditions are discussed in detail. Results illustrate that the microstructure effect dominated by the couple stress effect has an obvious impact on both the mechanical and electromagnetic behavior of structures with microscopic scales which will cause hardening of microstructural stiffness, whereas the macrostructures are minimally affected by the couple stress effect. Besides, microstructures with lower stiffness exhibit a more pronounced microstructure effect and a greater degree of stiffness hardening. The proposed IGA method could serve as a basis for the design and optimization of microelectromechanical devices with complex shapes. [ABSTRACT FROM AUTHOR]

We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two first terms of the outer expansion must satisfy. The new boundary value problems thus obtained are studied and compared with the classical Love-Kirchhoff plate model. Two examples of application illustrate the results. [ABSTRACT FROM AUTHOR]

The strength of laser-welded web-core sandwich plates is often limited by buckling. In design of complex thin-walled structures the combination of possible structural and material combinations is basically infinite. The feasibility of these combinations can be assessed by using analytical, numerical and experimental methods. At the early design stages such as concept design stage, the role of analytical methods is significant due to their capability for parametric description and extremely low computational efforts once the solutions have been established for prevailing differential equations. Over the recent years significant advances have been made on analytical strength prediction of web-core sandwich panels. Therefore, aim of the present paper is to show impact of this development to the design space of web-core sandwich panels in buckling. The paper reviews first, briefly the differential equations of a 2-D micropolar plate theory for web-core sandwich panels and the Navier buckling solution for biaxial compression recently derived by Karttunen et al. (Int J Solids Struct 170(1):82–94, 2019) by exploiting energy methods. By comparing the micropolar and widely-used classical first-order shear deformation plate theory (FSDT) solutions, it is shown that the different equivalent single layer (ESL) formulations and plate aspect ratios have a significant impact on the practical outcomes of the feasible design space and this way motivating further developments for micropolar formulations from practical structural engineering viewpoint. [ABSTRACT FROM AUTHOR]

In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced from a three-dimensional description of the system using rigorous dimension reduction techniques, based on the theory of Γ-convergence. The two-dimensional models are non-linear plate theories, in which deviations from a characteristic target curvature tensor cost elastic energy. Moreover, the stored energy functional cannot be minimised to zero, thus revealing the presence of residual stresses, as observed in numerical simulations. Three nematic textures are considered: splay-bend and twisted orientations of the nematic director, and a uniform director perpendicular to the mid-plane of the film, with variable degree of nematic order along the thickness. These three textures realise three very different structural models: one with only one stable spontaneously bent configuration, a bistable model with two oppositely curved configurations of minimal energy, and a shell with zero stiffness to twisting. [ABSTRACT FROM AUTHOR]

Marine structures are advanced material and structural assemblies that span over different length scales. The classical structural design approach is to separate these length scales. The used structural models are based on classical continuum mechanics. There are multiple situations where the classical theory breaks down. Non-classical effects tend arise when the size of the smallest repeating unit of a periodic structure is of the same order as the full structure itself. The aim of the present paper is to discuss representative problems from different length scales of ship structural design. [ABSTRACT FROM AUTHOR]

The purpose of this work is to develop a new analysis model for angular-contact, ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements. Axial and radial stiffness on an annular plate are developed based on plate, Timoshenko beam, and plasticity theories. The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method. The new analysis model is suitable for static and modal analyses of rotor-bearing systems. Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach. [ABSTRACT FROM AUTHOR]